Jeff Miller

GMAT OFFICIAL GUIDE DS – If x and y are integers…

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

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