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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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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.

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Question: 7
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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
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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
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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
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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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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
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Re: If n is an integer, is n + 1 odd? [#permalink]

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22 Jul 2016, 12:12
Bunuel wrote:
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.

We need to determine whether n + 1 is odd. Remember, if n is even, then n + 1 will be odd, and if n is odd, n + 1 will be even.

Statement One Alone:

n + 2 is an even integer.

Statement one tells us that n is an even integer (since 2 more than an even integer is also an even integer). Because n is an even integer, we know that n + 1 is odd. Statement one is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone:

n – 1 is an odd integer.

Since subtraction rules for even and odd integers are the same as addition rules for even and odd integers, we know that if n – 1 is odd, then n itself must be even, and hence n + 1 must also be odd. Statement two is sufficient to answer the question.

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

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03 Dec 2016, 18:09
Here is my solution->
Some Basic Rules before we attempt this Even/odd Question

Even+Even=Even
Even+Odd=Odd
Odd+Even=Odd
Odd+Odd=Even

Similarly

Even-Even=Even
Even-Odd=Odd
Odd-Even=Odd
Odd-Odd=Even

The Question is asking us whether n+1 is odd or not
n+1 will be odd only when n is even.
Hence question can be rephrased into "is n even"
Statement 1
n+2 is even => n=even -2 => even
Hence sufficient
Statement 2
n-1=odd
Hence n=odd+1=> even

hence sufficient
Hence D

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Re: If n is an integer, is n + 1 odd?   [#permalink] 03 Dec 2016, 18:09
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