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Re: If n is an integer, is n + 1 odd? [#permalink]
30 Jul 2012, 01:16

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.

Re: If n is an integer, is n + 1 odd? [#permalink]
03 Aug 2012, 04:05

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

Re: If n is an integer, is n + 1 odd? [#permalink]
03 Aug 2012, 04:46

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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