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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.

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

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03 Aug 2012, 04:05

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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

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.

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

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05 Aug 2015, 05:56

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(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.

Answer: D
_________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

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

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