Data Sufficiency

Vincen wrote:If x and y are integers and x<y, what is the value of x+y?

(1) x^y = 4
(2) |x| = |y|

The OA is D.

I don't know how to find the value of x+y. Experts, may you help me here? I would be thankful.

We are given that x and y are integers and x < y. We have to find out the value of x+y.

(1) x^y = 4

Case1: Say x = y = 2, then 2^2 = 4. But x is not less than y, so this is not a valid case.
Case2: Say x = -2 and y = 2, then (-2)^2 = 4. We have x < y, so it's a valid case. The value of x + y = -2 + 2 = 0.
Case3: Say x = 4 and y = 1, then 4^1 = 4. But x is not less than y, so this is not a valid case.
Case4: Say x = √2 and y = 4, then (√2)^4 = 4. But x is not an integer, so this is not a valid case.

There is no other case possible. Thus, x = y = 0. Sufficient.

(2) |x| = |y|

Since |x| = |y| and x <y, then x must be negative and y must be positive. Thus x = -y. Thus, x + y = -y + y = 0. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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