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Manhattan Question Set # 16

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by richachampion » Wed Oct 12, 2016 7:41 am
If y and z are nonzero integers, is the square of (y + z) even?

(1) y - z is odd.
(2) yz is even.

OA: A
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Source: — Data Sufficiency |

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by [email protected] » Wed Oct 12, 2016 10:29 am
Hi richachampion,

This DS question is build around several Number Properties; you can either use that NP knowledge or TEST VALUES to answer the question.

We're told that Y and Z are NON-0 INTEGERS. We're asked if the square of (Y+Z) is EVEN. This is a YES/NO question.

1) (Y - Z) is ODD.

Since Y and Z are integers, there are two possible ways for the above subtraction to end in an odd number:

Y = Odd, Z = Even

or

Y = Even, Z = Odd

In both cases, you have 1 even and 1 odd.
Odd + Even = Always Odd.
(Odd)^2 = Always Odd.
The answer to the question is ALWAYS NO.
Fact 1 is SUFFICIENT

2) (Y)(Z) is EVEN

With this Fact, we know that AT LEAST ONE of the variables is Even.

IF... Y = Even, Z = Even then the answer to the question is YES.
IF... Y = Even, Z = Odd then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Final Answer: A

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