## If x and y are integers…

## Solution:

We are given that x and y are integers and must determine the value of x + y.

**Statement One Alone: **

3 < (x+y)/2 < 4

We can start by multiplying the inequality 3 < (x+y)/2 < 4 by 2. This gives us:

6 < x + y < 8

We see that the sum of x and y must be between 6 and 8. Because x and y are integers, and 7 is the only integer between 6 and 8, x + y = 7. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

**Statement Two Alone: **

2 < x < y < 5

Since we know that x and y are integers and that x is less than y, x must equal 3 and y must equal 4 for the inequality to hold true. Thus x + y = 7. Statement two is also sufficient to answer the question.

**Answer:** D