Math Section

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 selected?

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?

I. 3

II. 7

III. 12

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, 3x/7=

25What is the sum of a certain pair of consecutive odd integers?

(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 tenth.)

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 offices?

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, in feet?

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 have?

(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.

Verbal Section

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 effect.

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

women’s lives.

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 American Revolution?

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 the following?

10In 1926, in her second attempt to swim across the English Channel, 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 passage?

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 this question.

According to the passage, which of the following is true about the role played by ground squirrels in the ecology of grassland-wetland complexes?

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 small teeth.

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 below?

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 very 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

their families.

25The author suggests which of the following about the New York Socialists’ commitment to the cost- of-living movement?

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 the 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 for many 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

independent variables—availability

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 other purchases?

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’ hypothesis?

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 diesel-powered vehicles.

38Doctors hope that one day the body’s master cells, called stem 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 the ocean 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.