单选题 The following 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 must indicate whether
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.

单选题 If 5a=9b=15c, what is the value of a+b+c?
(1) 3c-a=5c-3b
(2) 6cb=10a

【正确答案】 B

【答案解析】Statement (1) alone is insufficient; you can restate the equation as 3b=2c+a; if you multiply both sides of the equation by 3, you get 9b=6c+3a; you can determine from the equation 5a=15c that a=3c, so all this restated equation tells you is that 9b=15c=5a, which tells you nothing about the actual value of a or b. Statement (2) is sufficient. If you divide both sides of the equation by 2, you get 3cb=5a; you know that 5a=9b, so you can form the equation 3cb=9b, which you can reduce to c=3. With this value you can determine that a=9 and b=5, and you can thereby find a definitive answer to the question posed.

单选题 Stanley has gained 8 pounds a year ever since he turned 18. How much weight has Stanley gained since he turned 18?
(1) Stanley now weighs twice what he weighed when he turned 18.
(2) Stanley is now twice the age he was when he turned 18.

【正确答案】 B

【答案解析】alone is insufficient because it does not tell us what Stanley weighed when he turned 18. (2) alone is sufficient, because it tells us that he has aged 18 years since then, meaning that he has gained 18×8 pounds=144 pounds.

单选题 What is the value of the greater of two numbers if one of the numbers is three times the smaller number?
(1) One of the numbers is 12.
(2) The sum of the two numbers is 16.

【正确答案】 B

【答案解析】alone is insufficient because the two numbers could be 4 and 12 or 12 and 36. (2) alone is sufficient because the only two numbers that meet the stated conditions are 4 and 12.

【正确答案】 C

【答案解析】alone is insufficient because r could be several numbers less than 70, such as 64 or 49. (2) alone is insufficient because r could be several numbers greater than 49, such as 64 or 81. When the statements are combined, the only number that meets both criteria is 64, so the answer is C.