If k is an integer, is k even? (1) k 1 (2) k^2 is an even integer

Question

If k is an integer, is k even?

(1) k > 1
(2) k^2 is an even integer.

DS21186

BrentGMATPrepNow · Answer

Given : k is an integer

Target question :    k even?

Statement 1 : k > 1  
There are infinitely many values of k that satisfy statement 1. Here are two: 
 Case a : k = 2. In this case, the answer to the target question is  YES, k is even 
 Case b : k = 3. In this case, the answer to the target question is  NO, k is not even 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : k^2 is an even integer. 
In other words,   (k)(k) is even  
Since k is an INTEGER, we know that k must be ODD or EVEN
Let's examine each case:
 Case a : k is odd. In this case, we get:   (ODD)(ODD) is even  . This doesn't work. 
So, it CANNOT be the case that k is odd. 
 Case b : k is even. In this case, we get:   (EVEN)(EVEN) is even  .  This works . 
So  it must be the case that k is even 
Since we can answer the  target question  with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

achloes · Answer

If n is a positive integer, then x^n is always even if x is even and x^n is always odd if x is odd.

JeffTargetTestPrep · Answer

k is an integer, and we need to answer the question:

Is k even?

Statement One Alone:

=> k > 1

If k = 3, then k is odd. Whereas, if k = 2, then k is even.

Statement one is not sufficient. Eliminate answer choices A and D.

Statement Two Alone:

=> k^2 is an even integer.

If k were odd, then k^2 would be odd. Therefore, k must be even.

Statement two is sufficient.

Answer: B

If k is an integer, is k even? (1) k > 1 (2) k^2 is an even integer

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