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# MATH.13

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1 Math Section ------------------------------------------------------------------------------------------------------------ Q1: The population of City X is 50 percent of the population of City Y. The population of City X is what percent of the total population of City X and City Y? A. 25% B. 33 3 1 % C. 40% D...

Math Section

------------------------------------------------------------------------------------------------------------ Q1:

The population of City X is 50 percent of the population of City Y. The population of City X is what percent of the total population of City X and City Y?

A. 25%

1B. 33% 3

C. 40%

D. 50%

2E. 66% 3

------------------------------------------------------------------------------------------------------------ Q2:

Guy’s net income equals his gross income minus his deductions. By what percent did

Guy’s net income change on January 1, 1989, when both his gross income and his

deductions increased?

(1) Guy’s gross income increased by 4 percent on January 1, 1989.

(2) Guy’s deductions increased by 15 percent on January 1, 1989.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

------------------------------------------------------------------------------------------------------------ Q3:

Each participant in a certain study was assigned a sequence of 3 different letters from the

set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant

and if 36 of the possible sequences were not assigned, what was the number of

participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)

A. 20

B. 92

C. 300

D. 372

E. 476

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Q4:

Of the total amount that Jill spent on a shopping trip, excluding taxes, she spent 50

percent on clothing, 20 percent on food, and 30 percent on other items. If Jill paid a 4

percent tax on the clothing, no tax on the food, and an 8 percent tax on all other items,

then the total tax that she paid was what percent of the total amount that she spent,

excluding taxes?

A. 2.8%

B. 3.6%

C. 4.4%

D. 5.2%

E. 6.0%

------------------------------------------------------------------------------------------------------------ Q5: 3f x and y are positive, is xI > y?

x(1) > y

(2) x > y

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

------------------------------------------------------------------------------------------------------------ Q6:

The infinite sequence a, a,…, a,… is such that a = 2, a = -3, a = 5, a = -1, and a = 12n1234na for n > 4. What is the sum of the first 97 terms of the sequence? n-4

A. 72

B. 74

C. 75

D. 78

E. 80

------------------------------------------------------------------------------------------------------------ Q7:

For a certain race, 3 teams were allowed to enter 3 members each. A team earned 6 n points whenever one of its members finished in nth place, where 1 ? n ? 5. There were no ties, disqualifications, or withdrawals. If no team earned more than 6 points, what is

the least possible score a team could have earned?

A. 0

2

B. 1

C. 2

D. 3

E. 4

------------------------------------------------------------------------------------------------------------ Q8:

At a certain food stand, the price of each apple is ? 40 and the price of each orange is ? 60. Mary selects a total of 10 apples and oranges from the food stand, and the average

(arithmetic mean) price of the 10 pieces of fruit is ? 56. How many oranges must Mary

put back so that the average price of the pieces of fruit that she keeps is ? 52?

A. 1

B. 2

C. 3

D. 4

E. 5

Professor Vasquez gave a quiz to two classes. Was the range of scores for the first class

equal to the range of scores for the second class?

(1) In each class, the number of students taking the quiz was 26, and the lowest

score in each class was 70.

(2) In each class, the average (arithmetic mean) score on the quiz was 85.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

If x and y are positive integers, what is the value of x? xy(1) 35 = 1,125

(2) y = 3

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

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------------------------------------------------------------------------------------------------------------ Q11:

If d - 9 = 2d, then d =

A. -9

B. -3

C. 1

D. 3

E. 9

There are 11 women and 9 men in a certain club. If the club is to select a committee of 2

women and 2 men, how many different such committees are possible?

A. 120

B. 720

C. 1,060

D. 1,520

E. 1,980

------------------------------------------------------------------------------------------------------------ Q13:

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?

(1) Two of the interior angles of ABCD are right angles.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

\$10,000 is deposited in a certain account that pays r percent annual interest compounded

annually, the amount D(t), in dollars, that the deposit will grow to in t years is given by tD(t) = 10,000 {1+(r/100)}. What amount will the deposit grow to in 3 years?

(1) D(t) = 11,000

(2) r =10

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

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D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

------------------------------------------------------------------------------------------------------------ Q15:

If a and b are integers, is b even?

(1) 3a + 4b is even.

(2) 3a + 5b is even.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

The area of square S is equal to the area of rectangle R. What is the perimeter of square S?

(1) The length of one of the sides of rectangle R is twice the length of a side of

.square S

(2) The area of rectangle R is 36.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Q17:

A E

B C D

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In 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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is

sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

------------------------------------------------------------------------------------------------------------

Q18:

A certain company that sells only cars and trucks reported that revenues from car sales in 1997 were down 11 percent from 1996 and revenues from truck sales in 1997 were up 7 percent from 1996. If total revenues from car sales and truck sales in 1997 were up 1 percent from 1996, what is the ratio of revenue from car sales in 1996 to revenue from truck sales in 1996?

A. 1 : 2

B. 4 : 5

C. 1 : 1

D. 3 : 2

E. 5 : 3

------------------------------------------------------------------------------------------------------------

Q19:

6

11

10

9

8

7

6

5

4

3Number of Members2

1

0

1234567

Number of Hours

Yesterday each of the 35 members of a certain task force spent some time working on

project P. The graph shows the number of hours and the number of members who spent

that number of hours working on project P yesterday. What was the median number of

hours that the members of the task force spent working on project P yesterday?

A. 2

B. 3

C. 4

D. 5

E. 6

------------------------------------------------------------------------------------------------------------ Q20:

A certain list consists of 21 different numbers. If n is in the list and n is 4 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of

the sum of the 21 numbers in the list?

1A. 20

1B. 6

1C. 5

4D. 21

5E. 21

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------------------------------------------------------------------------------------------------------------ Q21:

Three printing presses, R, S, and T, working together at their respective constant rates,

can do a certain printing job in 4 hours. S and T, working together at their respective

constant rates, can do the same job in 5 hours. How many hours would it take R, working alone at its constant rate, to do the same job?

A. 8

B. 10

C. 12

D. 15

E. 20

When tossed, a certain coin has equal probability of landing on either side. If the coin is

tossed 3 times, what is the probability that it will land on the same side each time?

1A. 8

1B. 4

1C. 3

3D. 8

1E. 2

In the decimal representation of x, where 0 < x < 1, is the tenths digit if x nonzero?

(1) 16x is an integer.

(2) 8x is an integer.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

------------------------------------------------------------------------------------------------------------ Q24:

8

11of the number of girls is equal to of the total number of In a certain English class, 46

students. What is the ratio of the number of boys to the number of girls in the class?

A. 1 to 4

B. 1 to 3

C. 1 to 2

D. 2 to 3

E. 2 to 1

In the xy-plane, the vertices of a triangle have coordinates (0, 0), (3, 3), and (7, 0). What

is the perimeter of the triangle?

A. 13

34B.

43C.

D. 7;62

E. 12;32

If = 5, what is the value of n? n;5

2(1) n is not equal to 0. 2(2) n + 10n = 0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

A store’s selling price of \$2,240 for a certain computer would yield a profit of 40 percent

of the store’s cost for the computer. What selling price would yield a profit of 50 percent

of the computer’s cost?

A. \$2,400

B. \$2,464

C. \$2,650

D. \$2,732

E. \$2,800

9

If the volume of a small container is 14,520 cubic millimeters, what is the volume of the

container in cubic centimeters? (1 millimeter = 0.1 centimeter)

A. 0.1452

B. 1.452

C. 14.52

D. 145.2

E. 1,452

12622Which of the following is equal to ? 6322

63A. 2;263B. 229C. 23D. 2

E. 2

If the sequence x, xxx, … is such that x = 3 and x = 2x 1 for n ? 1, then x 12, 3, …, n1 n+1n20 x = 19

19A. 2 20B. 2 21C. 2 20 D. 2- 1 21 E. 2- 1

11In a certain English class, of the number of girls is equal to of the total number of 46

students. What is the ratio of the number of boys to the number of girls in the class?

A. 1 to 4

B. 1 to 3

C. 1 to 2

D. 2 to 3

E. 2 to 1

10

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