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# If n is an integer, is n + 1 odd?

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If n is an integer, is n + 1 odd? [#permalink]

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30 Jul 2012, 02:15
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86% (01:33) correct 14% (00:36) wrong based on 691 sessions

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The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

If n is an integer, is n + 1 odd?

(1) n + 2 is an even integer.
(2) n -1 is an odd integer.

Practice Questions
Question: 7
Page: 275
Difficulty: 550

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Re: If n is an integer, is n + 1 odd? [#permalink]

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30 Jul 2012, 02:16
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SOLUTION

If n is an integer, is n + 1 odd?

In order $$n+1$$ to be odd, $$n$$ must be even. So, the question basically asks whether $$n$$ is an even number.

(1) n + 2 is an even integer --> $$n+2=even$$ --> $$n=even-2=even$$. Sufficient.
(2) n -1 is an odd integer --> $$n-1=odd$$ --> $$n=odd+1=even$$. Sufficient.

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Re: If n is an integer, is n + 1 odd? [#permalink]

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30 Jul 2012, 20:58
1
KUDOS
A. N, N+1, N+2. If N+2 is even, then N+1 is odd
Sufficient

B. N-1, N, N+1. If N-1 is odd, then N+1 is odd.
Sufficient

[Reveal] Spoiler:
D
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Re: If n is an integer, is n + 1 odd? [#permalink]

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03 Aug 2012, 05:05
1
KUDOS
The following Rules will be handy in order to solve this question:

Even Number (+/-) Odd Number = Odd Number------->(a)
Even Number (+/-) Even Number = Even Number------>(b)
Odd Number (+/-) Odd Number = Even Number.------->(c)

Now coming to the question stem: is N + 1 = Odd. From the question stem itself we know that 1 is an odd number and that the result is odd. From equation (a) above we know that this is only possible when n is even. So, the question is actually asking as if n is even?

Statement (1): n + 2`= Even. "2" as we know is even so this result is only possible if n is even (b). SUFFICIENT

Statement (2): n- 1 = Odd. "1" is an Odd Number. This result is only possible if n is even (b). SUFFICIENT

Ans (D)
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Re: If n is an integer, is n + 1 odd? [#permalink]

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03 Aug 2012, 05:46
1
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Expert's post
SOLUTION

If n is an integer, is n + 1 odd?

In order $$n+1$$ to be odd, $$n$$ must be even. So, the question basically asks whether $$n$$ is an even number.

(1) n + 2 is an even integer --> $$n+2=even$$ --> $$n=even-2=even$$. Sufficient.
(2) n -1 is an odd integer --> $$n-1=odd$$ --> $$n=odd+1=even$$. Sufficient.

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Re: If n is an integer, is n + 1 odd? [#permalink]

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05 Aug 2015, 06:56
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Re: If n is an integer, is n + 1 odd? [#permalink]

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11 Sep 2015, 01:04
statement 1 :n+2=even, n=even, n+1 == odd, sufficient
Statement 2; n-1=odd,n=even, n+1 == odd, sufficient

hence D
Re: If n is an integer, is n + 1 odd?   [#permalink] 11 Sep 2015, 01:04
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