QUANTITATIVE SECTION
37 QUESTIONS • 75 MINUTES
Directions for Problem Solving Questions: (These directions will appear on your
screen before your first Problem Solving question.)
Solve this problem and indicate the best of the answer choices given.
Numbers: All numbers used are real numbers.
Figures: A figure accompanying a Problem Solving question is intended to provide infor-
mation useful in solving the problem. Figures are drawn as accurately as possible EXCEPT
when it is stated in a specific problem that its figure is not drawn to scale. Straight lines
may sometimes appear jagged. All figures lie on a plane unless otherwise indicated.
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Directions for Data Sufficiency Questions: (These directions will appear on your
screen before your first Data Sufficiency question.)
This Data Sufficiency problem consists of a question and two statements, labeled (1) and
(2), in which certain data are given. You have to decide whether the data given in the
statements are sufficient for answering the question. Using the data given in the
statements plus your knowledge of mathematics and everyday facts (such as the
number of days in July or the meaning of counterclockwise), you must indicate whether:
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to
answer the question asked;
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to
answer the question asked;
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the
question asked, but NEITHER statement ALONE is sufficient;
(D) EACH statement ALONE is sufficient to answer the question asked;
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question
asked, and additional data specific to the problem are needed.
Numbers: All numbers used are real numbers.
Figures: A figure accompanying a Data Sufficiency problem will conform to the
information given in the question, but will not necessarily conform to the additional
information in statements (1) and (2).

Lines shown as straight can be assumed to be straight and lines that appear jagged can
also be assumed to be straight.
You may assume that positions of points, angles, regions, etc., exist in the order shown
and that angle measures are greater than zero.
All figures lie in a plane unless otherwise indicated.
Note: In Data Sufficiency problems that ask you for the value of a quantity, the data
given in the statements are sufficient only when it is possible to determine exactly one
numerical value for the quantity.
To review these directions for subsequent questions of this type, click on HELP.
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Practice Test 5 563
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1. If a . b and c . d, which of the
following is true?
(A) b 2 c , a 2 d
(B) a 1 d . b 2 c
(C) b 2 d . a 2 c
(D) a 1 c . b 1 d
(E) a 1 b . c 1 d
2.
Which of the following is nearest in
value to
=
664 1
=
414?
(A) 16
(B) 33

(C) 40
(D) 46
(E) 68
3. In a group of 20 singers and 40
dancers, 20% of the singers are less
than 25 years old, and 40% of the
entire group are less than 25 years
old. What percent of the dancers are
less than 25 years old?
(A) 20
(B) 40
(C) 50
(D) 60
(E) 80
4. How many ounces of coffee remain in
a cup that has a 14-ounce capacity?
(1) Originally, the cup contained 12
ounces of coffee.
(2) The cup is currently filled to 50
percent of the cup’s capacity
with coffee.
5. If 0 , N , 30, is N a factor of 30?
(1) N is a factor of 12.
(2) N is a multiple of 3.
6.
A
B
C
D
2

In the figure above, which shows
rectangle ABCD tangent to a circle at
each corner,
AB is 2 units in length.
Is rectangle ABCD a square?
(1) The length of minor arc AB is
exactly half the length of
arc ABC.
(2) The length of minor arc AD is
p
=
2
2
.
7.
What is 150% of the product of
1
8
and
0.4?
(A) 0.025
(B) 0.075
(C) 0.25
(D) 0.75
(E) 2.5
8.
A recipe calls for
2
3
cup of butter to

make a batch of cookies. How big is
the batch?
(1) If each of six people wanted to
eat five cookies,
5
3
cup of butter
would be needed.
(2) Three batches would require
2 cups of butter.
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9. What is the sum of five numbers?
(1) The arithmetic mean (simple
average) of the five numbers is 9.
(2) The difference between the
greatest and least of the five
numbers is 9.
10.
Two square rugs, R and S, have a
combined area of 20 square feet and
are placed on a floor whose area is
112 square feet, as shown above.
Measured east to west, each rug is
placed the same distance from the
other rug as from the nearest east or
west edge of the floor. If the area of
rug R is four times the area of rug S,

how far apart are the rugs?
(A) 1 foot, 6 inches
(B) 2 feet
(C) 2 feet, 8 inches
(D) 3 feet
(E) 3 feet, 4 inches
11. If p 5 (3)(5)(6)(9)(q), and if q is a
positive integer, then p must be
divisible, with no remainder, by all
the following EXCEPT:
(A) 27
(B) 36
(C) 45
(D) 54
(E) 90
12.
=
10
=
2
3
=
5
=
2
5
(A)
=
10
2

(B)
5
=
2
2
(C)
2
=
5
(D) 10
(E)
25
2
13. For all integers a and b, where
b Þ 0, subtracting b from a must
result in a positive integer if
(A) |a 2 b| is a positive integer
(B) (a 1 b) is a positive integer
(C)
S
a
b
D
is a positive integer
(D) (ab) is a positive integer
(E) (b 2 a) is a negative integer
14.
In the figure above, m∠ACB 5 90°.
What is the length of
DB?

(A)
3
=
21 2 8
(B) 8
(C)
5
=
7 2 8
(D)
5
=
5
(E)
18 2 5
=
6
15. If 3x 1 2y 5 5a 1 b, and if 4x 2 3y 5
a 1 7b, then x 5
(A) a 1 b
(B) a 2 b
(C) 2a 1 b
(D) 4a 2 6b
(E) 17a 1 17b
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Practice Test 5 565
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16. What is the equation of the line that

is the perpendicular bisector of the
line segment connecting points (21,1)
and (3,5) on the xy plane?
(A) y 5 2x 1 1
(B) y 5 x 2 2
(C) y 52x 1 4
(D) y 523x 1 2
(E) y 5 x 1 3
17. If 2x 1 1 is a positive multiple of 5,
and if 2x 1 1 ≤ 100, how many
possible values of x are integers?
(A) 5
(B) 10
(C) 11
(D) 15
(E) 20
18. An empty swimming pool can be
filled to capacity through an inlet
pipe in 3 hours, and it can be
completely drained by a drainpipe in
6 hours. If both pipes are fully open
at the same time, in how many hours
will the empty pool be filled to
capacity?
(A) 4
(B) 4.5
(C) 5
(D) 5.5
(E) 6
QUESTIONS 19–20 REFER TO THE

FOLLOWING TABLE:
WORLDWIDE SALES OF
XYZ MOTOR COMPANY
(2004–05 Model Year)
Automobile Model
Basic Standard Deluxe
Purchaser
Category
U.S. institutions 3.6 8.5 1.9
U.S. consumers 7.5 11.4 2.0
Foreign institutions 1.7 4.9 2.2
Foreign consumers 1.0 5.1 0.8
Note: All numbers are in thousands.
19. Which of the following most nearly
describes sales totaling 9000 automo-
biles for the 2004–2005 model year?
(A) All U.S. institution sales of the
standard and deluxe models
(B) All foreign sales of the standard
model
(C) All foreign-institution sales
(D) All consumer sales of the
basic model
(E) All institution sales of the
standard model
20. Of the total number of automobiles
sold to the institutions during the
2004–2005 model year, which of the
following most closely approximates
the percentage that were NOT

standard models?
(A) 24%
(B) 36%
(C) 41%
(D) 59%
(E) 68%
21. What is Michael’s monthly salary?
(1) If Michael’s monthly salary were
cut by 25 percent while Sam’s
monthly salary were raised by
25 percent, they would earn the
same salary.
(2) Michael’s monthly salary is
$1000 more than Sam’s.
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22. In a room are five chairs to accommo-
date 3 people, one person to a chair.
How many seating arrangements are
possible?
(A) 45
(B) 60
(C) 72
(D) 90
(E) 120
23.
N is 83
1

3
% of what number?
(A)
6
5N
(B)
7N
8
(C)
5N
4
(D)
6N
5
(E)
N 1
50
3
24. Mona has $2.05 in quarters and
dimes. How many quarters does she
have?
(1) She has more quarters than
dimes.
(2) She has a total of ten coins.
25. What number must be subtracted from
the denominator of the fraction
7
16
to
change the value of the fraction to

4
9
?
(A)
1
4
(B)
5
16
(C)
7
9
(D)
3
2
(E)
5
3
26. Four people plan to rent a summer
cottage, apportioning the rent equally
among themselves. What is the total
amount of rent for the cottage?
(1) If one additional person were to
join in renting the cottage, each
person would pay 20 percent of
the total rent.
(2) Three of the four people would
pay a total of $2400 in rent.
27.
30

O
40
O
45
O
x
O
In the figure above, what is the value
of x?
(A) 25
(B) 30
(C) 40
(D) 45
(E) 65
28. In a geometric sequence, each term is
a constant multiple of the preceding
one. If the first three terms in a
geometric sequence are 22, x, and
28, which of the following could be
the sixth term in the series?
(A) 24096
(B) 21024
(C) 64
(D) 1024
(E) 2048
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Practice Test 5 567
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29. How long does it take Sam to eat an
entire large pizza?
(1) Thomas can eat the same large
pizza in 8 minutes.
(2) Sam and Thomas together can
eat the same large pizza in 6
1
2
minutes.
30. If x . 0, is x . y ?
(1) 5x 2 4y 5 3
(2) 4y 2 5x 5 3
31.
If x 5 2 and y 5 –2, then
x
4
2 y
5
x
4
y
5
5
(A)
2
3
32
(B) 0
(C)
1

32
(D)
1
16
(E) 1
32. What is the one, unique value of x ?
(1) x
2
2 4x 1 3 5 0
(2) x
2
2 2x 1 1 5 0
33.
A
B
C
D
If the length of arc ACB in the circle
above is 5p, is the length of
AB
greater than the length of
CD ?
(1) The length of
AB equals the
circle’s diameter.
(2) The length of
CD is 5.
34. A passenger train and a freight train
leave from the same station at the
same time. Over 3 hours, the passen-

ger train travels 45 miles per hour
faster, on average, than the freight
train. Which of the following ex-
presses the combined distance the
two trains have traveled after 3
hours, where x represents the
number of miles the freight train
traveled per hour, on average?
(A) 3x 1 45
(B) 6x 1 45
(C) 3x 1 120
(D) 3x 1 135
(E) 6x 1 135
35. If the total price of five grocery items
is $6.05, what is the price of the most
expensive of these items?
(1) The price of the most expensive
item is exactly 50 percent greater
than the price of each of the
other four items.
(2) The price of each item (except the
most expensive item) is $1.10.
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36. If s is an integer greater than 1, how
many 1-inch cubes can be packed
into a rectangular box having sides s,
s 1

3
2
, and s 2 1, measured in
inches?
(A) s
3
2 s
(B)
s
3
1
s
2
2
1
s
2
(C) s
3
2 2s 1 s
(D) s
3
1 s
2
2 s
(E) s
3
37. A bag of marbles contains twice as
many red marbles as blue marbles,
and twice as many blue marbles as

green marbles. If these are the only
colors of marbles in the bag, what is
the probability of randomly picking a
blue marble from the bag?
(A)
1
6
(B)
2
9
(C)
1
4
(D)
2
7
(E)
1
3
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Practice Test 5 569
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VERBAL SECTION
41 QUESTIONS • 75 MINUTES
Directions for Sentence Correction Questions: (These directions will appear on
your screen before your first Sentence Correction question.)
This question presents a sentence, all or part of which is underlined. Beneath the
sentence you will find five ways of phrasing the underlined part. The first of these

repeats the original; the other four are different. If you think the original is best, choose
the first answer; otherwise choose one of the others.
This question tests correctness and effectiveness of expression. In choosing your answer,
follow the requirements of Standard Written English; that is, pay attention to grammar,
choice of words, and sentence construction. Choose the answer that produces the most
effective sentence; this answer should be clear and exact, without awkwardness,
ambiguity, redundancy, or grammatical error.
Directions for Critical Reasoning Questions: (These directions will appear on your
screen before your first Critical Reasoning question.)
For this question, select the best of the answer choices given.
Directions for Reading Comprehension Questions: (These directions will appear
on your screen before your first group of Reading Comprehension questions.)
The questions in this group are based on the content of a passage. After reading the
passage, choose the best answer to each question. Answer all the questions following the
passage on the basis of what is stated or implied in the passage.
1. Raising a child alone and holding
down a full-time job require good
organizational skills, not to mention
a lot of support from friends and
coworkers.
(A) require good organizational
skills
(B) requires good organization
skills
(C) requires the skill of good
organization
(D) require a person to be well
organized
(E) requires good organizational
skill

2. J. S. Bach’s The Musical Offering,
long considered one of his minor
works, but nevertheless a masterful
composition, consisting of a series of
canons, fugues, and other pieces
based on the same musical theme.
(A) but nevertheless
(B) would instead be considered
(C) but rather
(D) and is nevertheless
(E) is nevertheless
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3. A reliable survey indicates that
college graduates change employers
four times on average during the
first ten years after college gradua-
tion. Therefore, in order to avoid
employee turnover, business adminis-
trators in charge of hiring new
employees should favor job applicants
who obtained college degrees at least
ten years earlier.
The advice about how to avoid
employee turnover rests on which of
the following assumptions?
(A) Employee turnover among
businesses that hire employees

without college degrees is
greater than among businesses
that hire only employees with
college degrees.
(B) Job changes within the same
company are less common than
job changes from one employer
to another.
(C) Employees who graduated from
college at least ten years ago
change employers less fre-
quently on average than other
employees.
(D) Most employees who leave their
jobs do so upon either request
or demand of their employers
rather than by their own
initiative.
(E) The survey excluded college
graduates who interrupted their
vocational careers to pursue
advanced academic degrees.
4. Although residents of the north-
central region of the United States
are not known to have any accent,
they nevertheless share certain
distinctive utterances that help
distinguish their speech from
other regions.
(A) distinguish their speech from

(B) distinguishes their speech from
those of
(C) distinguish their speech from
that of
(D) distinguish the way they
speak from
(E) distinguishes their manner of
speaking from
5. Driving excessively fast has been
demonstrated to decrease the number
of miles one can drive per gallon of
fuel. Gary has recently been experi-
encing a decrease in mileage per
gallon of fuel while driving his car.
This clearly proves that Gary has
been driving excessively fast lately.
Which of the following statements, if
true, would most seriously weaken
the conclusion about Gary’s driving?
(A) Recently Gary’s speedometer
has been indicating the speed of
his car as lower than the car’s
actual speed.
(B) Recently Gary has been driving
more miles per day on average
than before he began experienc-
ing a decrease in fuel mileage.
(C) Other tests have shown that a
car’s speed affects fuel mileage
more than any other single factor.

(D) Before Gary began driving
excessively fast his speedometer
over-represented his car’s
actual speed.
(E) Recently the tires on Gary’s car
have been losing air pressure,
and low tire air pressure is
known to lower fuel mileage.
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Practice Test 5 571
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6. Expensive television advertising
campaigns clearly help political
candidates win elections, as
evidenced by the fact that, in most
political elections, the candidate
with the most campaign money
ultimately wins.
Which of the following, if true,
would provide most support for the
argument above?
(A) Endorsements from minor
political office-holders generally
have no effect on a candidate’s
chances of winning an election.
(B) In most cases, candidates who
currently hold the office for
which they seek re-election

have more available campaign
money than their competitors.
(C) Expensive television advertising
campaigns are waged most
frequently by candidates who
have more available campaign
money than their competitors.
(D) When it comes to choosing
among candidates, the voting
public tends to disregard how a
candidate is portrayed in
television advertisements.
(E) Nearly any political candidate
can afford to wage some type of
television advertising campaign.
QUESTIONS 7–9 ARE BASED ON THE
FOLLOWING PASSAGE:
Line The twentieth-century discovery of
Archaeans, which did not fit into the
kingdom classification scheme for
biological life, led to the creation of the
domain classification level, above the
kingdom level. This new level included
the new domain Archaean. Prior to the
discovery of Archaeans, it had been
generally accepted that no life could
exist in temperatures much hotter
than 60 degrees centigrade. This limit
was set because it was thought that
the molecular integrity of vital cellular

components could not be maintained
beyond such temperatures. The
thermal capacity of cellular life, it was
believed, was a fixture across all
biological organisms. Archaeans, in
recent decades, have repeatedly
demonstrated that the previously
maintained thermal threshold for life
was far too low. So-called extremophilic
Archaeans have been discovered to
thrive in temperatures as high as 160
degrees centigrade. Such discoveries
have required a broadening of biology’s
conceptions concerning what environ-
ments are hospitable to life.
7. The author of the passage implies
that extremophilic Archaeans
(A) are able to maintain molecular
integrity of cellular components
past what was formerly ac-
cepted as the thermal threshold
of life.
(B) have been known to exist in
moderate environments for
some years, but their extremo-
philic properties have only
recently been discovered.
(C) are able to live and thrive in
temperatures higher than 160
degrees centigrade.

(D) were responsible for the
development of a distinct
kingdom in the classification
scheme for biological life.
(E) are the oldest known form of
multi-cellular biologic life.
8. The passage’s author suggests that
the “thermal threshold” (line 21) is
(A) the thermal capacity of extre-
mophiles.
(B) the critical point temperature at
which the metabolic pathways
of extremophiles become
functional.
(C) an environmental extremity
indicator.
(D) the temperature at which the
molecular integrity of cellular
components of an organism are
compromised.
(E) a biological constant across all
of nature.
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