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# If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.

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If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.  [#permalink]

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05 Mar 2019, 04:58
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25% (medium)

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74% (01:07) correct 26% (01:31) wrong based on 47 sessions

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If p and q are integers, is p + q odd?

(1) p/3 is not an odd integer.
(2) p − q is an even integer.

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Re: If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.  [#permalink]

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05 Mar 2019, 05:05
Bunuel wrote:
If p and q are integers, is p + q odd?

(1) p/3 is not an odd integer.
(2) p − q is an even integer.

we are asked to determine whether p + q is odd or not.

Statement 1: p/3 is not an odd integer. It indicates that p is even but we don't know the odd/even properties of q. NOT sufficient.

Statement 2: p - q = even. 2 cases here.

1. even - even = even.

2 Odd - Odd = even

even + even = even

odd + odd =even .

In both cases we get even as the sum of p + q. Sufficient.

p + q is not odd.

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If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.  [#permalink]

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Updated on: 05 Mar 2019, 12:10
Bunuel wrote:
If p and q are integers, is p + q odd?

(1) p/3 is not an odd integer.
(2) p − q is an even integer.

smart question
#1
p/3 is not an odd integer implies p can be even or a fraction ..
q not known in sufficient
#2
p − q is an even integer
means both p & q have to either odd or even
and sum of both odd & even integers is always even
so sufficient to say that p+q is not odd
IMO B

Originally posted by Archit3110 on 05 Mar 2019, 11:00.
Last edited by Archit3110 on 05 Mar 2019, 12:10, edited 1 time in total.
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Re: If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.  [#permalink]

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05 Mar 2019, 12:05
Statement 1 can't be sufficient, because it gives no information about q.

Addition and subtraction obey identical even/odd rules (because subtracting is addition, you're just adding a negative) so any time a-b is even, so is a+b, and vice versa, and Statement 2 is instantly sufficient to give a 'no' answer to the question, so the answer is B.

I should add that the above is true only if a and b are integers, but that's always going to be the case in a GMAT even/odd problem.
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Re: If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.  [#permalink]

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05 Mar 2019, 12:09
And I'd point out one mistake in the other posts above: Statement 1 says "p/3 is not an odd integer". That sentence does not mean that p is even. Certainly p might be even, but p could also be 7, say, since 7/3 is not an odd integer.

If instead the statement said "p/3 is an even integer", then that would ensure that p itself is even.
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Re: If p and q are integers, is p + q odd? (1) p/3 is not an odd integer.   [#permalink] 05 Mar 2019, 12:09
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