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# p and q are integers, is p even?

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Manager
Joined: 09 Jun 2018
Posts: 191
Location: United States
GPA: 3.95
WE: Manufacturing and Production (Energy and Utilities)
p and q are integers, is p even?  [#permalink]

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18 Nov 2018, 10:21
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Difficulty:

25% (medium)

Question Stats:

74% (01:10) correct 26% (01:02) wrong based on 41 sessions

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p and q are integers, is p even?

(1) 7p + 9q is even
(2) 7p + 6q is odd

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Re: p and q are integers, is p even?  [#permalink]

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25 Nov 2018, 22:30
nkin wrote:
p and q are integers, is p even?

(1) 7p + 9q is even
(2) 7p + 6q is odd

(1) When sum of two integers is even, then either both are even or both are odd.
So in this case, either both 7p and 9q are even, or both 7p and 9q are odd. First case will occur only when both p and q are even, while second case will occur when both p and q are odd.

So p could be either even or odd. We cannot determine, thus this statement is not sufficient to answer the question.

(2) 6q will always be even. So for the sum 7p + 6q to be odd, it will happen only if 7p is odd, and that in turn will happen only when p is odd.

So we know for sure that p is odd. This statement is thus sufficient to answer the question.

Re: p and q are integers, is p even?   [#permalink] 25 Nov 2018, 22:30
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