Data Sufficiency. 1. If 2 x (7 y ) = z, what is the value of z?

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1 Data Sufficiency Directions: Data Sufficiency problems consist of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements plus your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of counterclockwise), you are to fill in the oval if statement (1) ALONE is sufficient, but statement (2) alone is not sufficient. if statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. if BOTH statements TOGETHER are if EACH statement ALONE is sufficient. if statements (1) and (2) TOGETHER are 1. If 2 x (7 y ) = z, what is the value of z? (1) x y = 1 (2) 2 x = 8 statement (2) alone is EACH statement 220 Crash Course for the GMAT

2 2. In the Kennedy High School swim club, 120 members swim the backstroke or the crawl or both. If 30 of these members do not swim the backstroke, how many members swim both the crawl and the backstroke? (1) Of the 120 members, 72 do not swim the crawl. (2) A total of 48 members swim the crawl. statement (2) alone is EACH statement 3. If p and q are integers, is p + q odd? (1) p is not an odd integer. 3 (2) p q is an even integer. statement (2) alone is EACH statement Math Drills 221

3 4. At the beginning of last year, a furniture store had 75 armchairs in stock, which had cost the store $600 each. During the same year, the store purchased a number of additional armchairs. What is the total amount spent by the store on the armchairs it had in stock at the end of last year? (1) Last year, the store purchased 30 armchairs for $500 each. (2) Last year, the total revenue from the sale of armchairs was $16,500. statement (2) alone is EACH statement 5. What is the ratio of the number of boys to girls on the school bus? (1) The number of boys is 5 less than twice the number of girls. (2) The difference between the number of boys and the number of girls is 35. statement (2) alone is EACH statement 222 Crash Course for the GMAT

4 6. How long did it take Bob to complete the race? (1) If Bob were 2 faster, his time would 3 have been 3 hours. (2) Bob s average speed was 30 miles per hour. statement (2) alone is EACH statement 7. A B D C In the rectangular coordinate system above, is ABCD a square? (1) Both Points C and D have y-coordinates of 3. (2) ABD = 45 statement (2) alone is EACH statement Math Drills 223

5 8. If K = r 3, what is the value of K? p p 2p r (1) r = 2p (2) p = 5, and 2r 2p = 2p statement (2) alone is EACH statement 9. A drawer contains 12 socks, of which 8 are black and 4 are white. If 3 of the socks are removed, how many of the remaining socks are black? (1) The remaining socks have a ratio of 2 black to 1 white. (2) One of the first two socks removed is black. statement (2) alone is EACH statement 224 Crash Course for the GMAT

6 10. M N O Is MNO a right triangle? (1) MN = 2 2 (2) MNO = MON = 1 2 OMN statement (2) alone is EACH statement Math Drills 225

7 11. Train A leaves the station at 5:00, and travels north at 50 miles per hour. If train B leaves the same station some time later, heading in the same direction as train A, at what time will train B overtake train A? (1) Train B leaves the station at 6:00. (2) Train A travels at 5 the speed of train B. 6 statement (2) alone is EACH statement 12. If e is a nonzero integer, is less than 1? (1) e < 1 (2) e 2 > 0 1 greater than or e 2 statement (2) alone is EACH statement 226 Crash Course for the GMAT

8 13. What is the value of x? (1) x is the sum of two distinct prime numbers between 25 and 40. (2) The sum of the distinct prime factors of x is 19. statement (2) alone is EACH statement 14. What is the value of x? (1) x (x 1) = 12 (2) x (x + 6) = 9 statement (2) alone is EACH statement Math Drills 227

9 15. List Q contains 3 elements. What is the median of list Q? (1) The mean of list Q is 7. (2) The mode of list Q is 5. statement (2) alone is EACH statement 16. Does more than 50% of the population of Lakeside subscribe to magazine X? (1) Lakeside has 1,000 residents. (2) 400 people in Lakeside subscribe to magazine X. statement (2) alone is EACH statement 228 Crash Course for the GMAT

10 17. Is x + 1 odd? (1) 2x + 5 is odd. (2) x + 6 is odd. statement (2) alone is EACH statement 18. Does x have at least 3 prime factors? (1) x = 5b, where b is a positive integer. (2) b = 2c, where c is a positive integer. statement (2) alone is EACH statement Math Drills 229

11 19. What is the area of rectangle ABCD? (1) Side B is 7 units long. (2) The perimeter of rectangle ABCD is 20 units. statement (2) alone is EACH statement 20. What is the area of right triangle ABC? (1) Side B is 7 2 units long. (2) Triangle ABC is isosceles. statement (2) alone is EACH statement 230 Crash Course for the GMAT