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# P and Q are positive integers. Is P odd?

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Math Expert
Joined: 02 Sep 2009
Posts: 52935
P and Q are positive integers. Is P odd?  [#permalink]

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23 Feb 2015, 02:19
00:00

Difficulty:

5% (low)

Question Stats:

81% (00:57) correct 19% (01:35) wrong based on 100 sessions

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P and Q are positive integers. Is P odd?

(1) P^2*Q is odd
(2) P + Q is even

Kudos for a correct solution.

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Joined: 30 Mar 2013
Posts: 10
Location: India
Re: P and Q are positive integers. Is P odd?  [#permalink]

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23 Feb 2015, 03:24
1
Quote:
P and Q are positive integers. Is P odd?

(1) P^2*Q is odd
(2) P + Q is even

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.

Manager
Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 74
Re: P and Q are positive integers. Is P odd?  [#permalink]

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23 Feb 2015, 06:39
Odd*odd=odd
Even*odd=even
Even*even=even

Statement 1) p^2*q=p*p*q=odd> tells us p and q have to be odd, this is sufficient.
Statement 2) p+q=even, 3+3=6, 2+2=4, we cannot confirm if p is odd

Manager
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Concentration: General Management, Technology
GMAT Date: 03-02-2015
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Re: P and Q are positive integers. Is P odd?  [#permalink]

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23 Feb 2015, 07:37
Here we go:

St1: P^2*Q is odd

Product of two numbers is odd----> that means both the numbers have to be odd.

(P)^2 --> Odd
P---> Odd

St1 is sufficient.

St2: P + Q is even

{ even + even } = even
{odd + odd } = even

So we can't be sure

Option A is correct
Math Expert
Joined: 02 Sep 2009
Posts: 52935
Re: P and Q are positive integers. Is P odd?  [#permalink]

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02 Mar 2015, 06:09
Bunuel wrote:
P and Q are positive integers. Is P odd?

(1) P^2*Q is odd
(2) P + Q is even

Kudos for a correct solution.

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.

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Re: P and Q are positive integers. Is P odd?  [#permalink]

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04 Oct 2018, 07:12
Bunuel wrote:
P and Q are positive integers. Is P odd?

(1) P^2*Q is odd
(2) P + Q is even

Kudos for a correct solution.

P and Q > 0

1) P^2 * Q = Odd

means P = odd and Q = odd

So Q is odd, sufficient.

2)

P+Q = even
even + even = even
odd + odd = even

We cannot tell for sure whether Q is even or odd.
insufficient.

Re: P and Q are positive integers. Is P odd?   [#permalink] 04 Oct 2018, 07:12
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