GMAT Quantitative - Diagnostic Test 1

- 1 -

DIAGNOSTIC TEST

The Quantitative section of the GMAT test uses problem solving and data sufficiency questions to gauge your skill level. ■ Problem Solving Questions Solve the problem and indicate the best of the answer choices given. Numbers: All numbers used are real numbers. Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated. ■ Data Sufficiency Questions Each data sufficiency problem consists of a question and two statements, labeled (1) and (2), which contain certain data. Using these data and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), decide whether the data given are sufficient for answering the question and then indicate one of the following answer choices: 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. Note: In data sufficiency problems that ask 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.

- 2 -

Example:

In ΔPQR, what is the value of x ? (1) PQ = PR (2) y = 40 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. Explanation: According to statement (1) PQ = PR; therefore, ΔPQR is isosceles and y = z. Since x + y + z = 180, it follows that x + 2y = 180. Since statement (1) does not give a value for y, you cannot answer the question using statement (1) alone. According to statement (2), y = 40; therefore, x + z = 140. Since statement (2) does not give a value for z, you cannot answer the question using statement (2) alone. Using both statements together, since x + 2y = 180 and the value of y is given, you can find the value of x. Therefore, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. Numbers: All numbers used are real numbers. Figures: • Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2). • Lines shown as straight are straight, and lines that appear jagged are also straight. • The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. • All figures lie in a plane unless otherwise indicated.

- 3 -

------------------------------------------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------ 1. The sum of three consecutive positive integers must be divisible by which of the following?

(A) 2 (B) 3 (C) 4 (D) 5 (E) 6

2. Ιn a certain class, the ratio of men to women is 3:5. If the class has 24 people in it, how

many are women? (Α) 9 (Β) 12 (C) 15 (D) 18 (Ε) 21

3. What is the lowest positive integer that is divisible by each of the integers 1 through 7,

inclusive? (Α) 420 (Β) 840 (C) 1,260 (D) 2,520 (Ε) 5,040

4. If x < y , is x2 < y2 ?

(1) y > 0 (2) x > 0 (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) ΒΟΤH 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 ΝΟΤ sufficient to answer the question asked, and additional data are needed

- 4 -

5. Α class of 48 students will sit in rows with the same number of students in each row. Each row must contain at least 2 students and there must be at least 2 rows. Α row is parallel to the front of the room. How many different arrangements are possible? (A) 4 (B) 5 (C) 6 (D) 8 (E) 10

6. A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4,

respectively. How many acres were used for corn? (A) 188 (B) 258 (C) 376 (D) 470 (E) 517

7. If r, s, and t are nonzero integers, is r5s3t4 negative?

(1) rt is negative. (2) s is negative. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





8. (16)(20) (8)(32)+ =

(Α) 4 20 (Β) 24 (C) 25 (D) 4 20 + 8 2 (Ε) 32

- 5 -

9. If 2x + 4y = 11 and 3x + 3y = 8 , then y – x =

(A) 16

−

(B) 83

(C) 176

(D) 3 (E) 4

10. If the perimeter of a rectangular garden plot is 34 feet and its area is 60 square feet, what

is the length of each of the longer sides? (Α) 5 ft (Β) 6 ft (C) 10 ft (D) 12 ft (Ε) 15 ft

11. Α sum of $200,000 from a certain estate was divided among a spouse and three children.

How much of the estate did the youngest child receive?

(1) The spouse received 12

of the sum from the estate, and the oldest child received 14

of the

remainder. (2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





- 6 -

12. The organizers of a fair projected a 25 percent increase in attendance this year over that of

last year, but attendance this year actually decreased by 20 percent. What percent of the projected attendance was the actual attendance? (A) 45% (B) 56% (C) 64% (D) 75% (E) 80%

13. Which of the following inequalities is equivalent to – 2 < x < 4 ?

(A) | x – 2 | < 4 (B) | x – 1 | < 3 (C) | x + 1 | < 3 (D) | x + 2 | < 4 (E) None of the above

14. The average of twenty consecutive integers in increasing order of size is 32.5 . What is the

average of the last three integers? (A) 35.5 (B) 37 (C) 39 (D) 41 (E) 42

15. If x and y are integers, is xy even?

(1) x = y + 1

(2) xy

is an even integer.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





- 7 -

16.

If the operation ◙ is defined for all a and b by the equation a ◙ b = 2a b3

, then

2 ◙ (3 ◙ – 1) = (A) 4 (B) 2

(C) – 43

(D) – 2 (E) – 4

17. The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how

many years old will Fred be y years from now, in terms of y ? (Α) y – 6 (Β) 2y – 6

(C) y2

– 6

(D) 3y2

– 6

(Ε) 5y2

– 6

18. If y is an integer, is y3 divisible by 9 ?

(1) y is divisible by 4. (2) y is divisible by 6. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





- 8 -

19. Α necklace is made by stringing N individual beads together in the repeating pattern red

bead, green bead, white bead, blue bead, and yellow bead. If the necklace design begins with a red bead and ends with a white bead, then N could equal (Α) 16 (Β) 32 (C) 41 (D) 54 (Ε) 68

20. After winning 50 percent of the first 20 games it played, Team Α won all of the remaining

games it played. What was the total number of games that Team Α won? (1) Team Α played 25 games altogether. (2) Team Α won 60 percent of all the games it played. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





21. Α bookstore that sells used books sells each of its paperback books for a certain price and

each of its hardcover books for a certain price. If Joe, Maria, and Paul bought books in this store, how much did Maria pay for 1 paperback book and 1 hardcover book? (1) Joe bought 2 paperback books and 3 hardcover books for $12.50. (2) Paul bought 4 paperback books and 6 hardcover books for $25.00. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





- 9 -

22. What is the units digit of (13)4(17)2(29)3 ?

(A) 9 (B) 7 (C) 5 (D) 3 (E) 1

23. In the figure, what is the length of the side AC ?

(A) 5 3 (B) 8 2 (C) 12 (D) 5 6 (E) 10 2

24. Α gear 50 inches in diameter turns a smaller gear 30 inches in diameter. If the larger gear

makes 15 revolutions, how many revolutions does the smaller gear make in that time? (Α) 9 (Β) 12 (C) 20 (D) 25 (Ε) 30

25. A credit card number has 6 nonzero digits. The first two digits are 4 and 2 in that order, the

third digit is bigger than 6, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist? (A) 27 (B) 36 (C) 72 (D) 81 (E) 422

26. A company wants to spend equal amounts of money for the purchase of two types of

computer printers costing $600 and $375 per unit, respectively. What is the fewest number of computer printers that the company can purchase? (A) 13 (B) 12 (C) 10 (D) 8 (E) 5

- 10 -

27. Hoses X and Y simultaneously fill an empty swimming pοοl that has a capacity of 50,000 liters. If the flow in each hose is independent of the flow in the other hose, how many hours will it take to fill the pοοl? (1) Hose X alone would take 28 hours to fill the pοοl. (2) Hose Υ alone would take 36 hours to fill the pοοl. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





28. In the figure above, how many of the points on line

segment PQ have coordinates that are both integers? (A) 5 (B) 8 (C) 10 (D) 11 (E) 20

29. On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If

10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night? (A) $600 (B) $800 (C) $1,000 (D) $1,600 (E) $2,400

30. The time it took car A to travel 400 miles was 2 hours less than the time it took car B to

travel the same distance. If car A’s average speed was 10 miles per hour greater than that of car B, what was car B’s average speed, in miles per hour?

(A) 20 (B) 30 (C) 40 (D) 50 (E) 80

- 11 -

31. If a and b are positive integers, what is the value of a + b ?

(1) a 5b 8=

(2) The greatest common divisor of a and b is 1. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





32. Seven different numbers are selected from the integers 1 to 100, and each number is divided

by 7. What is the sum of the remainders? (1) The range of the seven remainders is 6. (2) The seven numbers selected are consecutive integers. (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





33. The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches.

A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume? (A) 3 (B) 4 (C) 5 (D) 6 (E) 8

- 12 -

34. In the figure above, 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 to answer the question asked





35. Α student is to take her final exams in three subjects. The probability that she will pass the

first subject is 34

, the probability that she will pass the second subject is 23

, and the

probability that she will pass the third subject is 12

. What is the probability that she will

pass at least one of these three exams?

(Α) 14

(Β) 1124

(C) 1724

(D) 34

(Ε) 2324

- 13 -

36.

One night a certain motel rented 34

of its rooms, including 23

of its air-conditioned rooms.

If 35

of its rooms were air-conditioned, what percent of the rooms that were not rented were

air-conditioned? (A) 20%

(B) 33 13

%

(C) 35% (D) 40% (E) 80%

37. If the two-digit integers M and N are positive and have the same digits, but in reverse

order, what is the value of M + N ? (1) M + N is less than 200 (2) M + N is a multiple of 17 (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked





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

GMAT Quantitative - Diagnostic Test 1

Documents

Transcript of GMAT Quantitative - Diagnostic Test 1