500 ACT Math Questions to Know by Test Day, 3rd Edition

McGraw Hill

500
ACT Math Questions

to know by test day

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McGraw Hill

500
ACT Math Questions

to know by test day

Third Edition

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CONTENTS

Introduction vii
Diagnostic Quiz  1

Questions 1–20

Chapter  1 Integrating Essential Skills: Rates, Percentages, and
Proportional Relationships  17

Questions 1–70

Chapter  2 Integrating Essential Skills: Basic Geometry  39

Questions 71–140

Chapter  3 Integrating Essential Skills: Average, Median,
and Expressing Numbers in Different Ways  67

Questions 141–200

Chapter  4 Preparing for Higher Math: Number and Quantity  83

Questions 201–250

Chapter  5 Preparing for Higher Math: Algebra  99

Questions 251–320

Chapter  6 Preparing for Higher Math: Functions  117

Questions 321–385

Chapter  7 Preparing for Higher Math: Geometry  137

Questions 386–450

Chapter  8 Preparing for Higher Math: Statistics
and Probability  163

Questions 451–500
Answers 181

  ‹  v

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INTRODUCTION

Congratulations! You’ve taken a big step toward ACT success by purchasing
McGraw Hill 500 ACT Math Questions to know by test day. We are here to help
you take the next step and score high on your ACT exam so you can get into the
college or university of your choice!

This book gives you 500 ACT-style multiple-choice questions that cover all
the most essential math material. Each question is clearly explained in the answer
key. The questions will give you valuable independent practice to supplement
your regular textbook and the ground you have already covered in your math
class.

This book and the others in the series were written by expert teachers who
know the ACT inside and out and can identify crucial information as well as the
kinds of questions that are most likely to appear on the exam.

This edition of McGraw Hill 500 ACT Math Questions to know by test day,
reflects the changes in the ACT Math test instituted in 2017 and includes
many new questions. The content is divided into two main categories. The
first category is “Integrating Essential Skills,” which constitutes 40 percent to
43 percent of the test. This category addresses content typically learned before
eighth grade including basic geometry, proportions, rates, and expression of
numbers in different ways. The second category is “Preparing for Higher Math,”
which constitutes 57 percent to 60 percent of the test. This category addresses
content typically learned in high school, including algebra, number and
quantity, functions, advanced geometry, trigonometry, statistics, and probability.
Overlapping both these categories are mathematical modeling problems that
involve producing, interpreting, understanding, evaluating, and improving
models. Modeling problems in this book are identified with the MODELING  icon after
the problem number.

You might be the kind of student who needs to study extra a few weeks
before the exam for a final review. Or you might be the kind of student who
puts off preparing until the last minute before the exam. No matter what your
preparation style, you will benefit from reviewing these 500 questions, which
closely parallel the content, format, and degree of difficulty of the math questions
on the actual ACT exam. These questions and the explanations in the answer key
are the ideal last-minute study tool for those final weeks before the test.

If you practice with all the questions and answers in this book, we are certain
you will build the skills and confidence needed to excel on the ACT. Good luck!

—The Editors of McGraw Hill

  ‹  vii

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McGraw Hill

500
ACT Math Questions

to know by test day

This page intentionally left blank

Diagnostic Quiz

  ‹  1

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GE T TING STARTED:
THE DIAGNOSTIC QUIZ

The following questions refer to different units in this book. These questions will
help you test your understanding of the concepts tested on the ACT exam by
giving you an idea of where you need to focus your attention as you prepare. For
each question, simply circle the letter of your choice. Once you are done with the
exam, check your work against the given answers, which also indicate where you
can find the corresponding material in the book.

Good luck!

  ‹  3

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DIAGNOSTIC QUIZ QUESTIONS

1. If x + 2 = x + 6, then what is the value of x?
3 6

(A) 1
(B) 2
(C) 4
(D) 5
(E) 6

2. The value of three consecutive odd integers is 567. What is the value of the

second of these three consecutive integers?
(A) 175
(B) 181
(C) 187
(D) 189
(E) 193

3. If 3x - y = 7 and x + 2y = 7, then what is the value of xy ?
(A) 6
(B) 9
(C) 12
(D) 18
(E) 24

4. If a six-sided die is thrown, what is the probability that the result of two

consecutive throws will be two sixes?

(A) 1
72

(B) 1
36

(C) 1
24

(D) 1
3

(E) 1
2

  ‹  5

›6    McGraw Hill 500 ACT Math Questions

5. Tim has a box with a set of 8 green, 5 blue, 6 yellow, and 7 black toys. What

is the probability that a random selection would yield a blue or black toy?

(A) 5
26

(B) 1
4

(C) 6
13

(D) 1
2

(E) 15
26

6. A company has three times more researchers employed than it does

support staff, while it also has twice as many support staff compared to
security. If the total number of researchers, support staff, and security staff
is 675, how many people work as support staff?
(A) 50
(B) 75
(C) 100
(D) 150
(E) 175

7. Rectangle A has a width of 8 centimeters and a length of 3 centimeters.

Rectangle B has a width of 6 centimeters and a length of 2 centimeters.
What is the ratio of the area of rectangle A compared to the area of
rectangle B?
(A) 1:3
(B) 1:2
(C) 2:1
(D) 3:1
(E) 4:3

8. The ratio of x to y is 7 to 18. If the value of x is 49, then what is the value of y ?

(A) 25
(B) 56
(C) 90
(D) 96
(E) 126

‹Diagnostic Quiz Questions    7

9. The rectangles shown below are similar. What is the value of x?

LK

DC
6

3

A 6 B I x J

(A) 9
(B) 12
(C) 15
(D) 18
(E) 24

10. Mitch became school council president by winning 64% of the vote. If his

opponent won 396 votes and all of the votes cast were valid, what was the
total number of votes cast?
(A) 618
(B) 694
(C) 791
(D) 1,025
(E) 1,100

›8    McGraw Hill 500 ACT Math Questions

11. Given the visual shown below, the ratio of x to y is 1 : 34. What is the value
of y?

C

5
x

A y B

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

12. Which of the following lines has a negative slope with a positive
x-intercept?
(A) 4

2

–6 –4 –2 0 246
–2
–4

‹Diagnostic Quiz Questions    9

(B) 4

2

–4 –2 0 246 8

–2 6
4
–4 2

(C)

–6 –4 –2 0 2 46
–2

›10    McGraw Hill 500 ACT Math Questions

(D) 4

2

–4 –2 0 2468
–2

–4

(E) 4

2

–4 –2 0 2 46
–2

–4

13. If the point (-3, y) lies on f (x) = -3x + 4, then what is the correct value

of y?
(A) -13
(B) -5
(C) 4
(D) 9
(E) 13

‹Diagnostic Quiz Questions    11

14. The length of a diagonal of a rectangle is 5 cm, and its width is 3 cm.

What is the area of the rectangle?
(A) 8
(B) 12
(C) 15
(D) 20
(E) 24

15. What is the greatest common factor of 16, 28, and 32?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8

16. The sum of 41 numbers is 1025. What is the average of these numbers?

(A) 23
(B) 25
(C) 31
(D) 41
(E) 50

17. Which of the following values of x satisfies the equation x2 + x - 12 = 0?

(A) -3 and 4
(B) 3
(C) 3 and -4
(D) 4
(E) 12

18. The sum of the values -2x, x + 2, and 3x - 4 is 12. What is the value of x?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 12

›12    McGraw Hill 500 ACT Math Questions

19. Jennifer’s parents are saving for retirement. The value of their investment

can be represented with the function FV(X ) = 12,500 (1 + 0.09)t, where
FV is the future value of the investment while t is the time in years that
has passed. Rounded to two decibels, what will be the value of their
investment in 25 years?
(A) 75,259.41
(B) 93.321.56
(C) 101,214.24
(D) 107,788.51
(E) 131,199.24

20. Which of the following could be a slope of a line perpendicular to one that

passes through (0, 2) and (4, 8)?

(A) -3

(B) − 3
2

(C) − 2
3
(D) 1
(E) 3

DIAGNOSTIC QUIZ ANSWERS

Chapter 1: Integrating Essential Skills: Rates, Percentages, and
Proportional Relationships

1. (B) The equation should first be simplified by multiplying it with 6. When doing so, the
value shall be 2x + 4 = x + 6. It can then be inferred that x = 2.

2. (D) This should be mathematically expressed as x + x + 2 + x + 4 = 567. Due to the fact
that the numbers are odd integers only, they will be spaced apart by two. By simplifying the
equation, it can be rewritten as 3x + 6 = 567, which can further be simplified to 3x = 561,
meaning that x = 187. This is the value of the smallest of the three integers. The second one
will be 189 as reflected in answer choice (D).

Chapter 5: Preparing for Higher Math: Algebra

3. (A) In order to find out the value, we either need to express x as y or combine these two
equations. In order to do so, the easiest approach would be to multiply the first equation by
two, thus resulting in 6x - 2y = 14 and x + 2y = 7.
When these equations are summarized, we can infer that 7x = 21, meaning that x = 3. By
inserting this value into the first equation, it can be calculated that 3 * 3 - y = 7. Therefore,
y = 2 and xy = 6 as identified in (A).

Chapter 8: Preparing for Higher Math: Statistics and Probability

4. (B) The chance of rolling a six on the first try is 16, while the chance of rolling a six
on the second try is also 16. The chance of this occurring both times can be calculated by
multiplying these odds, thus gaining the result
1 .
36

5. (C) The total number of possibilities is equal to the total number of toys, meaning
8 + 5 + 6 + 7 = 26. There are 7 black and 5 blue toys, so the total number of possibilities for

black or blue is 12, as either outcome is suitable. That means the probability is 12 = 6 .
26 13

  ‹  13

›14    McGraw Hill 500 ACT Math Questions

Chapter 3: Integrating Essential Skills: Average, Median, and
Expressing Numbers in Different Ways

6. (D) Assume that x represents security, y support staff, and z researchers. Based on the
statements earlier, we can determine that:
z = 3y
y = 2x
x + y + z = 675
We can express all of these as x, so that x + 2x + 6x = 775. This then leads to 9x = 775;
when divided by 9, we calculate that x = 75. As the number of security staff is 2x, then the
number of support employees is 150.

Chapter 2: Integrating Essential Skills: Basic Geometry

7. (C) The area of rectangle A is 8 * 3 = 24, while the area of rectangle B is 6 * 2 = 12. This
means that the area of rectangle A is twice as large as that of B.

Chapter 1: Integrating Essential Skills: Rates, Percentages, and
Proportional Relationships

8. (E) The ratio can be considered as x = 7. As 49 is 7 times 7, a straightforward way
y 18

to calculate is to multiply 18 with 7, and thus the result is (E).

Chapter 2: Integrating Essential Skills: Basic Geometry

9. (B) If they are similar, this means that the ratios between the length and width are
identical for the rectangles shown. Therefore, 3/6 = 6/x.
When solving this, we can determine that 3x = 36, meaning that x = 12.

Chapter 4: Preparing for Higher Math: Number and Quantity

10. (D) This can be mathematically represented as 396 = 0.36x because if all the votes were
validly cast, then Mitch’s opponent won 36% of the vote. By dividing 396 with 0.36, we
can calculate that the total number of votes cast was then 1,100.

Chapter 7: Preparing for Higher Math: Geometry

11. (B) This needs to be included in the formula that x2 + y2 = 25. Based on the ratio

above, it can be calculated that x = 4 y. By placing this into the formula instead of x we
can calculate 3 25. By
16 y2 y2 25 2
that 9 + = 25 which can further be simplified as 9 y =

multiplying the entire equation with 295, it is then clear that y2 = 9 . Given that the value
of y needs to be positive as it is the side of a triangle, the only possible solution is that y = 3.

‹Diagnostic Quiz Answers    15

12. (D) Both (A) and (B) have positive slopes. While answers (C) and (D), and (E) all have
negative slopes, only (D) has a negative x-intercept.

Chapter 6: Preparing for Higher Math: Functions

13. (E) Due to the fact that the function is -3x + 4, inserting the value of -3 will allow us
to calculate the value of y. When inserted this becomes 9 + 4 = 13.

Chapter 2: Integrating Essential Skills: Basic Geometry

14. (B) If the diagonal of the rectangle is 5 cm and the length is 3 cm, we can apply the
Pythagorean theorem to determine that the x2 + 32 = 52, where x is the unknown length of
the length of the rectangle.
We can solve the equation by determining that as x2 = 16 and the side of a rectan-
gle has to be a positive number. This means that the only possible option is that x = 4.
As the area is calculated by multiplying the length with the width, the correct answer is
4 * 3 = 12.

Chapter 4: Preparing for Higher Math: Number and Quantity

15. (C) The greatest common factor is the largest common value by which each of these
figures is divisible. It is clear that, as they are even numbers, all are divisible by 2 and that
28 is not at all divisible by 8 and 6. All of them are divisible by 4, making this the largest
common factor.

Chapter 3: Integrating Essential Skills: Average, Median, and
Expressing Numbers in Different Ways

16. (B) The average is the sum of all of the values divided by the number of them. In this
case, this is 1025/41 = 25.

Chapter 5: Preparing for Higher Math: Algebra

17. (C) The equation can be rewritten as (x - 3)(x + 4) = 0. By being rewritten in such a
manner, it is then clear that the correct answers are 3 and -4.

18. (D) If the sum of these values is 12, this can be mathematically written as -2x + x +
2 + 3x - 4 = 12.
This can then be simplified as 2x = 14 meaning that the value of x = 7.

Chapter 6: Preparing for Higher Math: Functions

19. (D) FV(t) = 12,500 (1.09)25 = 12,500 * 8.6231 = 107,788.51

›16    McGraw Hill 500 ACT Math Questions

Chapter 7: Preparing for Higher Math: Geometry

20. (C) Based on the equation f (x) = ax + b, as x is 0 for the first point, we can determine
that b = 2. After that we can utilize the second point to determine the following:

8 = 4a + b

As we know that b = 2, then it is possible to determine that

a = 3.
2

As this is the slope of the line, any other line will be perpendicular to it in case the result
of the multiplication of these slopes is -1. In order for that to be possible, the slope of the
perpendicular line would have to be as presented in answer choice (C).

1CHAPTER 

Integrating Essential Skills: Rates,
Percentages, and Proportional
Relationships

Use the following table to answer questions 1 and 2. It shows the class
level of the 500 students at Greenville High School.

Class Number of Students

Freshmen 125
Sophomores 80
Juniors 175
Seniors 120

1. What percentage of students at Greenville High School are seniors?
(A) 12%
(B) 14%
(C) 24%
(D) 40%
(E) 75%

MODELING 2. If the fraction of students who are freshmen is represented using a
circle graph (pie chart), what should be the measure (in degrees) of the
central angle of that portion of the graph?
(A) 12
(B) 25
(C) 40
(D) 65
(E) 90

  ‹  17

›18    McGraw Hill 500 ACT Math Questions

3. The following chart represents the final course grades for students in two
math classes. What fraction of students in the courses received a final
course grade of A or B?

20 20

15 15
Number of students
10
55

3

A BC D 2
Final grade F

(A) 1
9

(B) 2
9

(C) 3
9

(D) 4
9

(E) 5
9

‹Rates, Percentages, and Proportional Relationships    19

MODELING 4. The following circle graph represents the distribution of students in a local
high school. If there are 1000 total students in the high school, how many
more are 9th graders than 11th graders?

Distribution of students by grade level

24%

45% 9th grade
10th grade
11th grade
10%
12th grade

21%

(A) 500
(B) 450
(C) 350
(D) 120
(E) 100

MODELING 5. A factory can produce 100 bracelets every 15 minutes. How many
bracelets can the factory produce in three and a half hours?
(A) 300
(B) 350
(C) 550
(D) 1400
(E) 5250

MODELING 6. A cellular phone service contract requires customers to pay $45.00 a
month for basic service in addition to $0.15 for each text message. If a
customer’s bill is $61.50, how many text messages did the customer send?
(A) 10
(B) 110
(C) 410
(D) 510
(E) 710

›20    McGraw Hill 500 ACT Math Questions

7. The ratio of x to y is 5 to 12. If x is 45, what is the value of y?
(A) 38
(B) 52
(C) 60
(D) 84
(E) 108

8. There are three unknown values where y is twice as large as x while z is
three times larger than y. If z - 2x = 8, what is the value of z?
(A) 6
(B) 9
(C) 12
(D) 15
(E) 18

9. If M% of 135 is 54, then M =
(A) 2.5.
(B) 4.
(C) 25.
(D) 40.
(E) 81.

10. In a large company, the ratio of full-time to part-time employees is 3:2. If
there are 800 total employees, how many are part-time?
(A) 260
(B) 320
(C) 400
(D) 480
(E) 530

11. If the length of one side of a square is increased by 20%, then the
perimeter will increase by
(A) 5%
(B) 10%
(C) 20%
(D) 40%
(E) 80%

12. If 5% of x is y and 25% of y is z, then how many times larger than z is x?
(A) 4
(B) 30
(C) 80
(D) 95
(E) 125

‹Rates, Percentages, and Proportional Relationships    21

MODELING 13. A special garden design requires that the garden have three distinct square
sections whose areas follow the ratio 2:3:5. If such a garden is designed to
have a total area of 1550 square feet, then what would be the area of the
smallest section in square feet?
(A) 155
(B) 250
(C) 300
(D) 500
(E) 750

14. In the following figure, triangles ABC and DEF are similar. What is the
value of x ?

C

F
20

30 E x
2
B
8

D

A

(A) 5.0
(B) 7.5
(C) 15.0
(D) 24.0
(E) 36.5

15. If a is directly proportional to b and a = 1 when b = 10, then what is the
value of a when b = 35? 2

(A) 1
7
1
(B) 5

(C) 2
9
9
(D) 4

(E) 7
2

›22    McGraw Hill 500 ACT Math Questions

16. If 80% of x + 1 is 2, then x =
(A) 0.975.
(B) 1.25.
(C) 1.5.
(D) 4.
(E) 5.1.

MODELING 17. Greg can read w words a minute. How many minutes will it take Greg to
read an n-page document if each page contains 500 words?

(A) 500n
w

(B) 500w
n
(C) 500nw
(D) 500(n + w)
(E) 500n + w

18. Which of the following represents 1 of 1  ?
(A) 0.000025 2 20

(B) 0.00025
(C) 0.0025
(D) 0.025
(E) 0.25

19. In an election with two parties, Party A won 54% of the votes. If Party B
received 874 votes, how many votes were cast in total?
(A) 400
(B) 472
(C) 1619
(D) 1900
(E) 2102

20. Each side of square A has a length of 3 meters, while each side of square B
has a length of 9 meters. What is the ratio of the area of square A to the
area of square B?
(A) 1:1
(B) 1:3
(C) 1:6
(D) 1:9
(E) 1:12

‹Rates, Percentages, and Proportional Relationships    23

21. The ratio of the lengths of each of the sides of a triangle is 4:12:14. If the
shortest side has a length of 2 feet, what is the perimeter of the triangle in
feet?
(A) 15
(B) 24
(C) 34
(D) 57
(E) 68

22. In a college with 14,000 students, 490 are majoring in mathematics. What
percentage of the student body does the number of math majors represent?
(A) 0.0035%
(B) 0.035%
(C) 0.35%
(D) 3.5%
(E) 35%

23. In the following figure, the ratio of the lengths of AB to BC of rectangle
ABCF is 2:3, and C is the midpoint of DF. If AF = FE, what is the area of
triangle DEF ?

D

B 18 C

A F E

(A) 12
(B) 28
(C) 54
(D) 108
(E) 216

›24    McGraw Hill 500 ACT Math Questions

24. In the following figure, rectangles ABCD and EFGD are similar. What is
the perimeter of EFGD?

B 30 C

10 F3 G

AED

(A) 4
(B) 8
(C) 26
(D) 30
(E) 40

25. If 3x + 6xy + 9y = 15, then what is the value of x + 2xy + 3y equal to?
(A) 2
(B) 5
(C) 6
(D) 7.5
(E) 10

26. If 80% of a number is 122, what is 40% of the number?
(A) 48.8
(B) 61.0
(C) 73.2
(D) 83.0
(E) 244.0

27. A factory’s quality assurance specialist can inspect 28 hard drives in
40 minutes. How many minutes will it take the specialist to inspect
196 hard drives?
(A) 47
(B) 49
(C) 89
(D) 137
(E) 280

‹Rates, Percentages, and Proportional Relationships    25

28. If the ratio of A to B is 3:8 and the ratio of B to C is 1:6, what is the ratio
of A to C ?
(A) 1:2
(B) 1:14
(C) 1:16
(D) 1:24
(E) 1:48

29. A $154.99 graphing calculator can be purchased with a coupon that gives
a 15% discount. What is the price of the calculator if it is purchased with
the coupon?
(A) $23.25
(B) $68.47
(C) $131.74
(D) $139.99
(E) $152.67

30. The length of a rectangle is 40% larger than its width. If the area of the
rectangle is 140 square feet, what is the width of the rectangle in feet?
(A) 10
(B) 22
(C) 35
(D) 56
(E) 64

31. For x > 0, which of the following represents x % of 3  ?
4
3x
(A) 40

(B) 3x
400

(C) 3
400x

(D) 1
28

(E) 30x
4

›26    McGraw Hill 500 ACT Math Questions

32. What is 1 % of 1 ?
4 4

(A) 0.000250
(B) 0.000625
(C) 0.0025
(D) 0.0050
(E) 1

MODELING 33. The following table represents the percentages of employees in each of four
possible classifications at a certain company. If there are no other possible
classifications, what is the value of x ?

Classification Percentage

Part-time 35%
Full-time, hourly 20%
Full-time, salary 24%
Full-time, salary and bonus x %

(A) 1
(B) 21
(C) 44
(D) 79
(E) 65

34. If the ratio of x to y is 1:6, what is the difference between y and x when
x = 12?
(A) 5
(B) 12
(C) 17
(D) 60
(E) 72

‹Rates, Percentages, and Proportional Relationships    27

35. In the following figure, the ratio of x to y is 1:4. What is the ratio of the
area of the triangle with base x to the area of the triangle with base x + y ?

B

y

Ax yC

(A) 1:2
(B) 1:4
(C) 1:5
(D) 1:7
(E) Cannot be determined
36. Rectangles ABCD and PQRS in the following figure are similar. What is
the value of x ?

QR

BC

16
4

A 13 D P x – 13 S

(A) 13
(B) 25
(C) 38
(D) 52
(E) 65

›28    McGraw Hill 500 ACT Math Questions

37. If 95% of 3x is 39.9, what is the value of x ?
(A) 10
(B) 14
(C) 38
(D) 42
(E) 58

38. The circles in the following figure are centered at points O and P,
AB
respectively. If CD = 3, what is the ratio of the area of the circle centered

at point O to the area of the circle centered at point P ?

A BC D
OP

(A) 3:1
(B) 3:2
(C) 6:1
(D) 9:1
(E) 9:2

39. The number representing the length of one side of a square is 20% as large
as the number representing its area. What is the perimeter of this square?
(A) 5
(B) 15
(C) 20
(D) 34
(E) 60

‹Rates, Percentages, and Proportional Relationships    29

40. If the ratio of x to y is 2:5, and y is always 30% of z, then for all possible
x
nonzero values of x, y, and z, z =

(A) 112.

(B) 235.

(C) 23.

(D) 5 .
6

(E) 43.

41. If x × 280 = 112, then x % of 280 is
50

(A) 23.
(B) 56.
(C) 102.
(D) 188.
(E) 224.

›30    McGraw Hill 500 ACT Math Questions

42. The triangles in the following figure are similar. In terms of x, what is the
perimeter of triangle DEF ?

B

xE

80° 80° 80° 80°
A 18 C D6F

(A) x + 6
6

(B) x + 6
3

(C) 2x + 6
3

(D) 2x + 6

(E) 6x + 6

43. A weather station reported that 90% of the days in a 30-day period
had measurable snowfall. How many of these days received measurable
snowfall?
(A) 3
(B) 12
(C) 18
(D) 27
(E) 29

‹Rates, Percentages, and Proportional Relationships    31

44. Triangle A and triangle B are equilateral triangles such that the ratio of the
length of one side of triangle A to the length of one side of triangle B is 6
to 7. If the perimeter of triangle A is 9, what is the length of a single side
of triangle B ?

(A) 2
3

(B) 7
2
(C) 12
(D) 18
(E) 21

45. In the following figure, ABCD is a rectangle such that x = 51 . If the area of
ABPQ is 12, what is the area of ABCD ? y

BP C

4

AxQ y D

(A) 32
(B) 56
(C) 60
(D) 72
(E) 112

46. The ratio of x to y is 2 to 3. If the sum of x and y is 125, what is the value
of x ?
(A) 15
(B) 25
(C) 50
(D) 75
(E) 100

›32    McGraw Hill 500 ACT Math Questions

47. Which of the following represents 0.2% of 15 ?

(A) 1
25,000

(B) 1
2500

(C) 1
250

(D) 1
25

(E) 1
10

48. For any circle with radius r > 0, what is the ratio of the length of its radius
to its area?

(A) 1:p

(B) 1:2p

(C) 1:pr

(D) 1:2pr
(E) 1:pr2

MODELING 49. Every student enrolled in a science course is either a physics major or a
biology major. If the ratio of physics majors to biology majors is 3 to 1
and there are 21 physics majors enrolled, how many biology majors are
enrolled in the course?
(A) 7
(B) 15
(C) 23
(D) 45
(E) 63

50. Suppose that m is inversely proportional to n and that m = 1 when n = 6.
If n = 32, what is the value of m? 2

(A) 1
6
(B) 2
(C) 3

(D) 9
2
(E) 6

‹Rates, Percentages, and Proportional Relationships    33

51. If x +4 = x −3 , then what is the value of x?
y −2 2y −4

(A) –14
(B) –11
(C) –3
(D) 5
(E) 8

52. If y is directly proportional to txhaenrdelaiftiyon=s6hiwp hbeentwxee=n41x, then which of the
following equations describes and y ?

(A) y = 1 x
4

(B) y = 3 x
2

(C) y= 23 x
4

(D) y = 6x

(E) y = 24x

53. A rectangle has sides of length x and x + 1, where x is a positive number. If
the area of the rectangle is 12, then which of the following is equivalent to
the ratio of x to x + 1?
(A) 1:6
(B) 1:4
(C) 1:3
(D) 2:3
(E) 3:4

54. If the length of one side of a square is 28% of 50, then the area of the
square is equal to
(A) 70
(B) 84
(C) 140
(D) 196
(E) 289

›34    McGraw Hill 500 ACT Math Questions

55. If q% of 30 is 21, then q =
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90

MODELING 56. This week, the price of a plane ticket is $436.00. Over the next three
weeks, suppose the price of the ticket rises 5% in the first week, falls 10%
the next week, and then rises 20% in the third week. To the nearest cent,
what is the cost of the plane ticket in three weeks?
(A) $412.02
(B) $457.80
(C) $494.42
(D) $501.40
(E) $523.20

57. Of 600 items in a storage closet, 40% are pens or pencils, 10% are first-aid
items, and 5% are notebooks. How many items in the storage closet have
not been described?
(A) 45
(B) 60
(C) 240
(D) 270
(E) 300

58. A number a is four times as large as half of a number b. If a and b are
nonzero, what percent of a is b ?
(A) 20%
(B) 25%
(C) 50%
(D) 100%
(E) 400%

‹Rates, Percentages, and Proportional Relationships    35

MODELING 59. A particle can move along the x-axis of the (x, y) coordinate plane at the
1
rate of 3 units every 2 hour. If the particle begins at the origin and moves
in the positive what point will it be 1
x direction, at in 2 4 hours?

(A)  9 ,0
 8

(B)  27 ,0
 8

(C)  9 , 0
2

(D)  27 ,0
4

(E)  27 ,0
2

60. In the following figure, the ratio of x to y is 1:4. What is the value of x ?

y 2√—17

x

(A) 1
(B) 2
(C) 8
(D) 10
(E) 13

›36    McGraw Hill 500 ACT Math Questions

61. Points A, B, and C in the following figure are collinear. If the ratio of m to
n is 2:3, what is the value of n in degrees?

n° m°
A BC

(A) 36
(B) 94
(C) 108
(D) 120
(E) 170

62. If, for nonzero values of m, n, and x, m = 4 and n = 4 , then m =
n 9 x 3 x
1
(A) 27

(B) 1
3

(C) 16
27

(D) 31
12
16
(E) 3

63. If 2 % of x is 10, then 1 % of x must equal
5 5

(A) 5.
(B) 10.
(C) 20.
(D) 25.
(E) 30.

‹Rates, Percentages, and Proportional Relationships    37

64. Every 6 minutes, a red LED flashes to indicate that a machine is operating
correctly. If the machine operates correctly for 800 minutes, how many
times will the LED flash?
(A) 133
(B) 134
(C) 135
(D) 136
(E) 137

65. In the following figure, AC = CE = 4, C is the midpoint of BD, and ABDE
is a rectangle. What is the ratio of the area of triangle ACE to the area of
triangle ABC ?

BCD

A2E

(A) 2:1
(B) 4:1
(C) 8:1
(D) 10:1
(E) 15:1

66. If 1 % of x is 1 , then x =
2 14 4

(A) 7
(B) 70
(C) 700
(D) 7000
(E) 70,000

MODELING 67. A tenant’s monthly rent of $675 will be increased by 3% every year. To the
nearest cent, what will be the tenant’s monthly rent in 3 years?
(A) $695.25
(B) $735.75
(C) $737.59
(D) $781.02
(E) $794.66

›38    McGraw Hill 500 ACT Math Questions

68. If 2x = 4 , then how many times larger than x is y ?
y 7

(A) 7
4

(B) 7
2
(C) 4
(D) 14
(E) 28

69. A student’s parking pass costs $45 per semester this year, but last year
cost only $38 per semester. To the nearest tenth of a percent, by what
percentage has the price of a parking pass increased?
(A) 15.6%
(B) 18.4%
(C) 24.3%
(D) 28.6%
(E) 31.1%

MODELING 70. For the first two hours he is at work, Harrison files 14 folders each hour.
For the remainder of his workday, he files 22 folders every hour. Which
of the following best models the number of folders (F) Harrison files if he
works a total of H hours during his workday?
(A) F = 14 + 22H
(B) F = 28 + 22H
(C) F = 22 + 28H
(D) F = 28 + 22 (H − 2)
(E) F = 22 + 28 (H − 2)

2CHAPTER 

Integrating Essential Skills:
Basic Geometry

Use the following information to answer questions 71–72.
The front of a house, shown in the following unscaled diagram, was damaged
in a hailstorm. New wood trim is needed around the perimeter of the house
as well as around the door and window, but trim is not needed along the
base of the house and door. The wall and the trim also need 2 fresh coats of
paint. The window is a square with 4-foot sides, and the door is 6 feet tall
and 3 feet wide.

18 ft
10 ft

25 ft 25 ft

MODELING 71. House trim costs $0.50 per foot. How much money, to the nearest
dollar, must be budgeted to replace the trim?
(A) $50
(B) $52
(C) $72
(D) $75
(E) $83

  ‹  39