Question

If $x$ and $y$ are integers, is $x>y$?
(1) $x+y>0$
(2) $y^x<0$

• 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.

Answer 1

Answer: (C)

Both statements together are sufficient, but neither statement alone is sufficient.

Determine if the integer x is greater than the integer y.

1. It is given that x + y > 0, and so −x < y. If, for example, x = −3 and y = 4, then x + y = −3 + 4 = 1 > 0 and x < y. On the other hand, if x = 4 and y = −3, then x + y = 4 − 3 = 1 > 0 and x > y; NOT sufficient.
2. It is given that , so y < 0. If, for example, x = 3 and y = −2, then and x > y. On the other hand, if x = −3 and y = −2, then and x < y; NOT sufficient.

• Taking (1) and (2) together, from (2) y is negative and from (1) −x is less than y. Therefore, −x is negative, and hence x is positive. Since x is positive and y is negative, it follows that x > y.
• The correct answer is C; both statements together are sufficient.