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can never be the subject of the sentence. Eliminate (B) and (D) because both are plural. Compare
(A) and (C), and notice that the verb must be in present tense in order to maintain consistency
with the rest of the paragraph, which makes (A) the correct answer.
14. B This sentence is making a comparison between the time scales of computers and humans. This
means the correct choice will use a pronoun that is possessive to ensure that like things—in this
case, the time scale of computers and our time scale—are being compared. Eliminate (A), (C), and
(D). Choice (B) is the answer.
15. A Use POE and check each answer choice to see if it is consistent with the passage. Choice (A) works
because these descriptions clarify what the work of computers actually is. Choice (B) goes too far, as
the given list is not a complete list, and (C) is too broad because the passage does not discuss about
the intrusion of technology into human life. Eliminate (D) as well because these descriptions are not
discussed in the next paragraph. Choice (A) is correct.
16. A There isn’t a clear grammar rule being tested here, so use POE. The underlined portion doesn’t
appear to break any rules, so keep it. Eliminate (B) since it changes the meaning of the sentence
by moving the word working. Choice (C) changes the meaning of the sentence by rearranging
the words field and mind. Choice (D) is extremely wordy and awkward. Choice (A) is the clearest
answer, and therefore correct.
17. D Since there is STOP and HALF-STOP punctuation in the answer choices, use the Vertical Line
Test. The phrase leading up to the semicolon is an incomplete idea, so the semicolon is wrong.
Eliminate (A). Eliminate (B) as well because a period is also STOP punctuation. A dash (HALF-
STOP punctuation) must come after a complete idea, so (C) can be eliminated. One use for a
comma is to separate an incomplete and complete idea (GO punctuation), so (D) is the correct
answer.
18. D Use POE and check each answer choice against the graph. The vertical axis of the graph is in
the time unit of years, so clearly the average holding period of a stock in 1920 was not less than
22 seconds. Eliminate (A). The average holding period peaked in 1940 according to the graph, so
eliminate (B). Choice (C) is irrelevant, so get rid of it. Choice (D) is consistent with the graph and
is the correct answer.
19. C The sentence begins by discussing troubling permutations and then compares investing in the stock
market to gambling at the poker tables. Since this is an unusual comparison without the quotation
marks, use POE to find an answer that explains the necessity of the quotation marks. The quota-
tions are being used for a reason, so eliminate (A). There is no indication that the author wants a
different word, so eliminate (B). Choice (C) accurately explains the quotation marks’ use, so keep
it. Eliminate (D) because no investor is quoted in the passage. Choice (C) is correct.
20. D The question is asking for the LEAST acceptable alternative to province, so province is used prop-
erly in this sentence. In this context, province means “field of activity,” so find and eliminate all
1 6 | Practice Test 6: Answers and Explanations
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answer choices that are similar in meaning. Only (D) is different, as state refers to “a condition or
status,” so (D) is the answer.
21. B A pronoun is underlined in this sentence, so make sure the pronoun is consistent with the non-
underlined portion of the sentence. The noun partner for your is human traders, which is inconsis-
tent, so eliminate (A). Look for a third-person, plural pronoun to match the partner: (B) is correct.
22. A The answer choices tell you that the question is testing commas, so use POE to see if they
are used properly. Eliminate (B) and (D) because there is no reason to pause the flow of the sen-
tence after trend. Compare (A) and (C); the only difference is the commas before and after prob-
ably in (C). This is excessive usage, so eliminate it. Choice (A) is the answer.
23. A This question is testing comma usage involving lists, so find the answer in which a comma is used
after each item in the list and before and. Choice (A) places a comma after murder and theft, and
before the conjunction and, so it’s the correct answer.
24. C The answer choices contain STOP and HALF-STOP punctuation, so use the Vertical Line Test.
Choice (B) is incorrect because STOP punctuation (the semicolon) can only separate two complete
ideas, and guilt and innocence is an incomplete idea. Eliminate (A) because it alters the meaning
of the sentence; the commas suggest that issue, guilt, and innocence are all items in a list of three
things. Choices (C) and (D) could work since they use a colon to separate a complete idea before
the colon from an incomplete idea after it. Since there are only two things in the list, a comma is
not needed before the and that joins them, so eliminate (D). Choice (C) is the correct answer.
25. D Notice the question! The second paragraph immediately begins describing Morris’s story, but no
mention is made of him in the previous paragraph. The correct answer must mention Morris.
Eliminate (A) and (C). Get rid of (B) as well because the next paragraph is detailing a specific film
by Morris, not his entire filmography. Choice (D) is the answer.
26. B Since a comma comes after the name Randall Dale Adams, the description that follows must apply
to Adams. Choice (B) is the only answer that does this. Additional information in the paragraph
indicates that Adams is the one who was charged with the crime, so (B) is correct. Remember that
the correct answer will always feature phrases that are as precise as possible.
27. B Notice the question! The previous phrase before the underlined portion of this sentence is many of
those involved, so the correct answer must list who these many are. Eliminate (C) and (D) because
neither details who was involved in the case. Compare (A) and (B); (B) is the correct answer be-
cause it’s clear and concise.
28. C Since the question is asking for the LEAST acceptable response to the underlined portion, anarchy
is properly used. Anarchy means “disorder due to lack of authority,” so eliminate any other answer
choice that means this. Tyranny doesn’t fit since it means “oppressive authority,” so (C) is the cor-
rect answer.
|Practice Test 6: Answers and Explanations 17
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29. D Check each answer choice to find the answer that is consistent with the graph. Eliminate (A) be-
cause Morris’s film was released in 1988 (see the correct answer for question 25), and the number
of verdict reversals did not peak that year. Get rid of (B) since there is no mention in the graph
of repeated attempts at reversals. Choice (C) is wrong because in 1989, the reversal ratio was 40%.
Choice (D) works because Morris’s film was made in 1988, and the percentage of verdict reversals
decreases in the subsequent years. Choice (D) is correct.
30. A Look at the answer choices and notice the change in transition words. The sentence is clearly
contrasting Koenig’s stated purpose with her identification of a degree of uncertainty about the
trial’s verdict, so find a contrasting transition word. Eliminate (B) because without a transition
word, the sentence would have two complete ideas connected by only a comma (GO punc-
tuation). Choice (D) has the contrasting transition however, but the sentence would then have
two complete ideas with only a comma to connect them; eliminate (D). Also eliminate (C);
because should be used when two parts of the comparison agree, not when they contrast. Choice
(A) is the answer.
31. C On proposition questions, make sure the word or phrase has some precise and definable role within
the sentence or passage. Notice that the sentence opens with Unlike Morris, so the latter phrase as
Morris was is redundant. Eliminate (A) and (B). Choice (D) can be eliminated since the passage
never really examines the differences between a film and podcast. Choice (C) is correct.
32. A This question is comparing the film and podcast, so make sure it’s a correct comparison. Choice
(A) seems to work. Eliminate (D) because it implies Koenig also made a film. Eliminate (B) and (C),
as neither is structurally consistent with Morris’s film. Choice (A) is correct.
33. B The underlined portion of the sentence is a pronoun, so find its partner to make sure they are con-
sistent in number and that the pronoun is precise. There shouldn’t be a question as to who They are.
Choice (A) is a problem since they is ambiguous. Is it referring to Koenig and Morris or the imper-
fect actors of the previous sentence? The correct partner for they is Koenig and Morris, but since this
isn’t made clear with a pronoun, eliminate (A) along with (D), as both is also not clearly defined.
Choice (B) is unambiguous, so keep it. Choice (C) also doesn’t indicate whom the two is referring to,
so eliminate it. The correct choice will feature words that are as precise as possible, and that’s (B).
34. A Apostrophes are changing in the answer choices, so that’s what this question is testing. Since the
noun career comes after the person’s name, choose the answer that shows proper possession. Sin-
gular nouns are made possessive by adding an apostrophe and an s. This means the underlined
portion is correct, so (A) is the answer.
35. C Use POE to find the best placement for the underlined portion. Eliminate (A) and (D) because the
underlined portion clearly refers to Ochoa. Choice (B) is very awkward, so eliminate it. Choice (C)
is the answer.
1 8 | Practice Test 6: Answers and Explanations
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36. D Use the answer choices to help you figure out what the question is testing. It’s clear that pronouns
and verbs are the issues here. The subject of the sentence—device—is singular, so all pronouns and
verbs must be consistent with this since device is in the non-underlined portion. Eliminate (A) and
(B) because each has a plural pronoun. Choice (C) can be eliminated because it has a plural verb.
This leaves (D), which is the only consistent choice and therefore the correct answer.
37. A Notice the question! The underlined portion directly supports the popular applications mentioned
in the early part of the sentence, so (A) is a good fit. Choices (B), (C), and (D) include either irrel-
evant information or contradict the early part of the sentence. Choice (A) is the correct answer.
38. B Notice the question and use POE to find the answer choice that is consistent with the paragraph as
a whole. Eliminate (A) because the paragraph is not comparing schools. Choice (B) works because
the passage is interested specifically in Ochoa. Popular surnames are not discussed in the passage,
so eliminate (C); (D) is incorrect because the passage also does not discuss how long it takes to get
a degree. The correct answer is (B).
39. D The underlined portion uses the proper word but the wrong tense, so eliminate (A). Since both (B)
and (C) are different words, eliminate those as well. Choice (D) is correct, as the past tense is con-
sistent with the paragraph since each of her achievements happened in the past.
40. B Use POE to find the best answer choice consistent with the paragraph. Eliminate (C) and (D), as
these phrases should modify Ochoa, not Ochoa’s optical analysis device. Choice (A) is also not struc-
turally consistent because the verb uses appears later in the sentence. Choice (B) is correct.
41. D Whenever a question gives you the option to delete, check to see if the underlined portion serves a
precise function in the sentence or paragraph. The opening phrase of the sentence sets up a direct
contrast between digital technology and laser light technology, so there’s no need to restate this infor-
mation at the end of the sentence. Eliminate (A), (B), and (C), as all of them are redundant. The
answer is (D).
42. C Notice the question! This passage is primarily focused on Ellen Ochoa and her achievements, so
comparing design and utility patents is irrelevant. Eliminate (A) and (B). Choice (D) is also incor-
rect since it doesn’t matter how politically sensitive they are. This leaves (C), which is the correct
answer.
43. B Later in the sentence the phrase that image is used, so the correct answer must also be singular.
Eliminate (A), (C), and (D). Choice (B) is the only one that is singular and, therefore, the correct
answer.
44. C Each paragraph opens with a description of Ochoa’s achievements except for the third paragraph,
which details her early years before becoming a renowned scientist. Therefore, the third paragraph
should be first, and only (C) shows this, making it the correct answer.
|Practice Test 6: Answers and Explanations 1 9
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Section 3: Math (No Calculator)
1. B Subtract the one-time setup charge from David’s budget first: 150 – 35 = 115. Calculate
the number of people David can invite as follows: 115 ¸ 15 = 7.6. David can invite at most
7 people (including himself), so p ≤ 7. In (A), 15p ≤ 185, so p ≤ 12.3 or p ≤ 12.3. Eliminate
(A). Solve for p in (B) as follows: add 15p to both sides to get 15p + 35 ≤ 150, so 15p ≤ 115 and
p ≤ 7.6. The correct answer is (B).
2. C Whenever there are variables in the question and in the answer choices, think Plugging In. Let
d = 2. On the first day after Monday, 5 ´ 3 = 15 people will be infected. On the second day after
Monday, 15 ´ 3 = 45 people will be infected. Therefore, when d = 2, the result is 45. Plug 2 in for
d in the answer choices to see which answer equals the target number of 45. Choice (A) becomes
5 ´ 3(22) = 5 ´ 12 = 60. This does not match the target number, so eliminate (A). Choice (B)
becomes 5 ´ 23 = 40. Eliminate (B). Choice (C) becomes 5 ´ 32 = 45. Keep (C), but check the
remaining choice just in case. Choice (D) becomes 5 ´ 9(5) = 225. Eliminate (D) and choose (C).
3. A Whenever there are variables in the question, think Plugging In. The answers refer to what
happens when the temperature, x, increases, so plug in more than one value of x. Plug in x = 1
into the equation to get y = –3.65(1) + 915 = –3.65 + 915 = 911.35. Next plug in x = 2 to get
y = –3.65(2) + 915 = –7.3 + 915 = 907.7. As average daily temperature, x, increased, the number of
units sold, y, decreased. Therefore, the correct answer is (A).
4. B Plugging In could work on this one, but calculators aren’t permitted. Since the equation is fairly
simple, solving may be a better approach. Multiply both sides of the equation by r2 to get
5. D Fr2 = GMm. Divide both s13idepsoowf etrheisetqhueatsiaomnebyasMtamkitnoggtehteMFcrmu2b=e G . The correct answer is (B).
Taking a number to the root of the number. Therefore,
1 = 3 4s . The correct answer is (D). A shortcut is to just raise the coefficient to the power,
(4s)3
and then use POE. Because only one answer starts with 3 4 , that one must be correct. Another
approach is to plug in a number for s and let the calculator do the hard work, though that would
not help in this section because calculator use is not permitted.
6. C Sketch a picture and write the formulas for arc length and area: s = rθ, A = pr2. Start by find-
ing the radius. If the circle has an area of 16p, then 16p = pr2; divide both sides by π to get
16 = r2. The radius must be 4. So plug in the arc length and radius into your formula: 2p = 4θ.
Divide both sides by 4 to get π = θ. Choice (C) is correct.
2
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7. D According to the question, if t = 4, then v(t) = 740. Plug 4 in for t in the answer choices and see
if v(t) comes out to the target number 740. In (A) if t = 4, then v(t) = 740 – 4 = 736. Eliminate
(A). In (B), if t = 4, then v(t) =740 – 65(4) = 740 – 260 = 480. Eliminate (B). In (C), if t = 4, then
v(t) = 1,000 – 195(4) = 1,000 – 780 = 220. Eliminate (C). The correct answer is therefore (D).
8. D Whenever there are variables in the question and in the answers, think Plugging In. If s = 2, the
first expression becomes 8(22) – 6(2) + 2 = 8(4) – 12 + 2 = 32 – 12 + 2 = 22. Therefore, the first
expression multiplied by the second expression is 22(7) = 154. Plug in 2 for s in the answers to see
which choice equals the target number of 154. Choices (A), (B), and (C) yield 26, 70, and 198 re-
spectively. Choice (D) yields 154 and is the correct answer.
9. A Whenever the question includes variables and the answers are numbers, think Plugging In the An-
swers. In (A), x = 3 and y = –3. Plug these numbers into the equation to get –3 = 5(3 – 3)2 – 3. Solve
the right side of the equation to get –3 = 5(0)2 – 3 or –3 = 0 – 3. The correct answer is (A). None of
the other points work when plugged into the equation, so eliminate (B), (C), and (D).
10. B Plugging In would not be straightforward for this problem, given the fractions and negative num-
bers. A better approach would be to first simplify the expressions and then Plug In or solve. Dis-
tribute the (c + 2) term to both sides of the equation. On the left side, this will cancel out with the
(c + 2) term in the denominator. On the right side, make sure to distribute the (c + 2) to both terms
inside the parentheses. The equation becomes 3(c + 2) = 5(c + 2) – c(c + 2) or 3 = 5c + 10 – c.
c +2 c +2
Combine the c terms and subtract 10 from both sides to get –7 = 4c. Divide both sides by 4 to find
that c = – 7 . The answer is (B).
4
11. A Since the diameter is 10, the radius must be 5. A = pr2, so A = 25p. The shaded region takes
up π or 1 of the area, so minor arc XY must take up 1 of the circumference. C = pd so
25π 25 25
C = 10p. Therefore, the length of minor arc XY is 1 (10p), or 2π , which is (A).
25 5
12. D First, rewrite the equations so that they are in the slope-intercept form of a line, y = mx + b, where
m = slope. The first equation becomes 3y = –x + 42 or y = – 1 x + 14. The slope of this first line is
= –3x 3 y = 3x – 8. The slope of this line is
1
therefore – 3 . The second equation becomes –y + 8 or
therefore 3. The slopes of the two lines are negative reciprocals of each other, which means that the
two lines are perpendicular to each other. The correct answer is (D).
13. C The graph crosses the x-axis at three distinct points. When the function is set to 0, there should be
three real solutions for x. Use Process of Elimination to solve this question. Set the equation in (A) to
|Practice Test 6: Answers and Explanations 2 1
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0 to get 0 = (x – q)2. In this equation, the root is at x = q, thereby providing only one real value for x.
Eliminate (A). Set the equation in (B) to 0 to get 0 = (x – r)(x + s). The solutions for this equation
are x = r or x = –s. Therefore, there are only two real solutions for x. Eliminate (B). Set the equa-
tion in (C) to 0 to get 0 = (x – r)(x + s)(x + t). The solutions for this equation are x = r, x = –s, and
x = –t. Therefore, there are three real solutions for x. The correct answer is (C). Set the equation in
(D) to 0 to get 0 = (x – q)(x – r)(x + s)(x + t). The solutions for this equation are x = q, x = r, x = –s, and
x = –t. Therefore, there are four real solutions for x, so (D) is incorrect.
14. C When the quadratic is set to 0 the parabola crosses the x-axis at (–20, 0) and (20, 0). Because
parabolas are symmetrical, the vertex of the parabola is at (0, 40). Plug this point into the equa-
tion to get 40 = a(0 – 20)(0 + 20). Simplify the right side of the equation to get 40 = a(–20)(20) or
40 = –400a. Solve for a to get a = − 40 = − 1 . Therefore, the correct answer is (C).
400 10
15. B The line shown has a negative slope. Because the graph transformation asks for the negative value of
the transformed function, the resulting graph must have a positive slope. Therefore, eliminate (A).
Graph transformation rules state that if the number is within the parentheses, then the graph moves
left or right in the opposite direction of the sign, and if the number is outside the parentheses, the
graph moves up or down in the same direction of the sign. Therefore, this line will move 2 to the
right, and up 3. To follow the proper order of operations, draw out the graph transformation first,
and then deal with the negative outside the brackets. Move the line 2 units to the right to get the fol-
lowing graph:
y
(2, 1) x
(4, –3)
2 2 | Practice Test 6: Answers and Explanations
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Move the line up 3 to get this graph:
y
(2, 4) x
(4, 0)
The negative sign outside the brackets means to reflect, or flip, the line over the x-axis. When the
16. line is flipped from a positive to a negative slope, it will still go through point (4, 0). Therefore, the
correct answer is (B).
15 or 3.75
4
According to the question, h(t) = 120 and t = 8. Plug these values into the function to get
120 = 1 a(82). Simplify the equation to get 120 = 1 a(64) and 120 = 32a. Solve for a to get
22
a = 3.75. The correct answer is 3.75.
17. 2 Whenever there are two equations with the same two variables, they can be solved simultaneously
by adding or subtracting them. The key is to get one variable to disappear. Multiply the first equa-
tion by 3 to get 9h – 3j = 21. Stack the equations and add them.
9h – 3j = 21
2h + 3j = 1
11h = 22
Therefore h = 2, and the correct answer is 2.
18. 36 Plug in. Pick any values for the length, width, and height that will give you a volume of 24. If you
say the length is 2, the height is 3, and the width is 4, then the new length, height, and width will
be 1, 9, and 4 respectively. The new volume is 36. No matter what numbers you set for the initial
length, width, and height, you will always get 36 for the new volume.
|Practice Test 6: Answers and Explanations 2 3
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19. 5 or .833
6
Distribute the 6e on the left side of the equation and the 3e on the right side of the equation to get
6e2 + 18e = 6e2 + 12e + 5. Subtract 6e2 from both sides of the equation to get 18e = 12e + 5. Solve for
e to get 6e = 5, so e = 5 . The correct answer is 5 .
6 6
5
20. 12 or .416 or .417
Start by calculating the amount of vitamin C in the entire punch bowl and then calculate what the
equivalent in only one cup would be. To maximize the amount of vitamin C in the punch bowl,
Abeena will need to add as much orange juice, which has the highest concentration of vitamin C,
as she can. Given that the punch bowl holds 9 quarts, she will pour in 6 quarts of orange juice
(which is all she has) and 3 quarts of grape juice. The amount of vitamin C can be calculated as
follows:
# of quarts Orange Juice Grape Juice Total
Amount of vitamin C per quart 6 3 9
Total vitamin C 2 1
12 3 15
Therefore, the 9 quarts of punch contains 15 grams of vitamin C. Next, convert the quarts to cups.
The question tells us that there are 4 cups in 1 quart. Therefore, 9 ´ 4 = 36 cups in 9 quarts. To fig-
ure out how much vitamin C is in one cup, set up the following proportion: 15 grams = x grams .
36 cups 1 cup
15 5 5
Cross-multiply to get 36x = 15, or x = 36 = 12 . The correct answer is 12 . Only reduce a fraction
if it is necessary to make it fit in the grid-in box.
2 4 | Practice Test 6: Answers and Explanations
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Section 4: Math (Calculator)
1. A Whenever the question asks for a specific value and the answer choices are numbers,
think Plugging In the Answers. In (A), a = –0.75. Plug –0.75 in for a in the equation to get
16(–0.75)2 + 4(–0.75) – 6 = 0. Solve the left side of the equation to get 16(0.5625) + (–3) – 6 = 0,
or 9 – 3 – 6 = 0. Since, this statement is true, the correct answer is (A).
2. B So far the zoo has sold 4 × 48 = 192 tickets. To make a profit, the zoo will need to sell at least
350 – 192 = 158 additional tickets. Therefore, z needs to be at least 158. Calculate z in each of the
answers to see which gives you a value of z ≥ 158. In (A), z ≤ 350 – 4(48), so z ≤ 158. Eliminate (A).
Choice (B) gives you z ≥ 158. Keep (B). Choice (C) gives you z ≥ –158. Eliminate (C). Choice (D)
gives you z ≤ –158. Eliminate (D). Choice (B) is the correct answer.
3. D Line 1 shows exponential growth, because the line curves upward. Because birth rate and death
rate are per 1,000 people, a birth rate higher than a death rate will result in exponential growth
(because births – deaths will increase as the population increases). Immigration and emigration
numbers are per year and therefore have a linear effect on the graph (as the absolute change in
the population due to immigration—emigration is constant). South Zealand has more births per
1,000 than deaths per 1,000, so (D) accurately reflects Line 1.
4. A Start with Process of Elimination. Since the number of people in the theater decreases over time,
eliminate (D). Choices (A) and (B) are exponential functions, while (C) is linear. The number of
people that leave the theater every 15 minutes is not constant, since it is proportional to the num-
ber of people currently in the theater; therefore, this function is not linear, and you can eliminate
(C). Choice (A) must be correct because the function decreases quickly and then the number leav-
ing every successive 15 minutes is less than the time before (10% of 250 is more than 10% of 225).
5. B Cross-multiply to get 2y2 = 72. Solve for y to get y2 = 36, so y ± 6. Another way to solve would
be to Plug In the Answers, because the question asks for a specific value and there are numbers
in the answer choices. In (A), y = –6. Plug –6 into the equation and see if it works: 6 = −6 ,
or . Because this statement is true, one of the possible solutions 2(−6) 12
6 −6
−12 = 12 for the equation is
y = –6. Eliminate (C) and (D) because neither of these answers includes –6. According to (B), an-
other possible value for y is 6. Plug 6 into the equation to see if it works: 6 = 6 , or 6 = 6 .
2(6) 12 12 12
Since this statement is also true, the correct answer is (B).
6. C The 36-year-old runner ran under 3:00:00 when almost 3:30:00 is expected. The 39-year-old run-
ner ran slightly above 3:00:00 when 3:30:00 is expected. The 41-year-old runner ran slightly above
3:00:00 when about 3:45:00 was expected. Therefore, three runners ran at least 15 minutes faster
than predicted, which matches (C). If you chose (B), you may have based your choice on the num-
ber of runners who ran more than 15 minutes slower than their predicted time.
|Practice Test 6: Answers and Explanations 2 5
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7. C According to the table, the relative investment in wind resources in 2007 was 0.40 of the total
1.00. Probability is defined by the number of things that fit the requirements divided by the total
number of things. In this case, that would be 0.40 . You don’t need to worry about the actual dol-
1.00
lar values, because both of these numbers relate to the same total of $75 million. You do, however,
need to simplify this fraction. You can multiply it by 10 to get 4 , which then reduces to 2 .
10 10 5
You could also divide it on your calculator to get 0.4, and then divide each fraction in the answer
choices to see which one is also equal to 0.4. Either way, the correct answer is (C).
8. B Examine each answer choice and use Process of Elimination. For (A), the 2007 investment in
biofuels was 0.31 out of 1.00, or about one-third of the total, according to the chart. The total that
year was $75 million, so the Ballpark value would be about $25 million. The $50 million value in
(A) is too high, so eliminate it. Choice (B) refers to percents, but the chart is in “relative” invest-
ment. If the 2007 relative investment in wind is 0.40 out of 1.00, it is equivalent to 40% of the
total. The wind investment in 2017 is projected to be .32, or 32% of the total, which is a decrease
of 8%. Check out (C) and (D) just to be certain. For fuel cells, the percent of the total is projected
to double, but the total in 2017 is projected to be much higher. Therefore, the total dollar amount
invested in wind in 2017 will be much more than double the 2007 investment. For (D), the top three
energy types—biofuels, wind, and solar—are projected to be more equally invested in for 2017
than they were in 2007, so (D) is the opposite of what the chart shows. Eliminate (C) and (D), and
choose (B).
9. C Whenever there are variables in the question and in the answers, think Plugging In. If
m = 10, then Monster Truck Inc., receives a down payment of $3,200 plus 10 months’ worth
of monthly payments. This can be calculated as 3,200 + 10(380) = 3,200 + 3,800 = $7,000.
Plug in 10 for m in the answers to see which function equals 7,000. Choice (A) becomes
f(m) = 380 + 3,200(10) = 380 + 32,000 = 32,380. Eliminate (A). Choice (B) becomes
f(m) = 3,200 + 36(10) = 3,200 + 360 = 3,560. Eliminate (B). Choice (C) becomes f(m) = 3,200 +
380(10) = 3,200 + 3,800 = 7,000. Keep (C), but check (D) just in case it also works. Choice (D)
becomes f(m) = 10,480 – 380(10) = 10,480 – 3,800 = 6,680. Eliminate (D). The correct answer
is (C).
10. A Plugging In the point (6, –5) in the answer choices could work, but it will likely make more than
one equation true. The x-intercept is where the line crosses the x-axis, at the point where y = 0.
Therefore, one point on the line is (3, 0). The choices are all in the slope-intercept form, y = mx + b,
where m is the slope. To find the correct answer, calculate the slope of the line with the two points
known to be on the line. The slope of a line is determined by the equation y2 − y1 . Therefore, the
x2 − x1
2 6 | Practice Test 6: Answers and Explanations
SAT Premium Prep
slope of the line shown can be calculated as follows: −5 − 0 = −5 . Only (A) has a slope of −5 , so
6−3 3 3
that is the correct answer.
11. D There are 12 inches in one foot, so a reel is 12 ´ 1,000 = 12,000 inches long. Set up a pro-
portion to determine how many fbryam34estpoegr erteexl:=1341f6ria,n0mc0he0 x frames . Cross-multiply to get
= 12,000 inches Next, find the number
3 x = 12,000. Divide both sides frames per reel.
4
of frames the film requires. Convert the time to seconds. There are 60 minutes in an hour, so 2
hours and 47 minutes is equal to (2 ´ 60) + 47 = 167 minutes. There are 60 seconds in a minute,
so there are 60 ´ 10,020 seconds in this film. If each second consists of 24 frames, then there are
24 ´ 10,020 = 240,480 frames in this film. To determine the number of reels, divide by the num-
ber of frames per reel: 240, 480 = 15.03 reels. Because 15 reels does not hold quite enough frames,
16,000
the film requires 16 reels, which is (D).
12. C So far, Hua has received 1,350 + 900 = 2,250 surveys. Hua needs 3,800 – 2,250 = 1,550 additional
surveys. Given that Hua receives 1 completed survey for every 5 she sends out, she will need to
send out at least 5 ´ 1,550 = 7,750 surveys. Therefore, the correct answer is (C).
13. B Since line AE is perpendicular to the line containing segment AB and the line containing segment
DE, these two lines must be parallel. Therefore, ÐABC is equal to ÐCDE because they are both
small angles created by a line crossing two parallel lines. Since ÐDCE and ÐACB are opposite each
other, they must be equal as well, so these are two similar right triangles. The question also tells
you that C is the midpoint of BD, which means that BC and CD are equal. When you have two
sides and the included angle of one triangle congruent to two sides and the included angle of a sec-
ond triangle, you know that the triangles are congruent. This means that AB = DE and AC = CE.
Lastly, the question states that AC = DE, which means that AB = AC, and these must be isosceles
right triangles. Angle ABC is therefore 45°, and n, which is opposite ÐABC, must be 45° as well.
The correct answer is (B).
14. D Start with the easier equation and use Process of Elimination. The easier equation is related to the
total number of turkey and bread slides, t + b, on the 4 platters. According to the question, each
platter contains 100 slices, so the 4 platters contain 100 ´ 4 = 400 slices. Therefore, one of the
equations in the correct answer must be t + b = 400. Eliminate (A) and (B) because neither of these
|Practice Test 6: Answers and Explanations 2 7
SAT Premium Prep
answers contains that equation. The second equation deals with the weight of the slices. According
to the problem, the slices on each platter weigh 160 ounces. Therefore, the total weight of the slices
on all 4 platters is 160 ´ 4 = 640. Eliminate (C) because the total is wrong in the weight equation.
The correct answer is (D).
15. D Whenever there are two equations with the same two variables, they can be solved simultaneously
by adding or subtracting them. The key is to get one variable to disappear. Multiply the second
equation by –2, to get 6a – 2z = 20. Stack the two equations and add them.
4a + 2z = 10
6a – 2z = 20
10a = 30
Therefore, the correct answer is (D). Be careful of (C)—the question did NOT ask for the value
of a.
16. B We know that Isabella starts with $1,000 in her account, so this eliminates (D). She is earning
money from the interest, so the line must have a positive slope, eliminating (C), which has a con-
stant slope. The two best choices are (A) and (B), but in (A) Isabella’s money doesn’t begin to
increase until the 5-year mark, which doesn’t make sense—thus (B) is the correct answer.
17. A Find a point on the graph and plug that point into each of the answers to see which equation works.
The graph goes through the point (0, –6). Using that point, (A) becomes –6 = 02 – 0 – 6. Solve the
right side of the equation to get –6 = –6. Keep (A), but check the remaining answer choices just
in case. Choice (B) becomes –6 = 02 + 0 –12. Solve the right side of the equation to get –6 = –12.
This is not true, so eliminate (B). Choice (C) becomes –6 = 02 + 6(0) + 9. Solve the right side of the
equation to get –6 = 9. Eliminate (C). Choice (D) becomes –6 = 02 + 5(0) + 6. Solve the right side
of the equation to get –6 = 6. Eliminate (D). The correct answer is (A).
18. A The key to this problem is understanding that the three friends plan to climb an equal number of
stairs. Start with the building for which we know the number of stairs. Each of the friends is plan-
ning to climb 3,639 ¸ 3 = 1,213 stairs. Since 1,213 must be a part of the correct answer, eliminate
(B) and (D). Given that Dalia will complete only 75% of her goal, Dalia’s total must be multiplied
by 75%, or 0.75. This eliminates (C). The correct answer is (A).
19. C Let’s break this question into Bite-Sized Pieces. First, to find the number of U.S. residents who visit
European countries every year, we will need to determine how many residents hold passports: 36%
of 315 million = 0.36 ´ 315 = 113.4 million. Next, we can calculate how many of those passport-
holders travel internationally each year: 8% of 113.4 million = 0.08 ´ 113.4 = 9.072 million.
Finally, we can calculate how many of those international travelers visit Europe each year: 10% of
9.072 million = 0.1 ´ 9.072 = 0.9072 million. 0.9072 million is equivalent to 907,200, which is
(C). The percentage calculations can also be done in one step: 0.1 ´ 0.08 ´ 0.36 ´ 315 = 0.9072
million.
2 8 | Practice Test 6: Answers and Explanations
SAT Premium Prep
20. A Given that all of the answer choices are possible values for y, Plug In the Answers. In (A),
y = x – 6. Plug this value into (x + 2)y2 to get (x + 2)(x – 6)(x – 6). Multiply the last two fac-
tors together to get (x + 2)(x2 – 12x + 36). Multiply the two resulting factors together to get
x3 – 12x2 + 36x + 2x2 – 24x + 72. Combine like terms to get x3 – 10x2 + 12x + 72. This is the same
as the third degree polynomial in the question. Therefore, the correct answer is (A).
21. C In 2010, as counted, there were 354 + 225 + 757 = 1,336 elephants in Wakanda. If the margin
of error was 17.4, the lowest population of elephants that could fit within the margin of error
would be 1,336 – 17.4 = 1,318.6 elephants. Because there cannot be fractional elephants, 1,319 is
the smallest value that would be within the margin of error. The correct answer is (C).
22. C Start by using Process of Elimination to eliminate (D) because the entire question is about find-
ing the height, and (D) has nothing to do with height. The difference between the left and middle
stacks is 2 stacked sawhorses. The height added to the stack of sawhorses by adding two to the
stack can therefore be calculated as 92 – 60 = 32. Therefore, the added height of one stacked
sawhorse is 32 ¸ 2 = 16. From this information, keep subtracting the 16 inches added to the
top of a stack by each additional sawhorse until you get down to one sawhorse in the stack. If
three sawhorses are 60 inches tall, two will be 60 – 16 = 44 inches tall and one sawhorse will be
44 – 16 = 28 inches tall. Choice (A), the height of one sawhorse, can now be eliminated. Another
way to think about the height added to the stack of sawhorses by each additional sawhorse is to
think of it as the distance between the top of one sawhorse and the top of the next. Since all the
sawhorses are the same height, this distance is also the distance from the bottom of one sawhorse
to the bottom of the next. Since this distance is 16, eliminate (B). Therefore, the answer is (C). The
height of one sawhorse is 28, which is b + c, so the overlap, c, is 28 – 16 = 12.
23. B Remember that sin a = cos b means that a and b are complementary angles. Therefore, the
two triangles are similar and cos a = sin b as well. You can set up the following equation:
5 = 7 . Now that you have solved for EF (11.2), you can use the Pythagorean Theorem
8 EF
(a2 + b2 = c2) to solve for DF. 11.22 = 72 + DF2. The correct answer is (B). Alternatively, you could
have used the Pythagorean Theorem to solve for BC and then set up a proportion between the
similar triangles. Just make sure that you recognize that AC corresponds to DE rather than DF.
24. B First, solve for Rick’s hourly rate and Shane’s hourly rate. Since Work = Rate ´ Time, Rick
produces 8 widgets per hour (28 widgets ¸ 3.5 hours without breaks) and Shane produces
27 ¸ 4.5 = 6 widgets per hour. Now Plug In. Since you know they have a combined rate of 14
widgets per hour, choose a total amount that is divisible by 14. Let’s say they were each assigned 14.
This means that the total produced is 28, and at a total rate of 14 per hour. Therefore, it takes them
2 hours to finish. During this time, Rick would produce 16 widgets and Shane would produce
12 widgets. Therefore, Rick must have done 2 of Shane’s originally assigned 14 widgets, which is
14.3% of 14. Choice (B) is the correct answer.
|Practice Test 6: Answers and Explanations 2 9
SAT Premium Prep
25. D To answer this question, you need the formula for percent change: difference × 100.
original
For choice (A), plug in a difference of about 200,000 and an original of about 1,000,000:
200,000 × 100. This simplifies to 20%. For (B), plug in a difference of about 200,000 and an
1,000,000 about
original of 900,000: 200,000 × 100. This simplifies to about 22%, so you can eliminate
900,000
(A). Choice (C) is incorrect because the Sylvilagus brasiliensis population increased during that
time. (If you chose (C), you may have calculated the percent change of the Chrysocyon brachyurus
population.) For (D), plug in a difference of about 200,000 and an original of about 800,000:
200,000 × 100 . This simplifies to approximately 31%. This is the greatest percent decrease; there-
800,000
fore, (D) is correct.
26. C Start by setting the two equations equal to each other to get x2 – 2x = 2x – 1. Manipulate the equa-
tion into the ax2 + bx + c = 0 form, which is x2 – 4x + 1 = 0. Use the quadratic equation, which
states that x = −b ± b2 − 4ac to get x = −(−4) ± (−4)2 − 4(1)(1) . Solve for x to get
2a 2(1)
x = 4± 16 4
2 − , then x = 4± 12 or x = 4±2 3 , so x = 2 ± 3 . The greater of the two pos-
2 2
sible values for x is x = 2 + 3 . Therefore, the correct answer is (C).
27. B Cosecant is 1 or hypotenuse . Make a right triangle and plug in for the side lengths. Be-
sine opposite
cause hypotenuse , make the hypotenuse 1.66 and the side opposite the angle measure
opposite
θ equal to 1. Use the Pythagorean Theorem to solve for the missing side: 12 + x2 = 1.662;
1 + x2 = 2.7556; x2 = 1.7556; x ≈1.32. Make this the other leg of the triangle. To find tan θ, use
opposite : 1 , which is (B).
adjacent 1.32
28. D If two patients are added to the trial, there will be 12 total patients. If the mean height of 12
patients is 169 cm, then the 12 patients have a total height of 12 ´ 169 = 2,028 cm. The total
height of the first 10 patients is 184 + 176 + 181 + 157 + 168 + 154 + 148 + 165 + 190 + 162 =
1,685 cm, so the two new patients must have a total height of 2,028 – 1,685 = 343 cm. Add up the
heights and eliminate any choice that does not equal 343. Only (D) works.
3 0 | Practice Test 6: Answers and Explanations
SAT Premium Prep
29. D Plugging in the given point to see which equation is true is not easy on this one, since both val-
ues have weird decimals. The answer choices are also likely written so that more than one is true
for that point, so try to find another point on the line. The x-intercept of a line is where the line
crosses the x-axis. At that point, the value of y is 0. Therefore, (2, 0) is also a point on the line.
Plug this point into the answers, as it is easier to calculate. If it works in more than one equation,
plugging in the ugly point will determine the correct answer, which must work with both points.
Plug point (2, 0) into (A) to get 0 + 5.9 = 2.5(2). Solve both sides of the equation to get 5.9 = 5.
Eliminate (A). Plug (2, 0) into (B) to get 4(0) + 12(2) = 29.1. Solve both sides of the equation to
get 4 + 24 = 29.1, or 28 = 29.1. Eliminate (B). Plug (2, 0) into (C) to get 6(0) + 27.15 = 12(2). Solve
both sides of the equation to get 0 + 27.15 = 24. Since this is clearly not a true statement, elimi-
nate (C). Plug (2, 0) into (D) to get 10(0) – 13(2) = –26. Solve both sides of the equation to get
–26 = –26. Since (D) is the only answer for which the point (2, 0) works, the correct answer is (D).
30. B Whenever there are variables in the question and in the answers, think Plugging In. If P0 = 4,
k = 2, and t = 3, then P = (4)(10)6 = 4,000,000. Plug these values into the answer choices to see
log 4, 4
000,000
which answer works. Choice (A) becomes 3= 2 . Simplify the right side of the
log 1 −6
1, 000,000 2
equation to get 3 = , then 3 = , and finally 3 = –3. This isn’t true, so elimi-
2
4,000,000
log 4
nate (A). Choice (B) becomes 3 = 2 . Simplify the right side of the equation to
get 3 = log (1,000, 000) , then 3 = 6 , and finally 3 = 3. Keep (B), but check the remaining an-
2
2
( )swer log
choices just in case. Choice (C) becomes 3 = 4,000,000 × 4 . Simplify the right side
2
of the equation to get 3 = log (16,000,000) , or 3 ≈ 3.6. Eliminate (C). Choice (D) becomes
2
3 = 2 log 4 . Simplify the right side of the equation to get 3 = 2 log 1 , then
4,000,000 1,000,000
3 = 2(–6), and finally 3 = –12. Eliminate (D). The correct answer is (B).
|Practice Test 6: Answers and Explanations 3 1
SAT Premium Prep
31. 48 Set up a proportion: 1 euro = 40 euros . Cross-multiply and get x = 1.2 ´ 40 = 48.
1.2 dollars x dollars
32. 558 During the summer the ice cream vendor sells an average of 2(50) – 7 = 93 popsicles per day. Over
6 summer days, 93 ´ 6 = 558 popsicles are sold. The correct answer is 558.
33. 7 or 3.5
2
First, get rid of the decimals in the first equation by multiplying the first equation through by 10 to
get 13g + 17h = 50. In the second equation, move all the variables to the left of the equal sign to get
–13g + 3h = 20. Whenever there are two equations with the same two variables, they can be solved
simultaneously by adding or subtracting them. The key is to get one variable to disappear. Stack
the equations on top of each other and add them.
13g + 17h = 50
–13g + 3h = 20
20h = 70
Therefore, h = 70 . Because this number is too large to grid in, either reduce the fraction to 7 , or
20 2
convert the fraction to the decimal 3.5.
34. 16 To find the percent of registered Democrats planning to vote for Candidate A, divide the number
of Democrats planning to vote for Candidate A by the total number of registered Democrats:
1=2540 0=.16 16% , which makes 16 the correct answer.
35. 30 Start by drawing the picture, as this question doesn’t provide one. To do so, change each of the
equations into the slope-intercept form of an equation y = mx + b, where m is the slope and b is the y-
intercept. The second equation becomes 3y ≥ 2x – 12, or y ≥ 2 x – 4. The third equation
3
2
becomes 5y ≤ –2x + 20, or y ≤ – 5 x + 4. The ≥ sign in the second equation means that
everything above the line should be shaded, and the ≤ sign in the third equation means that every-
thing below that line should be shaded. To graph the first equation x ≥ 0, shade everything to the
right of the y-axis.
3 2 | Practice Test 6: Answers and Explanations
The resulting picture should look like this: SAT Premium Prep
y
y ≥ – 23x – 4
y ≤ – 52x + 4 x
x>0
The formula for the area of a triangle is A = 1 b ´ h. It is easiest to think of the side that is along
2
the y-axis as the base. That side goes from a y-coordinate of 4 to –4, for a length of 8. The height of
the triangle is the x-coordinate of the point where the two slanted lines meet; set the two equations
equal to find it. Start with 2 x – 4 = – 2 x + 4 and multiply everything by 15 to get 10x – 60 = –6x
3 5
+ 60. Then add 6x and 60 to both sides to get 16x = 120, so x = 7.5, and the height is 7.5. The result-
ing figure should look like this:
y
y ≤ – 2 x + 4 y ≥ – 2 x – 4
5 3
7.5 0 x
8
x>0
|Practice Test 6: Answers and Explanations 3 3
SAT Premium Prep
Plug the measurements for the base and the height into the area formula to get A = 1 (8)(7.5) = 30.
The correct answer is 30. 2
36. 0 Start by multiplying the terms together. To multiply (x2 + 2x – 3)(2x + 5), multiply each term in
the left parenthesis by each term in the right parenthesis to get 2x3 + 5x2 + 4x2 + 10x – 6x – 15.
Combine like terms to get 2x3 + 9x2 + 4x – 15. To multiply (x + 1)(x – 1)(x + 3), do one set of
parentheses first; then multiply that product by the remaining parenthesis. You may notice that
(x + 1)(x – 1) is a common quadratic, which equals x2 – 1. Then you need to multiply x2 – 1 by
(x + 3). As you did before, multiply each term in the first parenthesis by each term in the second
to get x3 + 3x2 – x – 3. Now you can do (2x3 + 9x2 + 4x – 15) – (x3 + 3x2 – x – 3). It is easiest to
distribute the negative sign into the second parenthesis: (2x3 + 9x2 + 4x – 15) + (–x3 – 3x2 + x + 3).
Now you can combine like terms to get x3 + 6x2 + 5x – 12. This is in the form ax3 + bx2 + cx + d, so
a = 1, b = 6, c = 5, and d = –12. This means a + b + c + d = 1 + 6 + 5 + (–12) = 0.
37. 195 Use the definition of inverse proportion: x1 y1 = x2 y2. Plug in 1.5 for x1, 260 for y1, 2 for x2, and
solve for y2: (1.5)(260) = (2)(y2); 390 = 2y2. Divide both sides by 2, and you find y2 = 195.
38. 15 Start by converting the qualifying distance of 68.58 meters into yards. Set up a proportion:
1 yard = x yards . Cross-multiply to get 0.9144x = 68.58. Divide both sides by
0.9144 meters 68.58 meters
0.9144 to find that the qualifying distance is 75 yards. If his current best is 60 yards, he needs to
throw 75 – 60 = 15 more yards.
Copyright © 2021 by TPR Education IP Holdings, LLC. All rights reserved.
3 4 | Practice Test 6: Answers and Explanations
RAW SCORE CONVERSION TABLE SECTION AND TEST SCORES SAT Premium Prep
Raw Score Math Reading Writing Raw Score Math Reading Writing Please note that the
Section Test Score and Section Test Score and numbers in the table may
(# of correct Score Language (# of correct Score Language shift slightly depending
answers) 10 Test Score answers) 28 Test Score on the SAT’s scale from
10 28 test to test; however, you
0 200 10 10 30 530 29 29 can still use this table to
1 200 11 10 31 540 29 30 get an idea of how your
2 210 12 10 32 550 30 30 performance on the prac-
3 230 13 10 33 560 30 31 tice tests will translate to
4 240 14 11 34 560 31 32 the actual SAT.
5 260 15 12 35 570 31 32
6 280 15 13 36 580 32 33
7 290 16 13 37 590 32 34
8 310 17 14 38 600 33 34
9 320 17 15 39 600 33 35
10 330 18 16 40 610 34 36
11 340 19 16 41 620 35 37
12 360 19 17 42 630 35 38
13 370 20 18 43 640 36 39
14 380 20 19 44 650 37 40
15 390 21 19 45 660 37
16 410 21 20 46 670 38
17 420 22 21 47 670 38
18 430 22 21 48 680 39
19 440 23 22 49 690 40
20 450 23 23 50 700 40
21 460 24 23 51 710
22 470 24 24 52 730
23 480 25 25 53 740
24 480 25 25 54 750
25 490 26 26 55 760
26 500 26 26 56 780
27 510 27 27 57 790
28 520 28 58 800
29 520 28
CONVERSION EQUATION SECTION AND TEST SCORES
Convert
READING TEST READING TEST
RAW SCORE SCORE
(10–40)
(0–52)
Convert + = x 10 =
WRITING AND WRITING AND READING TEST READING AND EVIDENCE-BASED READING
LANGUAGE TEST LANGUAGE TEST SCORE WRITING TEST AND WRITING
(10–40) SECTION SCORE
RAW SCORE SCORE SCORE (200–800)
(0–44) (10–40) (20–80)
+ = Convert +=
EVIDENCE-BASED READING
AND WRITING
MATH TEST MATH TEST MATH SECTION MATH SECTION SECTION SCORE TOTAL SAT
NO CALCULATOR CALCULATOR RAW SCORE SCORE (200–800) SCORE
RAW SCORE (0–58) (200–800)
RAW SCORE (400–1600)
(0–20) (0–38)
|Practice Test 6: Answers and Explanations 3 5
Practice Test 7:
Answers and
Explanations
SAT Premium Prep
PRACTICE TEST 7 ANSWER KEY
Section 1: Section 2: Section 3: Section 4:
Reading Writing & Language Math (No Calculator) Math (Calculator)
1. A 27. C 1. C 23. D 1. C 11. A 1. C 20. B
2. D 28. A 2. D 24. B 2. B 12. D 2. B 21. D
3. A 29. C 3. A 25. C 3. D 13. B 3. A 22. A
4. C 30. C 4. C 26. A 4. C 14. D 4. B 23. B
5. D 31. B 5. D 27. A 5. B 15. A 5. A 24. C
6. B 32. B 6. C 28. B 6. D 16. 5 6. D 25. D
7. A 33. A 7. B 29. C 7. A 17. 5/13 7. C 26. C
8. B 34. D 8. D 30. B 8. D 27. C
9. A 35. C 9. A 31. C 9. C or 8. B 28. A
10. C 36. C 10. B 32. A 10. D .384 9. A 29. B
11. A 37. A 11. B 33. A or 10. A 30. B
12. D 38. B 12. A 34. B .385 11. D 31. 5, 6,
13. A 39. C 13. B 35. A 18. 130 12. A
14. B 40. B 14. D 36. B 19. 2 13. B or 7
15. C 41. D 15. B 37. C 20. 17/4 14. A 32. 650
16. C 42. D 16. C 38. D or 15. B 33. 64.1
17. B 43. C 17. A 39. A 4.25 16. D 34. 365
18. C 44. B 18. B 40. C 35. 8
19. C 45. D 19. B 41. B 17. C 36. 5
20. B 46. D 20. A 42. C 18. D 37. 14
21. D 47. C 21. D 43. D 19. A 38. 114
22. A 48. A 22. D 44. A
23. C 49. B
24. D 50. A
25. B 51. B
26. C 52. A
2 | Practice Test 7: Answers and Explanations
SAT Premium Prep
PRACTICE TEST 7 ANSWERS AND EXPLANATIONS
Section 1: Reading
1. A The question asks for the main purpose of the passage. Since there is no reference window to use for
this question, it should be answered last. The passage first introduces Sir Walter Elliot, and then
describes his personality traits and his personal history: primarily the death of his wife, which
left him alone with three children. Although (C) may seem well supported, this answer is
too specific, as it only discusses Sir Walter’s personality traits and not the passage as a whole.
Choice (D) is also much too specific, as only the last paragraph of the passage discusses the
relationship between Sir Walter and Lady Russell. Choice (B) is too vague; the overview is
focused primarily on Sir Walter, not the entire family. Only (A) provides a description of the
main purpose of the passage.
2. D The question asks for a summary of the first two paragraphs. In general, and in this case, these
usually introduce and provide insight into the main topic of the story, which makes (D) the
best match, as the story is focused on Sir Walter and his habits. Choices (A) and (B) are not
supported by the passage, as there is no true indication that the family is “important” or that
the book it appears in is “one of the most popular.” Although (C) may be true based on the
passage, it is not the best summary of the two paragraphs, only a minor detail.
3. A The question asks why the author included the phrase with all the Marys and Elizabeths they
had married. The paragraph this phrase appears in summarizes the part of the family his-
tory that is not directly quoted from the Baronetage, and this phrase is included as part of
that summary. Choice (D) is the opposite of a summary, so it is not the best match. Choices
(B) and (C) are too far-reaching; there is no information provided about a type of woman or
British common names. The best match is (A), as it indicates the same information is repeated
over and over again.
4. C The question asks how Sir Walter can best be described, so the best match will be supported
by the passage. General questions such as this should be done after all of the specific questions.
Also note that the following question is a best evidence question, so this question and question
5 can be answered in tandem. Look at the answers for question 5 first. Although the passage
states that Sir Walter never took up any book but the Baronetage, this evidence does not connect
to any of the descriptions from the previous question, so (A) can be eliminated. Although Sir
Walter is described as the head of a family in both (B) and (C), there is no support for his be-
ing one of the foremost in England. In lines 50–54, Sir Walter is described as caring about his
rank and his appearance above all else, which matches (C) from question 4. No other answer
for question 4 is supported by a line reference from question 5. The correct answers are (4C)
and (5D).
|Practice Test 7: Answers and Explanations 3
SAT Premium Prep
5. D (See explanation above.)
6. B The question asks what “fine” means in this context. Read the window around line 47 and it
should be clear that these sentences are discussing Sir Walter’s vanity and pride in his personal
appearance. Since the word “fine” is being used to match “handsome” as used earlier in the
sentence, (B) is the best match. The other choices can be used as synonyms of “fine” but do not
match the meaning of “handsome” as it is used here.
7. A The question asks what can be inferred about Lady Elliot, so the answer must match the
passage as closely as possible. General questions such as this should be done after all of the
specific questions. Also note that the following question is a best evidence question, so this
question and question 8 can be answered in tandem. Look at the answers for question 8 first.
Lines 58–62 indicate that Lady Elliot was an excellent woman, sensible and amiable; however,
this does not match any of the answer choices in question 7, so eliminate (8A). Lines 62–64
describe how Lady Elliot humored, or softened, or concealed [Sir Walter Elliot’s] failings, which
matches (7A). Lines 64–68 state that Lady Elliot was not the very happiest being, but (7C) goes
beyond by saying she was unhappy most of her life; eliminate (8C). Lines 73–76 discuss Lady
Elliot’s one very intimate friend, which is not evidence of her being surrounded by friends in
(7D). Only (7A) is supported by any line reference in question 8. The correct answers are (7A)
and (8B).
8. B (See explanation above.)
9. A The question asks what can be inferred from the last paragraph, so the answer must match the in-
formation provided in that paragraph as closely as possible. Reading the window reveals that Sir
Walter and Lady Russell continue to live in same neighborhood, remaining both friends and
single. There is no mention of beauty in the last paragraph, so (D) is not supported. There is
also no indication that Sir Walter made an offer to be accepted by Lady Russell, nor is there
anything about Lady Russell’s friendship with Lady Elliot in this paragraph, so (C) is also not
supported. There is no mention of what Sir Walter and Lady Russell are or are not likely to do
in the future, so (B) can be eliminated. Be careful about answer choices that include predic-
tions. No matter how logical they may seem, you can’t prove the future, and you should always
be able to prove a correct SAT answer. The paragraph does state that the two did not marry
despite whatever might have been anticipated on that head by their acquaintance, indicating that
some may have anticipated that they would marry. This best matches (A).
10. C Remember to use the context of the passage when considering the definition of a word, and
not your own definition of head. Read the window around line 81 to determine a synonym
that works within the context of the passage. Something like “idea” would work, as the sen-
tence is referring to the idea that Sir Walter and Lady Russell may have married one another.
This is most synonymous with possibility, (C). Inevitability could have worked if the couple did
marry, but since such an event never actually happened possibility is the best choice. Face and
countenance in (A) and (B) are synonyms for head but do not work in this specific context.
4 | Practice Test 7: Answers and Explanations
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11. A The question asks about the position of the author. This passage is an informative review of
how adolescents divide their time over various activities, and it references “studies” on that
topic multiple times. This best supports (A), a social scientist presenting findings. There is no
indication in the passage that the author is a parent or an educator, eliminating (B) and (D).
Since the author is not focused on his time as an adolescent, but on current adolescents, (C)
can be eliminated as well.
12. D The question asks for how a very common word, commit, is being used in a specific context.
Remember to use the context of the passage when considering the definition of a word, and
not your own prior usage of commit. In this context, commit is being used synonymously with
“dedicate” or “allot.” The best match for this meaning of commit and those synonyms is give,
(D). Entrust, institutionalize, and pledge do not match that meaning in this context.
13. A The question asks what the references to various factors serve to do. Within this window, the
passage discusses the different focuses of studies on adolescent time use and the factors that
influence that time use. This reference serves as an example of those influences on adolescent
time use, indicated by the phrase’s location between a pair of dashes, clearly serving as ex-
amples of the circumstances...which serve as a backdrop. This best matches (A). It does not neces-
sarily include all of the differences that determine time use, eliminating (B). It is not a list of
activities, eliminating (C). And that reference applies only to studies on adolescent time use,
not adult time use, eliminating (D).
14. B The question asks what purpose the discussion of how boys and girls spend their time serves.
This part of the passage discusses the “increasing divergence in the activity sets of boys and
girls,” which makes (B) the best match. There is no discussion of societal roles, only a social
use of time, eliminating (A). There is also no discussion of biological differences between boys
and girls, only social ones, eliminating (D). The author does not indicate that there is anything
“disturbing” about this trend, so (C) is also incorrect. Be careful about trying to apply outside
information or prior knowledge. Stick with what’s in the text.
15. C Remember to use the context of the passage when considering the definition of a word, and
not your own prior usage of reflect. In this context, reflect is being used synonymously with
“show” or “demonstrate.” Reveal, (C), best matches this meaning. Return, redirect, and imitate
do not match that meaning in context.
16. C The question asks what is indicated about chores and jobs, which is a very open-ended ques-
tion. By reading the paragraph under that section heading, it is clear that the focus of this
paragraph is on the differences that exist between boys and girls when it comes to chores and
jobs. Neither (A) nor (D) focuses on this difference, and (D) is a direct contradiction of what’s
stated in the text. Eliminate them both. Choice (B) references the different social stereotypes
related to chores and jobs, which may seem like a well-supported answer choice. But (B) also
says that chores and jobs create those stereotypes, which is not supported by the passage (in
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which it says they reinforce those stereotypes). This leaves (C), which matches the discussion of
different activities boys and girls engage in.
17. B The previous question asked what is indicated about chores and jobs. Using line references to
support answer choices to the previous question, answer choices to this question can be quickly
eliminated. Choice (A) refers to a different paragraph of the passage that is not concerned with
chores or jobs, so eliminate it. The passage mentions that money is a greater motivating factor
than experience, which eliminates both (C) and (D) as support for (C) in the previous ques-
tion. The only line that supports an answer from the previous question is found in (B): chores
and jobs tend to be divided along gender lines, as boys and girls engage in different types of
those activities.
18. C This question asks about which of the answers would NOT affect student participation. Lines
80–85 mention factors that do affect participation. Gender is mentioned in line 81, so elimi-
nate (A). Autonomy, mentioned in line 85, means doing things for themselves, so eliminate (B).
Involvement of friends is mentioned in lines 83–84, so eliminate (D). Parental support is not
mentioned, so (C) is the correct answer.
19. C This question requires using the text and the table. Listening to music is not an activity listed
on the table, but it is mentioned in lines 66–70. The text says that adolescents spend as much as
four to six hours a day listening to music... and it begins to emerge as a significant backdrop to other
activities. Because they are listening to music 4–6 hours a day, (A) and (B) can be eliminated.
We know the researchers asked about the activity because there are specifics in the text. Elimi-
nate (D). Choice (C) is supported by the text and is the correct answer.
20. B The question asks for a summary of the information presented on the graphic, so the best
approach is likely POE. The graphic provides information on only one set of adolescents; it
does not compare one set of adolescents to another set a decade earlier. Eliminate (C). Since
more than a dozen activities are listed in the graphic, (A) can be eliminated, since that indi-
cates adolescents divide their time over only a dozen. The graphic does not account for why
there is a difference between the time boys and girls spend sleeping, so (D) can be eliminated.
The graphic does indicate that the majority of time spent by both boys and girls is on school
and sleeping, which best supports (B).
21. D Just like the previous question, this question asks for information presented on the graphic.
Checking each answer choice against the graphic demonstrates that (A) is incorrect, as a num-
ber of hobbies are not indicated, only the amount of time spent on them. Although boys do
spend less time on household work than girls do, this does not account for the stereotypical
gender roles that exist, eliminating (B). Choice (C) is incorrect, as girls spend one hour and
eleven minutes on personal care while boys spend a total of two hours and twenty-five minutes
on sports and TV combined. There is only one activity on which boys and girls spend the ex-
act same amount of time (0:10 Outdoors), which supports (D).
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22. A The first paragraph describes a rule—aggravated murder is the only crime punished by
death—and then states that we are even now deliberating whether the extreme penalty should be
retained in that solitary case. The second paragraph gives the parameters for the application
of the rule: by conclusive evidence, the greatest crime known to the law; and when the atten-
dant circumstances suggest no palliation of the guilt. Choice (A) best describes this structure.
Neither history nor counterarguments are offered in relation to the rule, so (B) and (C) are
incorrect. Additionally, the paragraphs never reject the rule, so (D) is incorrect.
23. C In these lines, the author states that to deprive the criminal of the life of which he has proved
himself to be unworthy…is the most appropriate punishment for his crimes. The author does
not advocate for the value of his life; in fact, he does the opposite. Choice (A) is incorrect. The
author does not discuss exonerating evidence or criminal remorse, so (B) and (D) are incorrect.
Choice (C) best matches the information provided in the text.
24. D The question asks for the purpose of the third paragraph. The author does not include an
anecdote or offer a concession to the opposition, eliminating (A) and (C). While the author
does present an argument in opposition to those who attack the penalty, he does not attack a
specific rival, eliminating (B). The author starts the paragraph by stating I defend this penalty,
when confined to atrocious cases, on the very ground on which it is commonly attacked. Choice (D)
summarizes this purpose.
25. B The author states that imprisonment with hard labor for life is less severe indeed in appearance
than capital punishment but far more cruel in reality. Choice (A) states the opposite, so it is in-
correct. The author does not state if imprisonment with hard labor for life is the best deterrent,
just that capital punishment is the least cruel deterrent, so (C) is incorrect. The author states
that life imprisonment with hard labor is the fate to which a murderer would be consigned by
the mercy which shrinks from putting him to death. This text matches (B) in that life imprison-
ment is a likely alternative, but not necessarily the next best alternative as in (D). Choice (B) is
correct.
26. C This question asks for the evidence you used to answer the previous question, so if you can’t
find lines to support your answer to question 25, take a moment to reassess. In this case, only
(C) supports the idea that life imprisonment with hard labor is the likely alternative to capital
punishment.
27. C This question asks why the author poses a question at the beginning of the fourth paragraph.
The first line asks, But has it been sufficiently considered what sort of a mercy life imprisonment
with hard labor is and what kind of life it leaves to criminals? The author goes on to answer
his question by pointing out possible lives a criminal of this sort might lead. Therefore, he is
not actually petitioning his audience for help, eliminating (D). While the author states that
one possible outcome of life imprisonment—immuring him in a living tomb—is far more
severe than capital punishment, he does not accuse his opponents of being innately cruel.
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Choice (A) is incorrect. Choice (B) contradicts the passage, so it can be eliminated. The ques-
tion does point out that there are additional questions that need to be answered, indicating life
imprisonment could be more cruel than its advocates assume. Choice (C) is the correct answer.
28. A This question asks what the author would agree with. General questions such as this should be
done after all of the specific questions. Also note that the following question is a best evidence
question, so this question and question 29 can be answered in tandem. Look at the answers
for question 29 first. Lines 33–35 and 40–44 do not support any answer from question 33;
eliminate (29A) and (29B). Lines 50–59 compare the short pang of a rapid death from capital
punishment to a long life in the hardest and most monotonous toil of life imprisonment, which
supports (29A). Lines 59–66 do not support any of the answers to question 28. Only (A) from
question 28 is supported by the lines in question 29. The correct answers are (28A) and (29C).
29. C (See explanation above.)
30. C The author compares life in prison to a living tomb because the criminals are debarred from all
pleasant sights and sounds, and cut off from all earthly hope. The phrase earthly hope means that
there is room for other kinds of hope, so (A) is incorrect. The author makes no reference to a
fear of the unknown, so (B) is incorrect. Life imprisonment is defined against capital punish-
ment, so (D) can be eliminated. Choice (C) best matches the language used in the text.
31. B Remember to read for the phrase in context and not just to leap to a conclusion based on your
prior knowledge. The passage says Yet even such a lot as this, because there is no one moment at
which the suffering is of terrifying intensity. From the context, this phrase refers to life imprison-
ment with hard labor, which can best be described as “a condition.” Choice (B) is correct.
32. B This question asks from whose perspective the article is written. The author references the re-
search of Sean O’Donnell, a biology professor at Drexel, throughout the piece, and discusses
O’Donnell’s findings at length. This perspective is best summarized by (B). The author himself
is not conducting this research, so (A) is incorrect. The author neither advocates for public un-
derstanding of wasps nor ascribes deep personal meaning to the passage’s subject. Choices (C)
and (D) are incorrect.
33. A The question asks for what Sean O’Donnell’s goal is in continuing his research. General ques-
tions such as this should be done after all of the specific questions. Also note that the follow-
ing question is a best evidence question, so this question and question 34 can be answered
in tandem. Look at the answers for question 34 first. Lines 27–31, 42–45, and 68–72 do not
support any of the answer choices from question 33. Lines 77–79 discuss O’Donnell’s future
research, which is to replicate the wasp research with termites and bees, which also offer a variety
of social complexity. This best matches (33A). Choice (33B) generalizes beyond invertebrates to
brain size in general, and (33C) and (33D) are not supported by any lines in question 34. The
correct answers are (33A) and (34D).
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34. D (See explanation above.)
35. C Remember to read for the phrase in context and not just to leap to a conclusion based on your
prior knowledge. The passage states that scientists have come up with an idea called the “social
brain hypothesis.” The passage then says Generally, it goes something like this: Social interac-
tion presents challenges that require a lot of brain power, as that interaction requires organisms to
navigate complicated territory, including avoiding conflict and building alliances. These lines do
not provide a mocking or jovial tone, so (B) and (D) can be eliminated. The idea had not been
previously explained, so (A) can be eliminated. The lines do explain a scientific concept with
straightforward language, so (C) is correct.
36. C Remember to read for the word in context and not just to leap to a conclusion based on your
prior knowledge. The passage states that Scientists believe the complexity of human societies
may be one of the reasons we have such large, developed brains. In context, the word complexity
refers to the nuanced sophistication of modern society, which best matches (C). Choice (B)
offers the opposite meaning, and there is no evidence for (A) or (D) in context.
37. A This paragraph expands the discussion of the social brain hypothesis: vertebrates that live in
societies have bigger brains. This best supports (A). The distinction between vertebrates and
invertebrates appears to be clearly established outside of this specific research and no inverte-
brate species are mentioned in this paragraph, eliminating (B). This paragraph is focused on
brain size rather than how vertebrates interact, so (C) can be eliminated. There is no indication
of differences in individual brain sizes based on intelligence, eliminating (D).
38. B The question asks what the author indicates about the wasp. General questions such as this
should be done after all of the specific questions. Also note that the following question is a
best evidence question, so this question and question 39 can be answered in tandem. Look at
the answers for question 39 first. Lines 14–18 are not about the wasp; eliminate (39A). Lines
32–34 discuss the various ways wasps live, which doesn’t support any of the answers in ques-
tion 38; eliminate (39B). Lines 58–59 indicate that insect societies, including wasps, consist of
cooperating close relatives with shared objectives. This supports (38B). Lines 60–64 indicate that
there is less social interaction in their societies, but (38C) and (38D) take this idea too far by
claiming that the society is simple, (38C), or does not require cooperation, (38D). Only (B) for
question 38 is supported by lines from question 39. The correct answers are (38B) and (39C).
39. C (See explanation above.)
40. B The graph shows the correlation between residual brain size in primates and the level of soci-
etal complexity. This relates most directly to the lines The more complex the organism’s society,
the bigger its brain regions for processing complex information will be, which is (B). The graph
does not compare insect societies and vertebrate societies, so the lines in (A) are not relevant.
The graph does not address wasp colonies, so (C) and (D) are also incorrect.
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41. D This question asks which statement is supported by the graph. The graph shows a direct cor-
relation between brain size and societal complexity, so (A) is incorrect. A harem is listed as
the type of society linked to the second largest residual brain, so it can be assumed that it is a
complex type of society. Choice (B) is incorrect. The bars show a clear difference between the
brain size of a solitary versus pair-bonded organism, so (C) is incorrect. The question tells you
that lemurs have a relatively large residual brain size compared to those of other animals. When
you look at the graph, the largest relative brain size occurs in multi-male groups, making (D)
the correct answer.
42. D The question asks why wetland mitigation is unsuccessful. General questions such as this
should be done after all of the specific questions. Also note that the following question is a best
evidence question, so this question and question 43 can be answered in tandem. Look at the
answers for question 43 first. Lines 1–6 do not support any of the answer choices from ques-
tion 42; eliminate (43A). Lines 11–15 support (A) from question 42; keep (43B). Lines 39–44
support (D) from question 42; keep (43C). Lines 44–52 do not support any choice from ques-
tion 42; (42C) says that banks are overly large and wasteful, which isn’t supported by these
lines, so eliminate (43D). Eliminate (42B) and (42C) because they are not supported by any
of the line references in question 43. Next, look for a reason to eliminate one of the remaining
pairs. Choice (42A) is not about wetland mitigation and therefore does not answer the ques-
tion; eliminate (42A) and its pair, (43B). The correct answers are (42D) and (43C).
43. C (See explanation above.)
44. B Remember to read for the phrase in context and not just to leap to a conclusion based on
your prior knowledge. The passage states Increasing population, development, farming, and
landowners’ rights have resulted in increasing amounts of our wetland resource being destroyed
and have increased the pressure on the wetlands that remain. Since many wetlands have been
destroyed, pressure refers to the strain put on the remaining wetlands to fulfill their ecological
function. Choice (B), demands, best matches this meaning.
45. D This question asks for the primary purpose of the second paragraph. The paragraph does not
argue against the efficacy of wetland mitigation projects or detail the mechanics by which
specific projects are accomplished, so (A) and (B) are incorrect. The paragraph lists the three
things on which wetland mitigation focuses, not on the three reasons it is necessary. Choice
(C) is incorrect. The second paragraph describes the focus and function of wetland mitigation,
as best matched by (D).
46. D The passage states that The historical flooding pattern of W29 Impaired Marsh illustrated the most
optimistic flooding regime that could have been expected in the absence of augmentation. These
lines suggest that flooding is usually more effective in the presence of augmentation, so (A) is
incorrect. The passage presents W29 Impaired Marsh as an example of non-augmented flood-
ing, not as the establishing event for a historical flood pattern, so (B) is incorrect. Although
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W29 Impaired Marsh suffered negative effects, it was not destroyed. Choice (C) is incorrect.
Choice (D) best matches the evidence provided in the text.
47. C Remember to read for the phrase in context and not just to leap to a conclusion based on
your prior knowledge. The passages states that The historical flooding pattern of W29 Impaired
Marsh illustrated the most optimistic flooding regime that could have been expected in the absence of
augmentation. In this context, regime refers to the status of the wetlands during the non-
augmented flooding. It does not refer to any manufactured establishment, organization, or
scheme, so (A), (B), and (D) can be eliminated. Choice (C) best matches the meaning in context.
48. A The paragraph states that without augmentation the wetlands would have lacked the soil mois-
ture conditions necessary for aquatic algae, wetland plants, and freshwater macroinvertebrates
to survive. These lines support (A) as the correct answer. Additionally, cypress tree mortality
would have been widespread in the absence of augmentation. Choice (B) states the opposite
and can be eliminated. The paragraph indicates that without augmentation the water table
would have been too deep for certain plants to survive. This suggests that (C) is incorrect. The
paragraph states that all wetlands experienced withdrawals, indicating that augmentation does
not force withdrawals. Choice (D) is incorrect.
49. B This question asks for the evidence you used to answer the previous question, so if you can’t
find lines to support your answer to question 45, take a moment to reassess. Only (B) supports
the idea that wetland augmentation helped prevent plants associated with dry land from devel-
oping within the wetland area.
50. A Passage 1 describes wetland mitigation and then lists several reasons as to why wetland mitiga-
tion might not be successful. Passage 2 uses the example of the non-augmented flood of the
W29 Impaired Marsh to indicate the benefits of augmentation, a type of wetland mitigation.
This relationship is best summarized by (A). Passage 1 does not describe wetland mitigation
in favorable terms, so (B) is incorrect. Passages 1 and 2 do not discuss the same research study,
so (C) can be eliminated. Passage 2 offers a practical, rather than a theoretical, approach to a
problem, and Passage 1 discusses the potential failure of that practical approach. Choice (D) is
incorrect.
51. B Passage 2 discusses a study in which augmented wetlands were shown to have particular benefits.
Choice (A) is therefore incorrect. However, while Passage 2 does see augmentation as beneficial,
it does not propose that it solves the problem of wetland deterioration. Choice (C) is incorrect.
Passage 1 is not discouraging people from saving the wetlands; it is merely questioning the
efficacy of a particular restorative strategy. Choice (D) is incorrect. Choice (B) is the correct
answer.
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52. A The correct lines need to refer to the importance of retaining certain wetland species. Choices (B),
(C), and (D) refer to the definition of wetland mitigation, different wetland types, and the mean-
ingfulness of wetland mitigation, respectively. Only (A) tells us that more than one-third of our
endangered species are associated with wetlands even though wetlands comprise less than five per-
cent of the landscape. It is the correct answer.
Section 2: Writing and Language
1. C When STOP or HALF-STOP punctuation is used in the answer choices, use the vertical line
test. The first idea (A new type…arenas) is complete, and the second part (they are…organism)
is also complete. Eliminate (A) and (B) since neither a comma by itself nor a FANBOYS by
itself can separate two complete ideas. Since they are is part of the underlined portion, (D) is
incorrect because a semicolon cannot be followed by an incomplete idea. HALF-STOP punc-
tuation can be followed by a complete or incomplete idea; therefore, (C) is the correct answer.
2. D This question tests concision. The non-underlined part of the sentence includes the word
“altered,” which is redundant with the word “changed” in (A), “different” in (B), and “has been
altered” in (C). The best and most concise answer is (D).
3. A The proposed addition is consistent with the information in the passage and should be added
for the reason stated in (A). The idea is further explaining ideas already presented in the pas-
sage, so eliminate (B). The addition does fit the structure of the paragraph, so eliminate (C).
The proposed addition is not redundant, so eliminate (D).
4. C Since the verbs are changing in the answer choices, check the subject to be sure the subject and
verb are consistent in number. Products is the subject, so the verb should be plural. Eliminate
(A) and (B), which both contain singular verbs. Using the verb phrase in (D) would make the
sentence incomplete. Only (C) has a subject and verb that are consistent in number and make
the sentence complete, so it is the correct answer.
5. D When the answers all say essentially the same thing, look for the shortest. In this case, that is
the single word harm that appears in (D). Choice (B) may say a similar thing, but it does so in
a less efficient way. Choices (A) and (C) do not work because they are not consistent with writ-
ten or spoken English expressions.
6. C The correct idiom when using the phrase not only is but also, making (C) the correct answer.
7. B The underlined portion is part of a list, so it should be consistent in structure with the other
items in the list: animal treatment and environmental stewardship. Because the items in the list
contain an adjective followed by a noun, eliminate (A) and (C) which do not match this pat-
tern. None of the other items in the list is preceded by a possessive pronoun, so eliminate (D).
The correct answer is (B).
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8. D Use POE. Sentence 3 should not be placed between sentences 2 and 4 because the general
confusion mentioned in sentence 4 should follow sentence 2 (labels are…misleading and
uninformative). Eliminate (A). Sentence 3 should not be placed between sentences 1 and 2
because those ideas are connected. Eliminate (B). Sentence 5 refers to these issues, issues that
are mentioned in sentence 4 (limited space and limited knowledge), so (C) is incorrect. Placing
sentence 3 after sentence 5 would conclude the ideas discussed in this paragraph and provide
the most clarity. Therefore, (D) is the correct answer.
9. A Notice the question and be sure to choose the answer that provides a specific detail that rein-
forces the main point of the previous sentence. The previous sentence states that most foods have
contained GMOs since the early 1990s. The only answer choice that specifically reinforces this
idea is (A).
10. B Whether is used to express a choice between alternatives—in this case, whether the bill is
passed or not. If is used to show that one thing depends on another. When is used to refer to a
time. Thus, the correct answer is (B).
11. B Use POE. In order to fulfill the writer’s the goal, the concluding sentence should restate the
main argument of the paragraph. The writer never discusses cheapness of food or argues that
people should look up how food is grown. Eliminate (A) and (D). The writer briefly mentions
in the third paragraph that labels, according to proponents of the bill, would provide impor-
tant information and allow people to choose products that align with their beliefs; however,
this idea is not the main argument of the last paragraph. Eliminate (C). Choice (B) restates
the author’s point that so many products already contain GMOs that people are not buying
products based on the information available (or lack thereof), but rather they’re buying what is
available to them. The correct answer is (B).
12. A Since all the phrases essentially mean the same thing, choose the one that is most concise and
is in keeping with the style and tone of the passage. Eliminate (C) and (D) because they are in-
formal in tone and are inconsistent with the style of the passage. Choice (B) is awkward when
inserted into the sentence and is not as concise as (A). The answer is therefore (A).
13. B Notice that the pronouns are changing in the answer choices. Since a possessive pronoun is
needed, (A) and (C) are incorrect. There refers to a location, and they’re is the contraction form
for they are. To see if the pronoun should be singular or plural, look at the non-underlined
portion. The sentence begins with Many businesses have been…. Therefore, a plural pronoun is
needed. Eliminate (D), and the correct answer is (B).
14. D Notice that the use of more versus most is changing in the answer choices. More is used when
comparing two things, while most is used when comparing more than two things. In the
context of the passage, there are many employee concerns, one of which the writer is about
to discuss, so eliminate (A) and (B). Since the underlined phrase needs to be incomplete, (C)
is incorrect because it is a complete idea. Choice (D) is consistent with the non-underlined
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portion (one of the most regularly dismissed) and makes the phrase incomplete by dropping the
subject, so it is the correct answer.
15. B The sentence in the question refers to a diversified workforce and why this has made the meta-
bolic equivalent measurement inaccurate. It also includes the transitional word however at the
beginning of the sentence, indicating a shift from the previous sentence. Since this informa-
tion provides an explanation as to why a measurement based on a 155-pound man is a flawed
approach to workplace temperature determinations, (B) is the answer. Choice (A) is wrong
because the new sentence doesn’t support the previous sentence, which has as much to do with
the average man becoming larger and heavier than in the 1930s as it has to do with women in
the workplace. Since this sentence directly connects to the last sentence of the paragraph, (C)
is not correct; this sentence would not be better placed elsewhere. And since this sentence is
aligned with the overall topic of temperature in the workplace, (D) is also incorrect.
16. C When STOP punctuation is used in the answer choices, use the vertical line test. The first idea
(While the human…sitting) is incomplete, so eliminate (A), (B), and (D). In (C), the idea after
the comma is complete. Since a comma can separate an incomplete and a complete idea, (C) is
the correct answer.
17. A Notice the question and be sure to choose the answer that will effectively introduce the writ-
er’s discussion of temperature and worker productivity. An introductory sentence is necessary
to maintain the flow between the previous paragraph and this paragraph, so eliminate (D).
Choice (B) doesn’t offer a smooth or effective transition because the writer never previously
or later refers to the “many people” who have asked this question. Choice (A) is more precise
than (C). Choice (A) clearly states the connection between temperature, the body, and worker
productivity that seamlessly connects the discussion of temperature and the body in the previ-
ous paragraph with the discussion of its effect on workplace productivity in this paragraph.
18. B When STOP or HALF-STOP punctuation is used in the answer choices, use the vertical line
test. The first idea (The longer…temperatures) is incomplete, so eliminate (C) and (D), which
both include STOP punctuation. Because a colon is a HALF-STOP, it must be preceded by a
complete idea, so eliminate (A). In (B), the idea after the comma is complete. Since a comma
can separate an incomplete and a complete idea, (B) is the correct answer.
19. B When the verbs are changing in the answer choices, check the subject to be sure the verb and
subject are consistent. The subject in this sentence is influences, so the verb should be plural.
Eliminate (C) and (D). The original sentence contains a diction error. Affect used as a noun
means an emotion or desire. Effect used as a noun means a result of something. In this context,
the result of the influences on the room temperature is a large amount of cost savings for the
company. Therefore, (B) is correct.
20. A Use POE and be sure the choice is consistent with the graph provided. Choice (A) is supported
by the data. Space heating, ventilation, and cooling account for 28% of electricity consumed
1 4 | Practice Test 7: Answers and Explanations
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by office buildings, while space heating accounts for 86% of the natural gas consumed by
office buildings. Eliminate (B) because it states the opposite of (A). The percentages used for
HVAC in (C) are not supported by either pie graph. Finally, (D) is incorrect since HVAC does
not account for the majority of the electricity consumed by office buildings. Choice (A) is the
correct answer.
21. D Read the chart as literally as possible. The questions that deal with visual representations of
data are typically fairly straightforward. Choice (A) can be eliminated because lighting makes
up 39% of electrical usage to cooling’s 14%. Choice (B) can be eliminated because office
equipment uses very little electricity and an unidentified or very small amount of natural gas.
Choice (C) can be eliminated because cooling is specifically identified only in terms of its
electricity use—its natural-gas use is not specified, so we can’t make any assumptions about it.
Only (D) remains, as it correctly states that cooling (14%) uses a larger share of electricity than
computers (10%).
22. D Notice the question and be sure to choose the answer that addresses the future of efforts to decrease
workplace expenditures and agrees with the main idea of the passage. Choices (B) and (C) do not
offer conclusions that agree with the main idea of the passage. Choice (A) does not address
efforts that would lead to a decrease in workplace expenditures because lowering temperatures
is more costly. Therefore, (D) is the correct answer since it fulfills both objectives of the writer.
23. D Notice that the pronouns are changing in the answer choices. Since a possessive pronoun is not
needed, (B) and (C) are incorrect. To see if the pronoun and verb should be singular or plural,
look at the non-underlined portion. The sentence begins with Google is taking…. In order for
the second part of the sentence to be consistent with the first, the correct answer is (D).
24. B Since all the answer choices mean essentially the same thing, choose the most concise option
that makes sense in context. The date 1900 has the same meaning as at the beginning (or turn)
of the last century, so the additional phrases in (A), (C), and (D) are redundant. The correct and
most concise answer is (B).
25. C Notice the question: it asks for the most specific information on the safety of elevators. Only
(C) makes reference to what made the first safety-elevator safe—it wouldn’t fall in the event of a
broken cable. While the other choices could be true, they are not consistent with the question
being asked. The correct answer is (C).
26. A Since there is a colon in the underlined portion, check to see if the first part of the sentence is a
complete idea. In this case, the first part (These were…functions) is complete, so a colon can be
used. The second part of the sentence (these operators…hand) is also complete. Therefore, elim-
inate (B) and (D) because neither a comma by itself nor a FANBOYS by itself can separate two
complete ideas. Choice (C) is incorrect because it contains no punctuation, leaving (A) as the
correct answer.
|Practice Test 7: Answers and Explanations 1 5
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27. A Notice that one of the answer choices is to DELETE the underlined portion. Check to see if
a transition word is needed at the beginning of the sentence. If the sentence begins without
a transition word, then there would be two complete ideas separated by a comma. Eliminate
(D). Next, pay attention to the type of transition words used. Choices (B) and (C) are same
direction transition words, while (A) indicates a contrast. A contrast is needed to show that
even though success was expected, the public did not embrace the idea of the new technology.
Therefore, (A) is the correct answer.
28. B The question specifically asks for the most effective way to set up the paragraph. The second
sentence begins with That year…, so the paragraph should begin with a reference to the year
that is discussed. Only (B) directly states in what year the strike occurred and is the correct
answer.
29. C As written, the sentence is awkward. The phrase upwards to is not idiomatically correct. Choice
(B) is also awkward when inserted into the sentence, so (A) and (B) can be eliminated. The
remaining two choices are synonymous, so choose the most concise option, which is (C).
30. B Notice the question: it asks for an additional example to emphasize the importance of lessen-
ing public fear toward automated elevators. Choice (B) provides a supporting example of how
people were able to test automated elevators in a safe environment (at state fairs, away from tall
buildings) in order to become more comfortable using them. The other answer choices do not
provide examples, or they introduce information that is off topic. Therefore, (B) is the correct
answer.
31. C Since apostrophes appear in the answer choices, check to see if the word industry should be
possessive. The experience belongs to the elevator industry, so an apostrophe is needed. Elimi-
nate (A) and (D). The industry is singular, so (B) is incorrect. Thus, (C) is the correct answer.
32. A The previous sentence states that Google is applying the lessons of history in a few creative
ways. This sentence then goes on to give some examples of those creative ways. As such, For
example, (A), provides the most suitable transition between the sentences. Choice (B) suggests
a contrast where one does not belong. Choice (C) inserts the ambiguous pronoun that, which
does not have a clear role within the sentence. Choice (D) uses the word surprisingly, but noth-
ing in what follows is presented as particularly surprising.
33. A Read the question carefully. The writer wants something that will conclude the paragraph
while emphasizing the fact that skepticism continues to exist. Choice (A) is the only one of the
choices that addresses this skepticism among users. Choices (B), (C), and (D) do not empha-
size the fact that skepticism continues to exist. Therefore, (A) is the answer because it fulfills
the goal stated in the question.
34. B Notice that the pronouns are changing in the answer choices. Since a possessive pronoun is
needed, (C) is incorrect. The pronoun should be consistent in number with the noun it refers
to, so (A) is incorrect because Congus magus is a singular noun. The use of his would not be
1 6 | Practice Test 7: Answers and Explanations
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inappropriate here, since the writer is discussing snails as a species or group. The correct answer
is (B).
35. A The underlined portion should be consistent with the non-underlined portion. Check to see
which transition would be appropriate in context. Choices (B), (C), and (D) all contain same
direction transition words. However, the sentence is setting up a contrast—this species of snail
is very interesting, but there’s one particular aspect of it that is very interesting to humans.
Therefore, (A) is the correct answer because a transition word that sets up a contrast (while) is
needed.
36. B Since the transition word is changing in the answer choices, check to see which one is consis-
tent with the sentence as a whole. A contrast is needed to show the opposition between lethal
and beneficial peptides. The only answer choice that contains a word that would set up a con-
trast is (B).
37. C When a pronoun is underlined, remember to check for precision. The use pronouns in (A) and
(D) would not be as precise as the nouns used in (B) or (C), so eliminate (A) and (D). Between
(B) and (C), choose the more concise option. Since the previous sentence already stated that
ziconotide is a synthetic chemical, the answer is (C).
38. D The underlined portion is part of a list, so it should be consistent in structure with the other
items in the list: brain, heart, nervous system, and bone. Eliminate (A) because of the article the
in front of nervous system. The remaining answer choices alter the comma placement. Nervous
system is one item of the list and should not be separated by a comma, so (B) and (C) are incor-
rect. Therefore, (D) is the correct answer.
39. A Since all the answer choices mean essentially the same thing, choose the most concise one that
makes sense in context. Choice (D) is not consistent in tone with the rest of the passage, and
(B) and (C) are wordier than (A). The correct and most concise answer is therefore (A).
40. C Since the transition word is changing in the answer choices, check to see which transition
would be appropriate in context. Choices (A), (B), and (D) all contain same direction transi-
tion words. In context, the writer has indicated that though the painkiller is very effective, it
has not gained the same widespread use as other (and less potent) painkillers. Therefore, a
contrast word is needed, making (C) the correct answer.
41. B Since the verbs are changing in the answer choices, check for consistency with the other verbs
in the sentence. The main verb of the sentence is in present tense (is); therefore, eliminate
(C), which is in the past tense. Also, since the word to precedes the verb, the infinitive form is
needed (inject). The answer is therefore (B).
42. C The sentence should not be deleted, so eliminate (A) and (B)—the information is relevant and
is not previously stated. The sentence does not give an example of a blood-brain barrier but
rather explains what a blood-brain barrier is. Thus, the correct answer is (C).
|Practice Test 7: Answers and Explanations 17
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43. D In order to find the most logical placement for the added sentence, check to see what this car-
rier refers back to. The carrier is referring to what the “Trojan Horse strategy” is attempting to
accomplish—creating a container constructed from viral proteins that can transport the Prialt
across the blood-brain barrier. Logically, the added sentence should follow sentence 4, so this
carrier can refer back to the container constructed from viral proteins. The correct answer is (D).
44. A The question is testing the difference between which word is appropriate (resolution versus solution)
and which verb is appropriate (could versus would). In this context, the researchers are trying
to develop a solution in order to administer Prialt in a less painful way, so eliminate (B) and
(D). In order to choose the appropriate verb, the correct choice will be consistent with the
other verbs. In the following sentence, could is used, so the correct answer is (A).
Section 3: Math (No Calculator)
1. C Start by isolating the x term in the equation. Subtract 3 from both sides to get 14 = 8x. Now,
you want to find 4x + 9, so instead of solving for x, divide by 2 to solve for 4x: 7 = 4x. Add 9 to
both sides to get 16 = 4x + 9, which is (C).
2. B Plug In! Start with h = 2. One hour after sunrise, the temperature will equal 5(2) + 61.4 =
10 + 61.4 = 71.4. One hour later, h = 3, so the temperature will be 5(3) + 61.4 = 15 + 61.4 =
76.4. The temperature increased 76.4 – 71.4 = 5 degrees in one hour, which matches (B).
3. D Start by Reading the Full Question: you want to know what “4” represents in the model. Next,
label what you know: H is the number of houses left, and t is the number of hours worked.
Next, try POE. “4” is associated with time; (C) doesn’t have anything to do with time, so
eliminate it. Try Plugging In. Make t = 2, so H = 35 – 4(2) = 35 – 8 = 27, so after 2 hours, Lee
has 27 houses left to inspect. Choice (A) isn’t fitting in; it’s going to take longer than 4 hours
to finish all the houses if he still has 27 left after 2 hours, so eliminate (A). Choice (B) doesn’t
make sense, as Lee has already inspected 8 houses, not 4, so eliminate (B) and choose (D).
4. C There are a couple of approaches that work here. One is to Plug In. Make x = 2. The problem
becomes y = 4(3(2) – 1)(5(2) – 1) = 4(5)(9) = 180. This is your target; circle it. Make x = 2 in
each answer choice and eliminate any choice that doesn’t equal 180. The only choice that
works is (C).
Alternatively, you can FOIL the right side of the equation: y = 4(15x2 – 3x – 5x + 1) =
4(15x2 – 8x + 1) = 60x2 – 32x + 4, which is (C).
5. B Start by cross-multiplying: 7x = 2(2x – 30) . Distribute the 2 on the right side of the equation:
7x = 4x – 60. Subtract 4x from both sides: 3x = −60. Divide both sides by 3: x = −20. Be care-
xx
ful! The question is asking for 2 , so you need to divide both sides by 2: 2 = −10, which is (B).
1 8 | Practice Test 7: Answers and Explanations
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6. D You could Plug In the Answers on this question, but the answer choices are not great to plug
in, so solve the question algebraically instead. Start by multiplying both sides by y – 7 to clear
the fraction: 4(y – 7) = y + 7 . Distribute the 4 on the left side of the equation: 4y – 28 = y + 7.
Subtract y from both sides: 3y – 28 = 7. Add 28 to both sides: 3y = 35. Finally, divide both sides
by 3 to find that y = 35 , which is (D).
3
7. A Find the slope-intercept forms of the equations of the two lines, y = mx + b, where m stands
for slope and b stands for the y-intercept. First, use the slope formula to find the slope of line
l: = y2 − y1 : 5−3 = 2. To find the y-intercept, plug in a point for the x- and y-values. Using
x2 − x1 2 −1
(1, 3), you get 3 = 2(1) + b, or 3 = 2 + b. Subtract 2 from both sides to find b = 1, so the equation
of line l is y = 2x + 1. You are already given the slope of line m, so you can do the same with the
point (1, 4) to find b: 4 = 1 + b. Subtract 1 from both sides and b = 3, so the equation of line
m is y = x + 3. At the point of intersection, the x- and y-values are equal, so you can set the x
portions of the equations equal to each other: 2x + 1 = x + 3. Subtract x from both sides to get
x + 1 = 3. Subtract 1 from both sides to find x = 2. To find the y-value at the point of intersec-
tion, plug x = 2 into one of the original equations: y = 2(2) + 1, so y = 5. Therefore, (a, b) is
(2, 5). Finally, the question wants a – b, so 2 – 5 = −3, which is (A).
8. D When two graphs intersect, the x-values are equal and the y-values are equal. The y-values of the
points of intersection are 36 (because all points on the line y = 36 have a y-value of 36). Make
y = 36 in the equation of the parabola and solve for the x-values of the points of intersection. If
36 = (x + 4)2, you can solve by first taking the square root of both sides (remember that you’ll
get positive AND negative values on the left side!): ±6 = x + 4. It will be easier to break this
into two equations: 6 = x + 4 and −6 = x + 4. Subtract 4 from both sides of both equations to
get 2 = x and −10 = x. That gives you two points: (2, 36) and (−10, 36). You don’t need the dis-
tance formula because the y-values are equal; simply take the positive difference of the x-values:
2 – (−10) = 12, (D).
9. C If f(2) = 6, then when x = 2, the function is equal to 6. Put these values into the equation and
solve for c: 6 = −2(22) + c; 6 = −8 + c; c = 14. Then, make x = −2 with the known value of c = 14:
f(−2) = –2(–2)2 + 14 = −8 + 14 = 6, which is (C).
10. D Apply the geometry basic approach, but use some flexibility and Plugging In. Because there is
already a diagram, start with labeling what you can. There are no values given in the question,
but you do have a relationship among the angles with measures a°, b°, c°, and d°. Because the
|Practice Test 7: Answers and Explanations 1 9
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angles with measures a° and d° are opposite angles, they must be equal; make a = d = 50 and label
it in the diagram. Plugging those values into the equation gives you 50 + c = b + 50. If you sub-
tract 50 from both sides, you get c = b. Angles with measures b° and c° also complete the straight
angle with the angle with measure a°. Therefore, a + b + c = 180, and because a = 50 and b = c,
50 + b + b = 180; 50 + 2b = 180; 2b = 130; b = 65. Label b = 65 and c = 65. Because the angle
with measure e° is opposite the angle with measure b°, the angle with measure e° must also
equal 65°. Because the angle with measure c is opposite the angle with measure f, f must equal
65°. Now that you have all angles indicated, you can go to the answers. You’re looking for the
choice that could be false, so eliminate anything that must be true. Both b and c are 65°, so
eliminate (A). The same is true for e° and f °; eliminate (B). Angles with measures c° and f ° are
also both 65°, so eliminate (C) and choose (D).
11. A This problem is a bit on the wordy side, so be sure to start by Reading the Full Question.
The question wants the average price of a cup of coffee when the two prices are equal; in
other words, what’s the value of T when T = M? To find this, set the two right sides of the
equations equal to each other to find y. Then plug that value back in to either equation to find
T. First, setting the two equations equal to each other yields 1.35 + 0.75y = 2.25 + 0.60y. You
want to isolate y, so start by subtracting 0.60y from both sides: 1.35 + 0.15y = 2.25. Subtract
1.35 from both sides: 0.15y = 0.90. Now, dividing with decimals can be tricky, so multiply
both sides by 100 to get rid of the decimals: 15y = 90. Divide both sides by 90 and you get
y = 6. The question wants the value of T (or M, as they’re equal), so you need to plug y = 6
back into one of the equations. It’s probably easier to use the T equation, based on what you’re
multiplying, so make y = 6 in the second equation: T = 2.25 + 0.60(6). Multiply 0.60 by 6:
T = 2.25 + 3.60. Add, and you get T = 5.85, which is (A).
12. D There are a few ways to find the vertex of this quadratic. In this case, the equation is given in
its factored form; this makes it easier to find the zeros of the quadratic. The x-value of the ver-
tex of a quadratic is the midpoint of its zeros (or any two points on the quadratic which share a
y-value); from there, you can find the y-value. First, to find the zeros, set y = 0: 0 = a(x + 6)(x – 2).
The question indicates that a is nonzero, so either (x + 6) or (x – 2) is equal to zero, which
means x = −6 or 2. Find the midpoint by finding the average of −6 and 2: −6 + 2 = −2 . This is
2
the x-value of the vertex. To find k (the y-value at the vertex), plug in x = −2 into the equation
and solve: y = a(−2 + 6)(−2 – 2) = a(4)(−4) = −16a, which matches (D).
13. B A line passing through the origin has a y-intercept of 0, so the slope-intercept form of the equa-
tion of this line is y = 6x. Plug in the x and the y from each answer choice until one works in
the equation. Remember that the x value comes first in the (x, y) pair. The only choice that
works is (B).
2 0 | Practice Test 7: Answers and Explanations
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14. D While you could plug in on this question, it is easier to solve this problem algebraically. Use the
bow tie to add the two fractions in the denominator to get a + 4 1 a + 5 = 1 .
+ 2a + 9
(a + 5)(a + 4) a2 + 9a + 20
When dividing fractions, remember to flip the second fraction and multiply to get
1× a2 + 9a + 20 = a2 + 9a + 20 .
2a + 9 2a + 9
15. A All of the answer choices resemble the quadratic formula (the square roots and the ± signs help
you recognize this). Start by putting the original equation into the ax2 + bx + c = 0 form of the
equation to get x2 + q x + 1 r = 0 . This means that a = 1, b = q 1 r = 1 . Plug these
3 2 3 , and c = 2 2
values into the quadratic formula, −b ± b2 − 4ac − q ± q 2 − 4 (1) r
2a 3 3 2
, to get . Simplify
2 (1)
− q ± q2 − 2r − q q2 − 2r
3 3 9
this expression to get 9 . Next, split the fraction into two to get ± .
2 2 2
Use Bite-Sized Pieces to solve. The first fraction becomes − q y 2 = − q u 1 = − q . Eliminate
3 3 2 6
(C) and (D). Next, determine a way to get rid of the fraction in the numerator of the second
fraction. To do so, multiply 2r by 9 to get q2 − 2r 9 = q2 − 18r . Factor out a 1 to
9 9 9 9 9 9
( )get 1 q2 1 q2 −18r . Now it’s clear that the radical in the numerator should be
9 − 18r = 3
q2 −18r , which means the correct answer is (A).
16. 5 Isolate x by first adding 25 to both sides of the equation to get x2 = 25. Next, take the square
root of both sides to get x = ± 5. Because the question indicates that x > 0, x must equal the
positive value 5.
|Practice Test 7: Answers and Explanations 2 1
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17. 5 or .384 or .385
13
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18. 130 Start by labeling the angle with measure c as 65. Because two sides of the triangle are equal,
you also know that the other angle adjacent to line m is also equal to 65. Because these angles
are part of a triangle, and all triangles have 180°, the measure of the remaining angle is 180 –
65 – 65 = 50; label that as well. To find b, use the equation given; if c = 65, then 180 – 2(65) = b,
so 180 – 130 = 50 = b; label the angle with measure b as 50. Finally, to find a, you know that
the full circle around the middle of the two triangles is 360°, so 50 + 50 + a + a = 360, or 100 +
2a = 360. Subtract 100 from both sides: 2a = 260. Divide both sides by 2, and you get a = 130.
19. 2 To find a, you want to find a way to clear the b terms from the system of equations. The coef-
ficients on the b terms are 3 and 1, so you can multiply the second equation by −3 and add the
equations together. Multiplying the second equation by −3 gives you −3a – 3b = 6. Stack the
equations and add:
a + 3b = −10
+ (−3a – 3b = 6)
−2a = −4
Divide both sides by −2 to find that a = 2.
20.
17 or 4.25
4
There are many ways to isolate y in this question. One of the more straightforward ways is to
actually find x first by clearing the y-terms. The coefficients on y are 8 and −4, so if you multi-
ply the second equation by 2 and add the two equations together, the y-terms cancel. Multiply-
ing the second equation by 2 gives you 6x – 8y = 86; stack this with the first equation and add:
2x + 8y = 74
+ 6x – 8y = 86
8x = 160
Divide both sides by 8 to find that x = 20. Now, go back to one of the original equations to
find y. In the first equation, make x = 20: 2(20) + 8y = 74; 40 + 8y = 74. Isolate y by first sub-
tracting 40 from both sides: 8y = 34. Next, divide both sides by 8: y = 34 , or 4.25. The frac-
8
2 2 | Practice Test 7: Answers and Explanations
SAT Premium Prep
tion will fit into the Grid-In boxes, so you don’t need to simplify.
Section 4: Math (Calculator)
1. C If Casey stopped for breakfast, then she isn’t moving relative to her home. Therefore, you want
the point on the graph where the y-value (distance from home) isn’t changing for 45 minutes.
That can be found between the hours of 10 a.m. and 11 a.m. It looks as though she stopped
somewhere shortly after 10 a.m., making (C) the correct answer.
2. B As with any Math question with figures, start by reading the axes. The vertical axis is “Sales
(thousands of homes)” and the horizontal axis is “Years since 2002.” Next, Read the Full Ques-
tion. Because the question wants the trend in home sales from 2002 through 2014, and the ver-
tical axis is years since 2002, the answer should describe the behavior of the entire graph. This
graph increases until 5 years after 2002 (which would be 2002 + 5 = 2007) and then decreases.
This matches (B).
3. A Because both pairs of lines are parallel, all big angles are equal, all small angles are equal, and
any big angle plus any small angle equals 180°. Angle 1 is a big angle, and angle 2 is a small
angle, so ∠1 + ∠2 = 180°. If angle 1 is 135°, then 135° + ∠2 = 180°. Subtract 135 from both
sides to find that ∠2 = 45°, (A).
4. B Use values from the chart to see which equation works. According to the chart, when x = 2,
g(x) = 4. So, in the answers, plug in 2 for x to see which answer returns a value of 4. Choice (A)
becomes 2(2) – 1 = 3. Eliminate (A). Choice (B) becomes 3(2) – 2 = 4. Keep (B), but check the
remaining answers just in case. Choice (C) becomes 4(2) – 3 = 5. Eliminate (C). Choice (D)
becomes 5(2) – 4 = 6. Eliminate (D).
5. A The question might be a little messy, but the answer choices help you figure out that you want
to solve the equation for d. Start by dividing both sides by 4πb, giving you L = d 2 . Take
4πb
L
the square root of both sides to get d = 4πb , which is (A).
6. D A positive association between two variables means that as one variable increases, the other vari-
able also increases. Choice (B) has w decreasing as n increases, so eliminate it. Additionally, (C)
has w increase and then decrease, rather than just increase; eliminate (C). For a weak positive
association, w should increase slowly as n increases; (A) has w increasing rapidly when compared
to (D). Choose (D).
7. C Plug In the Answers! The question wants the number of games Salazar played. Start with (B).
If Salazar played 27 games, and he played 13 more games than Perry, then Perry played
27 – 13 = 14 games, giving the two of them a total of 27 + 14 = 41 games. However, they
played a total of 53 games, which means you need a higher number; eliminate (A) and (B).
|Practice Test 7: Answers and Explanations 2 3
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Try (C). If Salazar played 33 games, then Perry played 33 – 13 = 20 games, giving a total of
33 + 20 = 53 games between the two of them, which is what you want. Choose (C).
8. B Whenever you have a graph question, always consider the axes. Here, the question wants you
to label the horizontal (x-) axis, which has only numbers so far. The question stem tells you the
total population is 3,489,000,000, so if you determine the total of the six countries as given in
the graph, you can determine the label. Adding up the six countries gives you about 3,500 as a
population. 3,489,000,000 is about a million times bigger than 3,500 (3,489,000,000 ÷ 3,500
≈ 1,000,000), so the label on the horizontal axis should be in millions of people, which is (B).
9. A Sketch a graph. Quadrant III is the lower-left quadrant of the xy plane, so draw a line that goes
through the other three quadrants but avoids Quadrant III:
y
II I
x
III IV l
To do so, you need to make line l have a negative slope, so m must be negative. This matches
(A).
10. A Start by labeling what you know: D is the dollars remaining, and x is the number of days since
payday. Because 165.29 is multiplied by x it is something that happens each day after payday.
Use POE. Choice (B) is about payday, not something that happens every day after payday.
Eliminate (B). Choice (D) is a fixed number and therefore not something that happens every
day after payday, so eliminate (D). Given that D is the amount of dollars remaining in Kabir’s
bank account x days after payday, Kabir must have had 2,314.05 in his account on payday.
Therefore, the difference between the amount of money in the Kabir’s account at payday and
the amount of money in his account must be 2,314.05 – D. Eliminate (C).
11. D With functions, remember to follow PEMDAS, especially working from inside to outside. To
find the value of g(f(6)), start with the innermost pair of parentheses. The question tells you
2 4 | Practice Test 7: Answers and Explanations
SAT Premium Prep
that f(6) = 5, so you can substitute 5 for f(6): g(f(6)) = g(5). The question then tells you that
g(5) = 7, so g(f(6)) = g(5) = 7, which is (D).
12. A Use the equation f = μN and the chart to determine the friction. The value of μ will be the co-
efficient between two pieces of wood, which is 0.28, and the value of N is the force pressing the
two pieces of wood together, 30 Newtons. Plugging these values into the equation gives you
f = (0.28)(30) = 8.4, which is (A).
13. B N is the force pressing the bodies together in newtons, and according to the question the force
pressing two stacked objects together is equal to the weight of the object on top. Begin by finding
the weight of the piece of wood. The given equation for friction is f = μN. The value of f is 22.5,
and from the chart the coefficient of friction between wood and stone, μ, is 0.30. Plug these val-
ues into the equation: 22.5 = 0.30N. Divide both sides by 0.30 to find the value of N: 22.5 = 75 .
0.30
Since the piece of wood will be placed on another surface, its weight of 75 N
remains the force pressing the two bodies together. To determine the new sur-
face, find the new coefficient of friction by using the value of N, 75, and the new val-
ue of friction, 46.5: 46.5 = μ(75). Divide both sides by 75 to isolate μ: 46.5 = 0.62 .
75
The chart indicates that the coefficient of friction equals 0.62 between wood and concrete, so
the new surface must be concrete, which is (B).
14. A Work this problem in Bite-Sized Pieces. You want to find the difference between compounding
monthly and compounding quarterly. The question indicates that n is the number of times per
year interest is compounded. If the interest is compounded monthly, then that would be 12
times per year, so n = 12. In the expression, that is 1 + 0.05 12 – 1. If the interest is compounded
12
0.05 4
quarterly, then that would be 4 times a year, so n = 4 and the expression is 1 + 4 – 1.
The question wants the difference between these two amounts, so you would subtract:
1 + 0.05 12 −1 − 1 + 0.05 4 −1 , which matches (A).
12 4
15. B The P-intercept will be when items sold, s, equals 0. When s = 0, P = 10, which means Jack’s
pay when he sells no items is 1,000 dollars (remember to check your units on each axis). Be-
|Practice Test 7: Answers and Explanations 2 5
SAT Premium Prep
cause this is Jack’s pay when he sells no items, any answer choice that refers to items doesn’t fit;
the only choice that does fit is (B).
16. D To find the expression that describes the graph, plug in a point on the graph. When
s = 10, P = 15. Plug these values into each choice and eliminate what is not true; the only
choice that is true with those values is (D).
17. C Plug in! Make w = 2. If the car costs $25.50 per day, and 2 weeks is 14 days, then the total cost
would be 25.50 × 14 = $357.00. This is your target; circle it. Make w = 2 in each answer choice
and eliminate any answer that doesn’t equal $357.00. Only (C) works.
18. D When confronted with a bunch of text in a Math section, start with the question first. The ques-
tion asks for the best conclusion “based on the design and results of the research.” So determine
the important facts about the design and results of the research and underline them. There was
a “wide range of vehicle makes, models, and model years” and “400 vehicles were randomly
selected.” Which vehicle received which oil was “random,” and the vehicles that receive oil E
had “substantial improvements in gas mileage” compared to the other group. Now, work POE
in the answer choices. You don’t know about other available engine oils, so you cannot claim
that E is better than “any other available engine oil”; eliminate (A). Choice (B) seems to fit the
facts, so keep it. Choice (C) is extreme; even though there was a random sampling of vehicles,
you don’t know about “any vehicle” (“any” implies “any and all”—every single vehicle without
exception), whereas (B) doesn’t have this issue. Eliminate (C). Choice (D) is similar to (B).
Comparing the two choices, (B) indicates that oil E was the “cause” of the improvement in the
gas mileage, but (D) says only that it is “likely to improve” gas mileage. Choice (D) is a safer
conclusion than (B) because it makes a less strong, less sweeping conclusion, so the best answer
is (D).
19. A The place where h(x) is at its maximum is when the y-value of the graph is at its highest. The
graph’s y-value is highest at (1, 2). (Be careful: the origin is NOT in the middle of the grid!)
Therefore, the x-value is 1, which is (A).
20. B The median household income represents the middle income if all incomes were listed consec-
utively. The mean household income is the average (total income divided by number of people).
For the mean to be higher than the median, there must be some values above the median (to
“pull” the mean above the median). In this case, that means there needs to be some incomes
greater than the rest to “pull” the mean above the median; this matches (B).
21. D Be sure to start by Reading the Full Question! You are given 2x – 3, and you want 2x + 3. To
get from 2x – 3 to 2x + 3, you would add 6, so add 6 to both sides of the inequality to get
2x + 3 ≤ 11. The greatest value of 2x + 3 would therefore be 11, (D).
22. A This question may look scary, but the answers give you a hint: you want to solve for ε0. Start by
2 6 | Practice Test 7: Answers and Explanations
SAT Premium Prep
getting ε0 out of the denominator by multiplying both sides by ε0: Eε0 = q . Divide both
4πR 2
q
sides by E and you get ε0 = 4πR 2E , which matches (A).
23. B Distance in the equation is given by R. If the electric field strength at point x is Ex and
1
the electric field strength at point y is Ey, then Ex = 25 Ey. Make Rx and Ry the distances
at points x and y, respectively, and substitute the equations for the electric field strengths:
q 1 q 4πε0
25 q
( )4πε0 (Rx )2 = 4πε 0 R 2 . Multiply both sides by to clear these elements from
of with
( )both sides y 1 1 1
25 Ry
the equation, leaving you (Rx )2 = 2 . Cross-multiply to get
25(Ry )2 = (Rx )2. Take the square root of both sides to get 5Ry = Rx. This means x must be 5
times further than y, which is (B).
24. C Work the problem in Bite-Sized Pieces. The standard form of the equation of a circle is
(x – h)2 + (y – k)2 = r2, where (h, k) is the center of the circle and r is the radius. If the center of the
circle is at (5, 0), then the left side of the equation should be (x – 5)2 + (y – 0)2, which is the same as
(x – 5)2 + y2. This must be part of the answer; eliminate (B) and (D). Next, you need to find the
radius. If 6, 12 is on the circle, then the distance from (5, 0) to 6, 152 will be the radius. Use
5
(6 − 5)2 + 152 − 02 = (1)2 12 2 144 169 13
5 25 25 5
the distance formula: d = + = 1 + = = .
But be careful! The standard form of the equation is equal to r2, not r, so the right side of the
13 2 169
5 25
equation should be , or , which gives you (C).
25. D Start by using Process of Elimination. The question wants the grams of methyl alcohol of solu-
tion T and solution S was 25% less than solution T, which means if solution S had 120 grams,
solution T must have more than 120 grams; eliminate (A) and (B). Next, Plug In the Answers.
|Practice Test 7: Answers and Explanations 2 7
SAT Premium Prep
Between (C) and (D), it will be easier to work with (D) because 160 is an easier number. The
question is asking for grams of methyl alcohol in solution T, so if solution T has 160 grams,
and solution S is 25% less, then solution S must be 160 – (0.25)(160) = 120 grams. This fits the
information in the question; choose (D).
26. C There are a lot of words here, so start by Reading the Full Question. The question wants the
statement that correctly compares the average rates of infection for the two populations of
trees. According to the graph, at first grapefruit increases faster than orange, but at the end,
orange has increased its rate to catch up to grapefruit. Eliminate (A) and (B) because both
indicate that the difference in the rates was constant, which contradicts one getting ahead and
then the other catching up. Choice (C) says that grapefruit was faster first, so keep it. Choice
(D) says that orange was faster first, which contradicts what the graph shows, so eliminate (D)
and choose (C).
27. C There’s a lot going on here, but the answer choices give you a clue: you want to solve the equa-
tion for R. Start by clearing the fraction by multiplying both sides by 1 + R : I 1 + R = PT
Divide both sides by I: 1+ R = PT . Clear the radical by squaring both sides: 1+ R = PT 2 .
I I
PT 2
Subtract 1 from both sides to get R = I −1, which is (C).
28. A Draw the lines into the given xy-plane. Both inequalities are written in slope-intercept form
y = mx + b, where m is the slope and b is the y-intercept. The first line has a slope of 1 and a
2
y-intercept of −5. Because y is greater than or equal to the other side of the inequality, the line
is solid, and all of the y-values above the line are shaded. The second line has a slope of 3 and a
y-intercept of −2. Because of the less than sign, the second line is a dotted line, and the portion
under the line is shaded. Your drawing should look like this:
2 8 | Practice Test 7: Answers and Explanations
SAT Premium Prep
y y < 3x − 2
II I
x
III IV
y≥ x −5
2
The only quadrant that has no portion of it shaded is Quadrant II, (A).
29. B By telling you that f(−5) = 3, the problem is telling you that when x = −5, the function (y) is
equal to 3. Choices (A), (C), and (D) all talk about the factors of the polynomial; factors are
when the function is equal to 0. You do not know when the function is equal to 0, so you can-
not know about any of the factors of f(x); eliminate (A), (C), and (D) and choose (B). (Note:
The Remainder Theorem states that the remainder when function f is divided by the binomial
(x – a) is equal to f(a); (B) essentially states this theorem as the answer.)
30. B Plug In the Answers to solve this question. First, solve for y: 2y = 10, which means y = 5. Next,
plug in 5 for y and the values for c and d given in the answers into the first equation to see if the
values work. Choice (A) gives you 5 = –6x2 + 6. Solve for x to get –1 = – 6x2, 1 = x2, and
6
1
± 6 = x. This is a real solution, so eliminate (A). Choice (B) gives you 5 = –5x2 + 4. Solve
for x to get 1 = – 5x2, – 1 = x2, and ± − 1 . Since the value of the square root of a negative
5 5
number is imaginary, these values for c and d will have no real solution, and the answer is (B).
31. 5, 6, or 7
Work Bite-Sized Pieces and translate English to math. If Al buys 1 milkshake and x cheese-
burgers, then he spends 1 times the cost of a milkshake ($4) and x times the cost of a cheese-
burger ($6), which translates to 4 + 6x. This must be at least $30; “at least” translates to ≥ in
math, so 4 + 6x ≥ 30. Subtract 4 from both sides to get 6x ≥ 26. Divide both sides by 6 to get x
≥ 4.3. You can’t order a fractional number of cheeseburgers, so try 5 cheeseburgers. This would
|Practice Test 7: Answers and Explanations 2 9
SAT Premium Prep
give a total of 4 + 6(5) = $34, which satisfies the question. Input 5 as your answer. 6 and 7 are also
acceptable answers, as those numbers of cheeseburgers will be $40 and $46, respectively.
32. 650 Break the problem into Bite-Sized Pieces. First, determine how much water is added in 50 minutes.
Rate = amount , so rate × time = amount. 7 × 50 = 350 milliliters added over 50 minutes. Add this
time
to the original 300 milliliters: 350 + 300 = 650.
33. 64.1 To find the mean, find the sum of all the ages and divide by the number of people:
57 + 59 + 65 + 48 + 81 + 76 + 40 + 58 + 63 + 69 + 71 + 63 + 77 + 71 = 898 = 64.1 .
14 14
34. 365 To solve for Siham, translate from English to math and solve the system of equa-
tions. Make the number of minutes Rama ran r and the number of minutes Siham ran
s. If Rama and Siham ran for a total of 670 minutes, then the number of minutes Rama
ran plus the number of minutes Siham ran equals 670, or r + s = 670. For the second
equation, Rama’s total amount of time was 60 minutes less than Sihams, so r = s – 60.
Because you want to solve for s, you can substitute s – 60 for r in the first equation: (s – 60) +
s = 670. Combine like terms: 2s – 60 = 670. Add 60 to both sides: 2s = 730. Divide both sides by 2
to get s = 365.
35. 8 Use the geometry basic approach. First, write down the formula you need: the volume of a cone,
1 1
which is V = 3 πr2h . Plug in what you know: 48π = 3 πr2(9) . Solve for r; start by combining like
terms on the right: 48π = 3πr2 . Divide both sides by 3π: 16 = r2. Take the square root of both sides,
and you find r = 4. Be careful! The question is asking for diameter, so double the radius to find the
diameter is 8.
36. 5 For this function to be undefined, the denominator must be equal to 0. So, set the denominator
equal to 0 and solve: (x – 12)2 + 14(x – 12) + 49 = 0 . Start by FOILing the first parenthesis and
distributing 14 in the second: x2 – 24x + 144 + 14x – 168 + 49 = 0 . Combine like terms: x2 – 10x
+ 25 = 0. You might recognize this as a perfect square; it factors to (x – 5)(x – 5) = 0. Therefore, the
value of x that makes function f undefined is 5.
37. 14 Use the formula provided and the information given. If it costs $900 for 150 customers, then
C1 = 900 and Q1 = 150. Similarly, if it would cost $1,600 for 200 customers, then C2 = 1,600 and
Q2 = 200. Plug these values into the equation and solve: M = 1,600 − 900 = 700 = 14.
200 −150 50
3 0 | Practice Test 7: Answers and Explanations
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