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 What is the value of y?
(1) y2+8y+16=0
(2) y＜0
【正确答案】 A
【答案解析】alone is sufficient because the equation can be restated as (y+4)(y+4)=0, so y=-4. (2) alone is insufficient because there are infinite negative numbers that meet the condition.
单选题 The integer x is how much greater than 4?
(1)
【正确答案】 D
【答案解析】Both (1) and (2) are sufficient, because in both cases the answer is that x=6, and therefore x is 2 greater than 4.
单选题 In triangle ABC above, if ∠BAD and ∠ADB have measures of 2n, and if ∠ACB has a measure of n, what is the length of side AB? (Figure not necessarily drawn to scale.)
【正确答案】 B
【答案解析】alone is insufficient because it offers no information about any lengths in the triangle. (2) alone is sufficient; the crucial principle to remember here is that an exterior angle of a triangle--such as ∠ADB--is equal to the sum of the remote interior angles of the triangle, in this case triangle BDC. Thus, n+ ∠CBD=2n, or ∠CBD=n. Since sides of a triangle opposite angles of identical degree are of identical length, BD is the same length as CD, or 4. By this same principle, BD and AB are of identical lengths, so AB is also 4.
单选题 A dairy farmer has two milk pails, M and P. Milk pail M is 1/3 full. How much milk is in P relative to M?
(1) If M is poured into P, P will be full.
(2) Milk pail P is smaller than M.
【正确答案】 E
【答案解析】alone is insufficient, because M could be the same size as P and 2/3 full to start with, or it could be 1/3 the size of P and empty to start with. (2) alone is insufficient, because it tells us nothing about the relative amounts of milk. If the statements are combined, there is still no clear answer, because M could be 2/3 the size of P and 1/2 full to start with, or it could be 1/3 the size of P and empty to start with.
单选题 Is y between 1 and 2, exclusive?
(1) y2 is less than y
(2) y2+y is between 1 and 2, exclusive
【正确答案】 D
【答案解析】alone is sufficient because the only values for y in which y2 is less than y are if y values between 0 and 1, so the answer is "no." (2) alone is sufficient because there is no value of y between 1 and 2, exclusive, for which this statement is true [the value 1, which is excluded in the question, gives the result 2, which is excluded in statement (2)], so the answer is "no./