Diagnostic Test - content.randomhouse.com

Diagnostic Test

MATH

Question 1 Question 4

y≠0 x and y are positive numbers.

Quantity A Quantity B Quantity A Quantity B
5y2 y2
x− y x −2 xy + y
−7
d The quantity in Quantity A is greater.
d The quantity in Quantity A is greater. d The quantity in Quantity B is greater.
d The quantity in Quantity B is greater. d The two quantities are equal.
d The two quantities are equal. d The relationship cannot be determined
d The relationship cannot be determined
from the information given.
from the information given.

Question 2 Question 5

Q 2 Quantity A Quantity B
60°
The least prime factor The least prime factor
of 72 of 27

P S 45° R d The quantity in Quantity A is greater.
d The quantity in Quantity B is greater.
Quantity A Quantity B d The two quantities are equal.
8 The length of line segment PR d The relationship cannot be determined

from the information given.

d The quantity in Quantity A is greater. Question 6
d The quantity in Quantity B is greater.
d The two quantities are equal. The average (arithmetic mean) of a, b, c, and d is 7.
d The relationship cannot be determined
Quantity A Quantity B
from the information given. 15
The average
Question 3 (arithmetic mean) of
4a – 5c, b – 24,
8c – a, and 3d + 2b

Quantity A Quantity B d The quantity in Quantity A is greater.
d The quantity in Quantity B is greater.
35,043 × 25,430 35,430 × 25,043 d The two quantities are equal.
d The relationship cannot be determined
d The quantity in Quantity A is greater.
d The quantity in Quantity B is greater. from the information given.
d The two quantities are equal.
d The relationship cannot be determined

from the information given.

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Question 7 Question 9

In the figure above, the width of the larger The volume of a cube with edge of length 2
square is equal to the diagonal (not shown) of is how many times the volume of a cube with
the smaller square. edge of length 2 ?

Quantity A Quantity B d 2
d 2
The area of the smaller The area of the shaded d 2 2
square region d 4
d 8

d The quantity in Quantity A is greater. Question 10
d The quantity in Quantity B is greater.
d The two quantities are equal. BILLIE’S TIME SHEET FOR JULY 2
d The relationship cannot be determined
Time in: 8:57 in the morning
from the information given. Time out: 5:16 in the afternoon
Time spent
Question 8 stacking shelves: 80% of total time spent at work

Quantity A 11 < y < 17 According to the time sheet above, Billie
Quantity B spent approximately how many hours stack-
y +17 ing shelves on July 2 ?
y y +11
11

d The quantity in Quantity A is greater. d 5 1
d The quantity in Quantity B is greater. 3
d The two quantities are equal.
d The relationship cannot be determined d 6 2
3
from the information given.
d 7 1
3

d 8 2
3

d 9 1
3

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Question 11 Question 13

What is the probability that the sum of two If mx + qy – nx – py = 0, p – q = 2, and
different single-digit prime numbers will NOT
be prime? y = − 1 , then which of the following is true?
x 3
d 0
d 2
1 n − m = 3
2
d d 2
3
n − m = −

d 2 d 2
3 3
m + n =
d 5
d m + n = 3
6 2

d 1 d 3
2
m + n = −

Question 12

Question 14

To fill a larger concert hall, a madrigal The “hash” of a three-digit integer with three
singing group consisting of sopranos, altos, distinct integers is defined as the result of
and basses, in a 5:7:3 ratio, needs at least interchanging its units and hundreds digits.
40 singers. What is the least number of The absolute value of the difference between
basses the group will need? a three-digit integer and its hash must be
divisible by

d 9
d 7
d 5
d 4
d 2

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Questions 15-16 refer to the following graphs.

SENIOR MANAGEMENT OF COMPANY Y

Average Salaries of Senior Managers at Company Y Number of Senior Managers at Company Y
120 25

100 20
Salary (in thousands)
Salary (in thousands)

Senior Managers
80
15

60
10

40 Average Salaries of Senior Managers at Company Y

20 120 5

0 100 0
1950 1960 1970 1980801990 2000 1950 1960 1970 1980 1990 2000
Ye ar
Year
60

in 1950 dollars 40
in actual-year dollars 20

Question 15 0 Question 16
1950 1960 1970 1980 1990 2000

If from 1980 to 2007, the number of senior Ye a r Which of the following statements can be
managers increased by 60 percent, then what inferred from the charts above?
was the increase in the number of senior
managers from 2000 through 2007, inclusive? Indicate all such statements.

d 2 W From 1990 to 2000, the average salary,
d 4
d 6 in actual-year dollars, increased by
d 9 more than 10%.
d 12
W In 1960, there were fewer than 5 senior

managers.

W For the decades shown, the number

of senior managers increased by the
greatest percentage between 1980
and 1990.

|Diagnostic Test    2 7

Question 17 Question 19

The positive sequence s1, s2, s3 sn  is P Q
defined by sn = sn−1 + 5 for n ≥ 2. If s1 = 7, x° R
then the nth term in the sequence is O • x°

d 5n – 5 S
d 5n – 2
d 5n In the circle with center O above, PS = 8.
d 5n + 2 If x = 75, then what is the perimeter of the
d 5n + 7 shaded region?

Question 18 d 6 − 2 3

Rachel and Rob live 190 miles apart. They d 2π
both drive in a straight line toward each other 3
to meet for tea. If Rachel drives at 50 mph
and Rob drives at 70 mph, then how many d 2π + 8
miles apart will they be exactly 45 minutes 3
before they meet?
d 2π − 2 3 +6
d 50 3
d 60
d 70
d 90
d 100

d 2π + 2 3 +6
3

Question 20

If x = 32, then what is the value of xx ?

d 34
d 38
d 39
d 312
d 318

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VERBAL Question 3

Question 1 The development of hydrogen-powered cars
will always be (i)________ by the physical fact
British modernists used the literary tropes that hydrogen, while containing more energy
of fragmentation and failure to explore the per gallon than does gasoline, is much less
impending (i)________ of British colonialism; dense than gasoline; hydrogen thus carries
illustrating the imminent (ii)________ of the less energy per pound, making it (ii)________
empire through their literature. for any vehicle to carry enough hydrogen on
board for long trips.
Blank (i) Blank (ii)
avarice sunset Blank (i) Blank (ii)
castigation enhanced convenient
dissolution rise hindered
wealth parodied austere
ungainly
Question 2
Question 4
Contemporary authors are much more at
liberty to be candid than were authors of One of the rarest of celestial events, the total
previous centuries, but modern writers solar eclipse only happens when the Moon, in
nevertheless often find themselves _______ its orbit around the Earth, fully (i)________ the
portions of their works. view of the sun from a particular location on
Earth. Because the Moon is relatively small, in
W emancipating celestial terms, and its umbra, the central part
W censoring of the Moon’s shadow caused by its block-
W refuting ing the sun, only traces a narrow path on the
W censuring Earth, total eclipses are such (ii)________ oc-
W ameliorating currences that they have been known to draw
W expurgating hundreds of thousands of onlookers.

Blank (i) Blank (ii)
secularizes atypical
epitomizes desultory
occludes momentous

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Question 5 Question 7

To (i)________ people accurately, census Over the last several decades, the demand
workers must be (ii)________: because there for Country Y’s automobiles increased in
are often residents of a household with the Country X but demand for Country X’s auto-
same name, or people whose names have mobiles in Country Y has remained stagnant.
unusual spellings, workers who are anything Initially, this disparity was plausibly due to
less than (iii)________ in following correct Y’s manufacturers having superior technol-
procedures and reviewing cases may result ogy, which has yielded more fuel efficient
in the same resident getting counted multiple cars with cheaper maintenance. However,
times, or even not at all. now Country X’s cars are comparable—if not
slightly superior—in these respects. What
Blank (i) Blank (ii) Blank (iii) Country X’s manufacturers fail to acknowl-
rectify derivative meticulous edge is that Country Y’s drivers drive on
tally fastidious perfunctory the left side of the road. Clearly, to help
impute industrious lessen this trade imbalance, Country X
inexact manufacturers should produce more cars
with right-side steering wheels.
Question 6
Which of the following is an assumption
The journalist was (i)________ in his pursuit of made by the argument?
the scandal he suspected: despite a lack of
support from his editors, he was determined d Reversing the trade imbalance requires
to investigate day and night, follow every lead,
and write until dawn to get the story first and making right-side steering wheels.
finally (ii)________ the big news agencies.
d If Country X makes automobiles with
Blank (i) Blank (ii)
decorous scoop right-side steering wheels, most con-
digressive forestall sumers from Country Y will chose to
indefatigable purchase a car from Country X.
deprecate
d If consumers from Country Y drive

on the left side of the road, these
consumers are less inclined to buy
steering wheels found on the left-side
of the car.

d Cars from Country X will continue to

improve their fuel efficiency and
reduce their maintenance costs.

d The government of Country Y requires

all its citizens to purchase cars with
right-side steering wheels.

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Questions 8-11 refer to the following passage. as much power as the critical theorists contend,
they would surely censor or marginalize the
Comparative historian Marc Ferro claims that works of social scientists in this field. Further-
the largest discrepancy in knowledge between more, graduates of “elite” preparatory schools
what academic historians and what the aver- are exposed to alternative interpretations of
age citizen knows about history is found in the history, subversive teachers, and unfiltered
United States. How has this situation come primary source materials more frequently than
about? Certainly the problem does not lie with are students at public institutions. This would
the secondary literature. Whereas in the past, seem to indicate that the powerbrokers have
American historians were handicapped by sec- little control over what happens at their very
ondary literature that was clearly biased towards own schools, let alone far flung rural schools or
a European viewpoint, since the civil rights schools deep in urban territory. The real culprit
movement of the 1950s and 60s, the secondary may be something not as insidious as a vast up-
literature in American history has become far per class conspiracy, but more along the lines of
more comprehensive. And it cannot be simply pernicious forces working at a highly local level.
a matter of space constraints; the average high Almost half of the states have textbook adoption
school history textbook is well over a thousand boards consisting of members of the commu-
pages in length. nity. These boards review and recommend what
books are taught in neighborhood schools. And
One theory holds that American history text- because textbook publishers are first and fore-
books are simply the socializing instruments of most seeking to maximize profit, it is these local
a controlling elite. The stratification of American boards that they must appease.
society is preserved, according to this theory,
by the creation of what Marx termed “false Question 8
consciousness.” The theory holds that the way
people think about their society and their history Consider each of the following answer
is crucial to maintaining the status quo. If the choices separately and select all that apply.
power elites come to believe that their success
is the deserved product of their hard work and According to the passage, proponents of the
ingenuity, then there will be no desire to change critical theory believe which of the following?
the system. Similarly, if the lower classes are
taught that their plight is solely due to their fail- W The creation of a false consciousness
ings, they will be more likely to accept their fate
and less likely to rise up in revolution. Griffin is a significant element in maintaining
and Marciano contend that history textbooks the stratification of American society.
promote nothing more than hegemony.
W It is not in the interests of the powerful
Many educational theorists share this view-
point, which in their discipline is often known classes of society to engender criti-
as critical theory. Proponents of this view, in- cal reflection among the majority of
cluding Kozol, Freire, and Giroux, argue that the citizens.
dominant classes would never create or foster
an educational system that taught subordinate W Alternative interpretations of history may
classes how to critically evaluate society and the
injustices it contains. As long as schools serve be taught to members of the upper
to transmit culture, the power elite will never classes, but not to members of the
allow any real reform in the system. subordinate classes.

It is all too easy to blame citizens’ poor un-
derstanding of American history on some shad-
owy coterie of cultural aristocracy. But critical
theory and other theories that lay the blame for
American ignorance of history on the doorstep
of the elites cannot explain their own success.
Is it not a paradox that critical theory scholarship
dominates its field? If the titans of society had

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