1A student’s average (arithmetic mean) test score on 4
tests is 78. What must be the student’s score on a 5th test for the student’s average score
on the 5 tests to be 80?
2From a group of 3 boys and 3 girls, 4 children are to
be randomly selected. What is the probability that equal numbers of boys and girls will be
3If x and y are positive integers and 1 + x + y + xy =
15, what is the value of x + y?
4If Ann saves x dollars each week and Beth saves y
dollars each week, what is the total amount that they save per week?
(1) Beth saves $5 more per week than Ann saves per week.
(2) It takes Ann 6 weeks to save the same amount that Beth saves in 5 weeks.
5If x is a positive integer, is the remainder 0 when
3x + 1 is divided by 10?
(1) x = 4n + 2, where n is a positive integer.
(2) x > 4
6If r, s, and w are positive numbers such that w = 60r
+ 80s and r + s = 1, is w < 70?
(1) r > 0.5
(2) r > s
7If a code word is defined to be a sequence of
different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the
ratio of the number of 5-letter code words to the number of 4-letter code words?
8Which of the following fractions has a decimal
equivalent that is a terminating decimal?
9Company S produces two kinds of stereos: basic and
deluxe. Of the stereos produced by Company S last month, 2/3 were basic and the rest were
deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a
basic stereo, then the number of hours it took to produce the deluxe stereos last month was
what fraction of the total number of hours it took to produce all the stereos?
10A certain machine produces 1,000 units of product P
per hour. Working continuously at this constant rate, this machine will produce how many
units of product P in 7 days?
11If 5x – 5x- 3 =
(124)(5y), what is y in terms of x?
12Lines k and m are parallel to each other. Is the
slope of line k positive?
(1) Line k passes through the point (3, 2).
(2) Line m passes through the point (-3, 2).
13Theater M has 25 rows with 27 seats in each row. How
many of the seats were occupied during a certain show?
(1) During the show, there was an average (arithmetic mean) of 10 unoccupied seats per row
for the front 20 rows.
(2) During the show, there was an average (arithmetic mean) of 20 unoccupied seats per row
for the back 15 rows.
14The number of defects in the first five cars to come
through a new production line are 9, 7, 10, 4, and 6, respectively. If the sixth car through
the production line has either 3, 7, or 12 defects, for which of theses values does the mean
number of defects per car for the first six cars equal the median?
15The figure above shows two entries, indicated by m
and n, in an addition table. What is the value of n + m?
(1) d + y = -3
(2) e + z = 12
16On a map Town G is 10 centimeters due east of Town H
and 8 centimeters due south of Town J. Which of the following is closest to the
straight-line distance, in centimeters, between Town H and Town J on the map?
17If x is the product of the positive integers from 1
to 8, inclusive, and if i, k, m, and p are positive integers such that x = 2i3k5m7p, then i + k + m + p =
18In the xy-plane, the line with equation ax + by + c
= 0, where abc ≠ 0, has slope 2/3 . What is the value of b?
(1) a = 4
(2) c = −6
19This year Henry will save a certain amount of his
income, and he will spend the rest. Next year Henry will have no income, but for each dollar
that he saves this year, he will have 1 + r dollars available to spend. In terms of r, what
fraction of his income should Henry save this year so that next year the amount he was
available to spend will be equal to half the amount that he spends this year?
20Leo can buy a certain computer for p1 dollars in
State A, where the sales tax is t1 percent, or he can buy the same computer for p2 dollars
in State B, where the sales tax is t2 percent. Is the total cost of the computer greater in
State A than in State B?
(1) t1 > t2
(2) p1t1 > p2t2
21Is x an odd integer?
(1) x + 3 is an even integer.
(2) x/3 is an odd integer.
22The surface of a certain planet reflects 80 percent
of the light that strikes it. The clouds around the planet then absorb 40 percent of the
reflected light. What percent of the light that strikes the planet is reflected from the
surface and passes through the clouds without being absorbed?
23The selling price of an article is equal to the cost
of the article plus the markup. The markup on a certain television set is what percent of
the selling price?
(1) The markup on the television set is 25 percent of the cost.
(2) The selling price of the television set is $250.
24If 7x/3 + a = 8 and a > 8, then, in terms of a,
25What is the sum of a certain pair of consecutive odd
(1) At least one of the integers is negative.
(2) At least one of the integers is positive.
26If an automobile averaged 22.5 miles per gallon of
gasoline, approximately how many kilometers per liter of gasoline did the automobile
average? (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest
27In the figure, points A, B, C, D, and E lie on a
line. A is on both circles, B is the center of the smaller circle, C is the center of the
larger circle, D is on the smaller circle, and E is on the larger circle. What is the area
of the region inside the larger circle and outside the smaller circle?
(1) AB = 3 and BC =2
(2) CD =1 and DE = 4
28A certain company assigns employees to offices in
such a way that some of the offices can be empty and more than one employee can be assigned
to an office. In how many ways can the company assign 3 employees to 2 different
29If the sequence x1, x2,
x3, …, xn, … is such that x1 = 3 and xn+1 =
2xn – 1 for n ≥ 1, then x20 – x19 =
30If y is the smallest positive integer such that
3,150 multiplied by y is the square of an integer, then y must be
31A certain quantity is measured on two different
scales, the R-scale and the S-scale, that are related linearly. Measurements on the R-scale
of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What
measurement on the R-scale corresponds to a measurement of 100 on the S-scale?
32If x3y4 = 5,000, is y = 5?
(1) y is a positive integer.
(2) x is an integer.
33The table above shows the results of a survey of 100
voters each responded “favorable” or “unfavorable” or “not sure” when asked about their
impressions of candidate M and of candidate N. What was the number of voters who responded
“favorable” for both candidates?
(1) The number of voters who did not respond “favorable” for either candidate was 40.
(2) The number of voters who responded “unfavorable” for both candidates was 10.
34If n is a positive integer, what is the remainder
when 38n+3 + 2 is divided by 5?
35The interior of a rectangular carton is designed by
a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to
height of 3 : 2 : 2. In terms of x, which of the following equals the height of the carton,
36How many integers from 0 to 50, inclusive, have a
remainder of 1 when divided by 3 ?
37How many different factors does the integer n
(1) n = a4b3, where a and b are different positive prime numbers.
(2) The only positive prime numbers that are factors of n are 5 and 7.
1Because of wireless service costs plummeting in the
last year, and as mobile
Phones are increasingly common, many people now using their mobile phones
To make calls across a wide region at night and on weekends, when numerous
Wireless companies provide unlimited airtime for a relatively small monthly fee.
2In two months, the legal minimum wage in the country
of Kirlandia will increase
from five Kirlandic dollars(KD5.00) Per hour to KD5.50 per hour. Opponents of
this increase have argued that the resulting rise in wages will drive the inflation
rate up. In fact its impact on wages will probably be negligible, since only a
very small proportion of all Kirfandic workers are currently receiving less than
KD5.50 per hour.Which of the following, if true, most seriously weakens the argument?
Mel: The official salary for judges has always been too low to attract the best
Candidates to the job. The legislature’s move to raise the salary has
done nothing to improve the situation, because it was coupled with
a ban on receiving money for lectures and teaching engagements.
Pat: No, the raise in salary really does improve the situation. Since very few
judges teach or give lectures, the ban will have little or no negative
Pat’s response to Mel is inadequate in that it
4Recent findings lend strong support to the theory
that a black hole lies at the center of the Milky Way and of many of the 100 billion
other galaxies estimated to exist in the universe.
5For many revisionist historians, Christopher Columbus
has come to
personify devastation and enslavement in the name of progress that
has decimated native peoples of the Western Hemisphere.
Q6 TO 9:
Linda Kerber argued in the mid-
1980’s that after the American Revolution
(1775-1783), an ideology of “republican
linemotherhood” resulted in a surge of edu-
5cational opportunities for women in the
United States. Kerber maintained that
the leaders of the new nation wanted
women to be educated in order to raise
oolitically virtuous sons. A virtuous citi-
10zenry was considered essential to the
success of the country’s republican form
of government; virtue was to be instilled
not only by churches and schools, but
by families, where the mother’s role
15was crucial. Thus, according to Kerber,
motherhood became pivotal to the fate
of the republic, providing justification for
an unprecedented attention to female
20Introduction of the republican moth-
erhood thesis dramatically changed
historiography. Prior to Kerber’s work,
educational historians barely mentioned
women and girls; Thomas Woody’s 1929
25work is the notable exception. Examining
newspaper advertisements for acade-
mies. Woody found that educational
opportunities increased for both girls
and boys around 1750. pointing to “An
30Essay on Woman” (1753) as reflecting
a shirt in view. Woody also claimed that
practical education for females had
many advocates before the Revolution,
Woody’s evidence challenges the notion
35that the Revgolution changed attiludes
regarding female education, although it
may have accelerated earlier trends.
Historians’ reliance on Kerber’s “repub-
lican mother hood” thesis may have
40obscured the presence of these trends,
making it difficult to determine to what
extent the Revolution really changed
6According to the passage, kerber main-
Tained that which of the following led to
An increase in educational opportunities
For women in the United States after the
7According to the passage. Kerber argued
That political leaders thought that the form
Of government adopted by the United States
After the American Revolution depended on
Which of the following for its success?
8According to the passage, within the field
Of educational history, Thomas Woody’s
1929 work was
9The passage suggests that, with regard
to the history of women’s education in the
United States, Kerber’s work differs from
Woody’s primarily concerning which of
10In 1926, in her second attempt to swim across the
Gertrude Ederle not only crossed the Channel against currents that
Forced her to swim thirty-five miles instead of the minimal twenty-one,
but she set a record for speed as well, by swimming the distance in
almost two hours faster than anyone had yet done.
11which of the following most logically completes the
On the whole, scientists do their most creative work before age forty, a
tendency that has been taken to show that aging carries with it a loss of
creative capacity. An alternative explanation is that by age forty most
scientists have worked in their field for fifteen or more years and that by
then they have exhausted the opportunity for creative work in that field.
Supporting this explanation is the finding that ____
12In Kantovia, physicians’ income comes from insurance
companies, which require
physicians to document their decisions in treating patients and to justify deviations
from the companies’ treatment guidelines. Ten years ago physicians were allowed
more discretion. Most physicians believe that the companies’ requirements now
prevent them from spending enough time with patients. Yet the average amount of
time a patient spends with a physician during an office visit has actually increased
somewhat over the last ten years.
Which of the following, if true, most helps to resolve the apparent discrepancy
between physicians’ perceptions and the change in the actual time spent?
Q13 to Q15:
Grassland songbirds often nest in
the same grassland-wetland complexes
as waterfowl, particularly in a certain
linepart of those complexes, namely,
5upland habitats surrounding wetlands.
Although some wildlife management
procedures directed at waterfowl, such
as habitat enhancement or restoration,
may also benefit songbirds , the impact
10of others, especially the control of
waterfowl predators, remains difficult to
predict. For example, most predators
of waterfowl nests prey opportunistic-
ally on songbird nests, and removing
15these predators could directly increase
songbird nesting success. Alterna-
tively, small mammals such as mice
and ground squirrels are important
in the diet of many waterfowl-nest
20predators and can themselves be
important predators of songbird
nets. Thus. Removing waterfowl-nest
predators could affect songbird nesting
success through subsequent increases
25in small-mammal populations.
In 1995 and 1996, researchers
trapped and removed certain waterfowl-
nest predators. primary raccoons and
striped skunks, then observed subse-
30quent survival rates for songbird nests.
Surprisingly. They observed no sig-
nificant effect on songbird nesting
success. This may be due to several
factors. Neither raccoons nor striped
35skunks consume ground squirrels,
which are important predators of song-
bird nests. Thus, their removal may
not have led to significant increases
in populations of smaller predators.
40Additionally, both raccoons and striped
skunks prefer wetlands and spend little
time in upland habitats; removing these
species may not have increased the
nesting success of songbirds in the
uplands enough to allow detection.
13NOTE: You must scroll to read the answer choices for
According to the passage, which of the
following is true about the role played
by ground squirrels in the ecology of
14Which of the following best describes
the function of the sentence “Neither
raccoons…songbird nests” (lines 34-37)
in the context of the passage as a whole?
15The primary purpose of the passage is to
16A Harvard anthropologist has proposed that using
fire to cook
food could be dated back to almost two million years and that
it could explain hominid features like having a large brain and
17Until recently, the Inuit people led a nomadic
existence, sheltering in
igloos, the ice-block domes that are peculiar to north-central Canada,
and in structures made of stones, bones, driftwood, and skins.
18In contrast to environmentalists proposals to limit
emissions of certain
pollutants, the administration proposed calling for mandatory restrictions of
only three such pollutants from power plants-mercury, sulfur dioxide, and
nitrogen oxides-and the plan would delay such cuts until 2010 or later.
19From 1980 to 1989, total consumption of fish in the
country of Jurania increased
by 4.5 percent, and total consumption of poultry products there increased by
9.0 percent. During the same period, the population of Jurania increased by
6 percent, in part due to immigration to Jurania from other countries in the region.
If the statements above are true, which of the following must also be true on the
basis of them?
20Most states impose limitations on the authority of
the legislature to borrow money, with their objectives being to protect taxpayers and
the credit of the state government.
21Which of the following most logically completes the
Editorial in Golbindian Newspaper: For almost three months, opposition parties
have been mounting daily street demonstrations in the capital in an effort to
pressure the ruling party into calling an election. Though the demonstrations
were well attended at first, attendance has declined steadily in recent weeks.
However, the decline in attendance does not indicate that popular support for
the opposition’s demands is dropping, since _____
22Springfield Fire Commissioner: the vast majority of
false fire alarms
are prank calls made anonymously from fire alarm boxes on street
corners. Since virtually everyone has access to a private telephone,
these alarm boxes have outlived their usefulness. Therefore, we
propose to remove the boxes. Removing the boxes will reduce the
number of prank calls without hampering people’s ability to report a fire.
Which of the following, if true, most strongly supports the claim that the
proposal, if carried out, will have the announced effect?
23Because fish look through water, their eyes are
different from a mammal.
24Although improved efficiency in converting harvested
trees into wood products
may reduce harvest rates, it will stimulate demand by increasing supply and
lowering prices, thereby boosting consumption.
Q25 to Q28:
In mid-February 1917 a
women’s movement independent
of political affiliation erupted in
5New York City, the stronghold of
(5) the Socialist party in the United
states. Protesting against the high
cost of living, thousands of women
refused to buy chickens, fish, and
vegetables. The boycott shut.
10down much of the City’s foodstuffs
marketing for two weeks, riveting
public attention on the issue of
food prices, which had increased
partly as a result of increased
15exports of food to Europe that had
been occurring since the outbreak
of the First World War.
By early 1917 the Socialist
party had established itself as a
20major political presence in New
York City. New York Socialists,
whose customary spheres of
struggle were electoral work and
trade union organizing, seized the
25opportunity and quickly organized
an extensive series of cost-of-
living protests designed to direct
the women’s movement toward
Socialist goals. Underneath the
30Socialists’ brief commitment to
cost-of-living organizing lay a
basic indifference to the issue
itself. While some Socialists did
view price protests as a direct
35step toward socialism, most
Socialists ultimately sought to
divert the cost-of-living movement
into alternative channels of protest.
Union organizing, they argued,
40was the best method through which
to combat the high cost of living.
For others, cost-of-living or oganiz-
ing was valuable insofar as it led
women into the struggle for suf-
45frage, and similarly, the suffrage
struggle was valuable insofar as
it moved United States society
one step closer to socialism.
Although New York’s Social-
50ists saw the cost-of-living issue
as, at best ,secondary or tertiary
to the real task at hand, the boy-
cotters, by sharp contrast, joined
the price protest movement out of
55an urgent and deeply felt commit-
ment to the cost-of-living issue.
A shared experience of swiftly
declining living standards caused
by rising food prices drove these
60women to protest. Consumer
organizing spoke directly to their
daily lives and concerns; they
saw cheaper food as a valuable
end in itself. Food price protests
65were these women’s way of orga-
nizing at their own workplace, as
workers whose occupation was
shopping and preparing food for
25The author suggests which of the following about
the New York Socialists’ commitment to the cost-
26It can be inferred from the passage that the goal
of the boycotting women was the
27Which of the following best states the function of
passage as a whole?
28According to the passage ,most New York
Socialists believed which of the following about
the cost-of-living movement?
29The army cutworm moth is a critical source of fat
of Yellowstone National Park’s grizzly bears; they overturn
rocks to find them and consuming as many as 40,000 apiece
in a single day.
Museums that house Renaissance oil paintings typically store them in environments that
are carefully kept within narrow margins of temperature and humidity to inhibit any deteri-
oration. Laboratory tests have shown that the kind of oil paint used in these paintings
actually adjusts to climatic changes quite well. If, as some museum directors believe,
paint is the most sensitive substance in these works, then by relaxing the stan-
dards for temperature and humidity control, museums can reduce energy costs
without risking damage to these paintings. Museums would be rash to relax those
standards, however, since results of preliminary tests indicate that gesso, a compound
routinely used by Renaissance artists to help paint adhere to the canvas, is unable to
withstand significant variations in humidity.
In the argument above, the two portions in boldface play which of the following roles?
31New items developed for automobiles in the 1997
model year included
a safer air bag , which, unlike previous air bags, eliminated the possibility
that a burst of smoke would appear when the bag inflated, and making an
already terrified passenger think the car was on fire.
32Nitrogen dioxide is a pollutant emitted by
automobiles. Catalytic converters,
devices designed to reduce nitrogen dioxide emissions, have been required
in all new cars in Donia since 1993, and as a result, nitrogen dioxide emis-
sions have been significantly reduced throughout most of the country. Yet
althouth the proportion of new cars in Donia’s capital city has always been
comparatively high, nitrogen dioxide emissions there have showed only an
insignificant decline since 1993.
Which of the following, if true, most helps to explain the insignificant decline
in nitrogen dioxide emissions in Donia’s capital city?
Q33 to Q35:
In corporate purchasing,
competitive scrutiny is typically
limited to suppliers of items that are
linedirectly related to end products.
5With “indirect” purchases (such as
computers, advertising, and legal
services), which are not directly
related to production, corporations
often favor “supplier partnerships”
10(arrangements in which the
purchaser forgoes the right to
pursue alternative suppliers), which
can inappropriately shelter suppliers
from rigorous competitive scrutiny
15that might afford the purchaser
economic leverage. There are two
of alternatives and ease of changing
suppliers—that companies should.
20use to evaluate the feasibility of
subjecting suppliers of indirect
purchases to competitive scrutiny.
This can create four possible
25In Type 1 situations, there are
many alternatives and change is
relatively easy. Open pursuit of
alternatives—by frequent corn-
petitive bidding, if possible—will
30likely yield the best results. In
Type 2 situations, where there
are many alternatives but change
is difficult—as for providers of
employee health-care benefits—it
35is important to continuously test
the market and use the results to
secure concessions from existing
suppliers. Alternatives provide a
credible threat to suppliers, even if
40the ability to switch is constrained.
In Type 3 situations, there are few
alternatives, but the ability to switch
without difficulty creates a threat that
companies can use to negotiate.
45concession from existing suppliers.
In Type 4 situations, where there
are few alternatives and change
is difficult, partnerships may be
33Which of the following best describes the
relation of the second paragraph to the first?
34Which of the following can be inferred about
supplier partnerships, as they are described
in the passage?
35According to the passage, which of the following
factors distinguishes an indirect purchase from
If the statements above are true, then it is also possible that in Patton City
36The chemical adenosine is released by brain cells
when those cells are active.
Adenosine then binds to more and more sites on cells in certain areas of the
brain, as the total amount released gradually increases during wakefulness.
During sleep, the number of sites to which adenosine is bound decreases. Some
researchers have hypothesized that it is the cumulative binding of adenosine to a
large number of sites that causes the onset of sleep.
Which of the following, if true, provides the most support for the researchers’
37Though the law will require emissions testing of all
diesel vehicles, from
tractor trailers to excursion buses, it will have no effect on sport utility
vehicles, almost all of which are gasoline powered, and will not be sub-
jected to emissions-control standards as stringent as they are for
38Doctors hope that one day the body’s master cells,
cells, can be directed to grow in organs or tissues appropriate for
transplant, use them to test drugs and potentially toxic chemicals,
and may study them to gain insight into basic human biology.
39Navigators have known for thousands of years that
has variable currents, but it is only in the last half century that
a reasonably clear picture has emerged of the patterns and
causes of ocean currents.
40For similar cars and drivers, automobile insurance
for collision damage has
always cost more in Greatport than in Faimont. Police studies, however,
show that cars owned by Greatport residents are, on average, slightly less
likely to be involved in a collision than cars in Fairmont. Clearly, therefore,
insurance companies are making a greater profit on collision-damage
insurance in Greatport than in Fairmont.
Which of the following is an assumption on which the argument depends?
41Prospecting for gold during the California gold rush
was a relatively
easy task, because of erosion, prehistoric glacier movement, and
ancient, gold-bearing riverbeds thrust to the surface by volcanic
activity put gold literally within reach for anybody with a pan or shovel.