GMAT Practice Set 12 - Quantitative

1. If the Board of Selectmen contains 4 positions, and if in the current election two candidates are running for each position, how many different combinations of candidates could be elected to the Board? A. 6 B. 8 C. 12 D. 16 E. 24

2. Dan and Craig stand back-to-back at point X. Dan begins to rollerblade in a straight line away from Craig at a rate of 4 miles per hour. Thirty minutes later, Craig begins to bicycle in a straight line in the exact opposite direction at a rate of 12 miles per hour. What is the positive difference, in hours, between the amount of time it takes Craig to cover the exact distance that Dan has covered and the amount of time it would take Craig to cover 50% more distance than Dan has covered? Round your answer to the nearest hundredth. A. .08 B. .16 C. .25 D. .50 E. .75

3. A college student is studying a population of fungi for his senior thesis. The population of fungi grows at a constant rate, and at 4 p.m., he places 3,000 fungi in a petri dish. Although he is supposed to check the population at every hour, he falls asleep and does not wake up until 8 p.m., at which point the fungi population is 243,000. What was the fungi population at 7 p.m.? A. 24,000 B. 27,000 C. 60,000 D. 81,000 E. 90,000

4. What is the average of p, q, and r? (1) p + 3q - 2r = 5 (2) 4p + 2q + 7r = -5 A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

5.

In the diagram above, if arc ABC is a semicircle, what is the length of AC? (1) AD = 2.5 (2) DC =10 A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

6. Given that the mean of Set A is 10, what is the range of two standard deviations above and below the mean? (1) One standard deviation above and below the mean ranges from 7 to 13. (2) The median of set A is 11. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

7. Last year, the 10 associates at the Tally Group received an average of $5,500 in bonuses. What was the average bonus received by the same associates this year? (1) Each of 5 associates received $600 more in bonuses this year than last, and each of the other 5 received $500 less. (2) Five of the associates received 10% more in bonuses this year, and 5 received 10% less. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

8. Of the 50 guests at a party, 10 percent are smokers. How many non-smokers must leave in order to bring the number of smokers up to 50 percent of the guests? A. 5 B. 10 C. 20 D. 35 E. 40

9. A fruit drink advertises that it has 5 percent apple juice. Children pour themselves another

cup of this fruit drink and then add

cup of fruit drink that has 50 percent apple juice.

Which is most nearly the percent of apple juice in the children's mixed drink? A. 12.5% B. 16.3% C. 17.5% D. 55.0% E. 65.0%

10. At a holiday store, the average price of the German nutcrackers is $225, and the average price of all nutcrackers is $205. What is the average price of the non-German nutcrackers? (1) The combined price of all the nutcrackers in the store is $2,050. (2) Sixty percent of the nutcrackers in the store are German. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

11.

What is the degree measure of angle a in the figure above? o

(1) d + e = 275 (2) b + c = 290

o

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

+2

12. What is the value of 11x- 11x , where x is the largest integer such that 11x is a factor of 30,030? A. -1331 B. -1320 C. -121 D. -120 E. -1

13. If James' Games sold 110,000 newspapers last year, how many will it sell this year? (1) Two years ago, James' Games sold 100,000 newspapers. (2) Three years ago, James' Games sold 90,000 newspapers. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

2

14. For all values of the integer x, is the product (x + 3)(x + 3x + 2) divisible by 4?

(1)

is an odd integer

(2) x is divisible by 16 A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

15. If it is true that -6 true? A. n

n

8

B. n = -6 C. n D. -10

-8 n

7

E. none of the above

10, which of the following must be

16. Set S consists of 7 integers. Is the range of set S less than 7? (1) The mean of set S is 4. (2) The standard deviation of set S is 0. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

17. The circular base of a planter sits on a level lawn, and just touches two straight garden walls at points W and Y. The walls come together at point X, which is 15 inches from the center of the planter. What is the area of the base of the planter? (1) Both points Y and W are 9 inches from the center of the planter. (2) Point W is 12 inches from point X. A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

18. Working alone at a constant rate, Alan can paint a house in a hours. Working alone at a constant rate, Bob can paint of the same house in b hours. Working together, Alan and Bob can paint

of the house in c hours. What is the value of b in

terms of a and c?

A.

B.

C.

D.

E.

19.

In the figure above, quadrilateral ABCD is a rhombus, and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus? Note: A rhombus is a quadrilateral with 4 equal sides. (1) AE || BD. (2) A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

20. If two sides of a triangle are 12 and 8, which of the following could be the area of the triangle? I. 35 II. 48 III. 56 A. I only B. I and II only C. I and III only D. II and III only E. I, II, and III

21. In the quadrilateral ABCD, side AD is parallel to side BC. Is ABCD a parallelogram? (1) AB = CD (2) AD = BC A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

22. If polygon A has fewer than 6 sides, how many sides does polygon A have? (1) The sum of the interior angles of polygon A is divisible by 30. (2) The sum of the interior angles of polygon A is divisible by 27. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

23. If

, is z

(1) x (2) |y|

8?

4 4

A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

24. In 2006, Top Tier University's recorded enrollment was 20% greater than in 2005. In 2005, Top Tier's enrollment was 25% greater than in 2004. What was the enrollment in 2004? (1) For every 40 students enrolled in 2004, 60 enrolled in 2006. (2) In 2006, enrollment was 2,000 students more than 2005. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

25. If both x and y are positive integers that are divisible by 10, is 10 the greatest common factor of x and y? (1) x = 4y (2) x - 3y = 10 A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

26. Several students are studying together for an exam. 60% of the students who studied less than 10 hours a week feel unprepared. 80% of students who studied 10 hours or more each week feel prepared. If 75% of the students studied less than 10 hours per week, what percent of the students feel prepared for the exam? A. 20 B. 25 C. 30 D. 35 E. 65

27. All but 50 of the 1,000 plants at the annual flower show were sold. Of the plants sold, 30 percent were sold at a discount of 25 percent off the full price, and the remaining plants were sold at the full price of $12. What was the total revenue from the plant sales? A. $8,550 B. $8,835 C. $10,545 D. $11,100 E. $12,000

28. If S is a set of integers with n members, is the median of S odd? (1) All members of S are odd. (2) n is even. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

29. What percentage of the agents at Best Be Safe insurance company sell insurance for cars but not boats? (1) Ninety percent of the agents at Best Be Safe sell insurance for cars, and 55% of the agents at Best Be Safe do not sell insurance for boats. (2) The number of agents at Best Be Safe who sell insurance for boats is half the number of agents who sell insurance for cars. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

The Job Dilemma Jennifer has an interview scheduled for a job that she believes could be an extraordinary opportunity for her. Not only will it provide her the means to move to the city, but it will provide contacts that could prove very beneficial to her career. An acquaintance of hers has also been asked to interview for the job. Jennifer travels to the city for her interview and leaves believing it went quite well. She is optimistic that she will be offered the job and pleased because the opportunity appears even better than she originally believed it to be. Jennifer has several hours to wait for her train home, so she walks around the city for an hour and then finds a café where she plans to have a leisurely lunch. Her table is in the corner of the café and is partially hidden by a large plant. As she overhears two men converse at a nearby table, she realises that the diners at that table do not know that anyone is sitting nearby and that their conversation can be heard. Although she tries not to listen, Jennifer recognises one of the voices finds it increasingly difficult not to pay attention. The voice she recognises begins to talk about two interviews he recently conducted for an open position at his company. He notes that the first candidate is better qualified, and then lowers his voice as he uses racial epithets to note why he does not want to offer the job to this candidate. He then states that he'll offer the job to the girl who's sufficiently qualified and a member of a racial group with whom he's more comfortable working. Jennifer glances at the men and, with a start, realises that the voice she recognises is that of the hiring manager who interviewed her earlier. Unsure of what to do, she waits until the men are gone before she exits the café and walks to the train station.

The following day, the hiring manager calls Jennifer and offers her the job. What is your opinion? How do you feel about each of the following statements? 30. Ethics dictates that a person not knowingly benefit from others' prejudices. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

31. If you do not cause an unjust situation, you are not required to remedy it. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

32. If a personal sacrifice will not remedy an injustice, it is foolish to make the sacrifice. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

33. It is important to do the right thing. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

34. You must look out for yourself first and foremost. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

35. If you know someone has been the victim of discrimination, you have an obligation to inform that person. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

36. Competition does not always have to be fair. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

37. Doing the right thing can put you at a disadvantage. A. Strongly Agree B. Agree C. Disagree D. Strongly Disagree

38. What is the remainder when

is divided by 10?

(1) x is a multiple of 3. (2) x is a multiple of 5. A. Statement (1) by itself is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) by itself is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. D. Either statement by itself is sufficient to answer the question. E. Statements (1) and (2) taken together are not sufficient to answer the question, requiring more data pertaining to the problem.

39. Until a recent acquisition, two partners held all of the stock in the company Initrode. During the acquisition, each of the partners sold some of his shares and exchanged the rest for shares of Initech. If the senior partner sold 1,200 shares, and the junior partner exchanged 800 shares, what is the greatest possible number of shares the senior partner exchanged? (1) Before the acquisition, there were 4,000 shares of Initrode. (2) Fewer than half the Initrode shares were sold. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

40. In a certain school district, math teachers are considered qualified if they have either a math degree or a teaching credential in math. If 5% of math teachers have both a math degree and a teaching credential in math, what percentage of math teachers are considered qualified? (1) Fifteen percent of math teachers lack a teaching credential in math, and 90% lack a math degree. (2) Eighty percent of math teachers have a teaching credential in math but not a math degree, and 5% have a math degree but not a teaching credential. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

41. Every student at the Performing Arts Academy must take at least one of the two drama courses offered, Classical Theater or Improvisation. If 15% of the students who take Classical Theater also take Improvisation, how many students take both Classical Theater and Improvisation? (1) Ten percent of the students who take Improvisation also take Classical Theater. (2) The Performing Arts Academy has a total of 450 students. A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.

42. If the sides of a triangle have lengths x, y, and z, x + y = 30, and y + z = 20, then which of the following could be the perimeter of the triangle? I. 28 II. 36 III. 42 A. I only B. II only C. I and II only D. I and III only E. I, II, and III

43. If x, y, and z are integers, is x -y odd? 2

(1) x = z - 4y + 4 2

(2) y = z - 2z + 1 A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. EITHER statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.