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If a and x are integers, and a is even, is x even too?

(1) x^a is odd.

(2) a·x=12

OA -- C

Can experts help why OA shall be C. My answer is A.

If x^a is odd, it will be possible only when x is odd ==> A is sufficient. I am sure I am missing something here.

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by Brent@GMATPrepNow » Mon Jul 15, 2013 7:16 am
shailendra.sharma wrote:If a and x are integers, and a is even, is x even too?

(1) x^a is odd.

(2) a·x=12

OA -- C

Can experts help why OA shall be C. My answer is A.

If x^a is odd, it will be possible only when x is odd ==> A is sufficient. I am sure I am missing something here.
Your statement above (in green) is almost always true. However, if a = 0 (an even number) then x^a = 1, for values of x that are even or odd. For example 4^0 = 1 and 1 is odd, and 4 is even.

Here's my full solution:

Target question: Is x even?

Given: a and x are integers, and a is even

Statement 1: x^a is odd.
There are several pairs of values that meet this condition. Here are two:
Case a: x = 3 and a = 2, in which case x is odd
Case b: x = 4 and a = 0, in which case x is even
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: ax=12
There are several pairs of values that meet this condition. Here are two:
Case a: x = 3 and a = 4, in which case x is odd
Case b: x = 6 and a = 2, in which case x is even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined:
From statement 1, we see that the ONLY way that x can be even is if a = 0. Otherwise x must be odd.
From statement 2, we can conclude that a does not equal zero.
So, we can conclude that x must be odd.
In other words, x is not even.
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

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Brent
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by Matt@VeritasPrep » Mon Jul 15, 2013 9:25 am
This one is really clever and a great example of why your mantra on test day should be "If a question seems easy, it ISN'T!" Oftentimes if you're working out of a book a question that seems easy really is easy, but if you're taking a good CAT, anything that seems easy (after the first question) is almost certainly a trap.