If x and y are integers…
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.