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23 Feb 2015, 03:19
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
84% (00:59) correct
16%
(01:28)
wrong
based on 131
sessions
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Not Attempted Yet
P and Q are positive integers. Is P odd?
(1) P^2*Q is odd
(2) P + Q is even
(1) P^2*Q is odd
(2) P + Q is even
23 Feb 2015, 04:24
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Quote:
We have to figure out whether P is odd or not.
Statement 1 says P^2*Q is odd.
=> Both P & Q are odd.
Statement 1 is sufficient.
Statement 2 says P + Q is even.
=> Both P & Q are even or both P & Q are odd.
We cannot decide among the above two choices
=> Statement 2 is not sufficient.
Correct Answer: A
02 Mar 2015, 07:09
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Bunuel
MAGOOSH OFFICIAL SOLUTION:
P and Q are positive integers. Is P odd?
Statement #1: P^2*Q is odd
The only way a product can be odd is if each of the factors is odd; therefore, if P^2*Q is odd, then P^2 and Q each must be odd. The only way the square of a positive integer can be odd is if the original integer is odd: therefore, if P^2, the P must be odd. This statement, alone and by itself, is sufficient to give a definitive “yes” answer to the prompt question.
Statement #2: P + Q is even
Here, both P & Q together can be even, or both P & Q together can be odd. On the basis of this statement alone, which don’t know which of those two possibilities is the case. Therefore, we are no position to give a definitive answer to the prompt question. This statement, by itself, is insufficient.
Answer = A
