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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
When p, m, and n are integers, is p an even?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 89% (01:09) correct 11% (00:55) wrong based on 125 sessions

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When p, m, and n are integers, is p an even number?

1) m+n=even
2) p+m=even

* A solution will be posted in two days.

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Re: When p, m, and n are integers, is p an even?  [#permalink]

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From

1)

m + n = even

which means either a) both are even or b) both are odd.

2) p + m = even.

a) if m is even, p is even
b) if m is odd, p is odd.

There's no evidence to whether m is odd or even. Hence even on combining both, we can't find the answer. So E
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Re: When p, m, and n are integers, is p an even?  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

When p, m, and n are integers, is p an even?

1) m+n=even
2) p+m=even

In the original condition, there are 3 variables, which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), m=n=p=2 -> yes, m=n=p=1 -> no, which is not sufficient.
Thus, E is the answer.
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GRE 1: Q169 V154 Re: When p, m, and n are integers, is p an even?  [#permalink]

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1
The only thing that can be inferred from the two statements combination is that all the three integers have the same even/odd nature.
Smash that E
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Re: When p, m, and n are integers, is p an even?  [#permalink]

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Top Contributor
MathRevolution wrote:
When p, m, and n are integers, is p an even number?

1) m+n=even
2) p+m=even

Target question: Is p an even number?

Given: p, m, and n are integers

Statement 1: m + n = even
No information about p, so there's no way to determine whether p is even or odd
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: p+m=even
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: p = 1 and m = 1, in which case p is ODD
Case b: p = 0 and m = 0, in which case p is EVEN
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values

Statements 1 and 2 combined
There are still several values of m, n and p that satisfy both equations AND yield contradictory results.
Case a: p = 1, m = 1 and n = 1, in which case p is ODD
Case b: p = 0, m = 0, and n = 0, in which case p is EVEN
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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Re: When p, m, and n are integers, is p an even?  [#permalink]

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_________________ Re: When p, m, and n are integers, is p an even?   [#permalink] 16 Jan 2019, 10:50
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