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Manhattan Question Set # 5

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by richachampion » Sun Oct 09, 2016 5:58 pm
If w, y, and z are positive integers, and w = y - z, is w a perfect square?

(1) y + z is a perfect square.
(2) z is even.

OA: E
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by [email protected] » Sun Oct 09, 2016 7:53 pm
Hi richachamption,

To start, this should be in the DS Forum. That having been said, this prompt can be solved rather easily by TESTing VALUES.

We're told that W, Y and Z are POSITIVE INTEGERS and that W = Y - Z. We're asked if W is a perfect square. This is a YES/NO question.

1) (Y+Z) is a perfect square

IF... Y=7, Z=2 then W = 7-2 = 5 and the answer to the question is NO.
IF... Y=5, Z=4 then W = 5-4 = 1 and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) Z is even

This tells us NOTHING about Y, but the two TESTs that I used in Fact 1 (above) also 'fit' Fact 2...

IF... Y=7, Z=2 then W = 7-2 = 5 and the answer to the question is NO.
IF... Y=5, Z=4 then W = 5-4 = 1 and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that already fit both Facts, so no new work is needed.
Combined, INSUFFICIENT.

Final Answer: E

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