单选题 Is x2 - y2 a positive number?(1) x - y is a positive number. (2) x + y is a positive number.

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.

【正确答案】 C

【答案解析】Since x2 -y2 = (x + y)(x - y), it follows that x2 - y2 will be a positive number if both x + y and x -y are positive numbers or if both are negative numbers.(1) It is given that x - y is a positive number. If, for example, x = 2 and y = -3, then x -y is a positive number, but x + y is not a positive number, so x2 — y2 is not a positive number. On the other hand, if x = 3 and y = 1, then x - y is a positive number and x + y is a positive number, so x 2 - y 2 is a positive number; NOT sufficient.(2) It is given that x + y is a positive number. If, for example, x = -2 and y = 4, then x + y is a positive number, but x — y is not a positive number, so x 2 - y 2 is not a positive number. On the other hand, if x = 3 and y = 1, then x + y is a positive number and x -y is a positive number, so x2 - y 2 is a positive number; NOT sufficient.Taking (1) and (2) together, both x + y and x - y are positive numbers, so x2 - y2 is a positive number.The correct answer is C;both statements together are sufficient.