Question

If $x$ and $y$ are integers, what is the value of $x+y$?
(1) $3<\frac{x+y}{2}<4$
(2) $2<x<y<5$

• 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: (D)

Each statement alone is sufficient.

Determine the value of x + y for integers x and y.

1. Given that , then 6 < x + y < 8. Since x + y is an integer and 7 is the only integer greater than 6 and less than 8, it follows that the value of x + y is 7; SUFFICIENT.
2. Given that 2 < x < y < 5, then 2 < x < 5, and hence x = 3 or x = 4. Likewise, 2 < y < 5, and hence y = 3 or y = 4. With the additional restriction that x < y, it follows that x = 3 and y = 4, and thus x + y = 7; SUFFICIENT.

• The correct answer is D; each statement alone is sufficient.