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 n is a positive integer and m=6.25×10ⁿ what is the value of n?
(1) 500＜m＜5,000
(2) m＜6,250

【正确答案】 A

【答案解析】alone is sufficient because the only value for m that meets the stated conditions is 625, which means that n=2. (2) alone is insufficient because m could be equal to 6.25, 62.5, or 625.

单选题 If p+q=400 and p＜q, is p+q＜r+s?
(1) p+r+s=600
(2) q+r＞400

【正确答案】 A

【答案解析】alone is sufficient because we know from the question that p＜200, because p is less than q and p+q=400, so if p+r+s=600, then r+s＞400, so it is greater than p+q and the answer is "yes." (2) alone is insufficient, because the statement could be consistent with either a "yes" or "no" answer to the question, since it does not tell us the values for any of the variables.

单选题 If n is an integer, and n≠0, is [*] a positive integer?
(1) n²=25
(2) 5n=25

【正确答案】 B

【答案解析】Statement (1) alone is insufficient, since n could be either 5 or -5, so the equation could be either positive or negative. Statement (2) alone is sufficient because it only has one solution, n=5, in which case the equation above equals 25, which is a positive integer.

单选题 Over the weekend, a shoe store sold 1/3 of the shoes in its stock. The average price of the shoes sold was $60 per pair. What was the total revenue from shoe sales over the weekend for this shoe store?
(1) When the store closed on Sunday night, 600 pairs of shoes were still in stock.
(2) The store began the weekend with 900 pairs of shoes.

【正确答案】 D

【答案解析】Since we know the average price per pair of shoes sold, all we need to determine is the number of pairs of shoes sold. Statement (1) provides this answer, because we can determine that if 2/3 of the original stock is 600, then the original stock was 900; 1/3 of 900 is 300 pairs of shoes; 300×$60=$18,000. Statement (2) is also sufficient because 1/3 of 900 is 300; 300×$60=$18,000.

单选题 Ajar contains 30 coins, of which 20 are nickels and 10 are dimes. If 7 coins are removed, how many nickels are left?
(1) More nickels are removed than dimes.
(2) The remaining coins in the jar are worth $1.55.

【正确答案】 B

【答案解析】From the question, we know that the original value of the coins in the jar was $2.00. Statement (1) is insufficient; it leaves us with four different possibilities for the number of nickels left, since 4, 5, 6, or 7 nickels could have been removed. Statement (2) tells us that $0.45 was removed from the jar. The only configuration of 7 nickels and dimes that equals $0.45 is 2 dimes and 5 nickels. Therefore, the only possible answer is that 15 nickels are left. (2) alone is sufficient.