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Is N/2 an odd integer? (1) 2N is even (2) N is even

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Is N/2 an odd integer? (1) 2N is even (2) N is even [#permalink] New post 27 Feb 2012, 06:04
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Is N/2 an odd integer?

(1) 2N is even.
(2) N is even.

Here the answer is E, but for me is D. here my explanation.

N/2= Odd ??

N= 2 x Odd= Even....so : N is Even ??

1) 2N= even Yes

2) N= Even

Or should I consider also the case where N/2 is even ??
[Reveal] Spoiler: OA

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Re: Is N/2 an odd integer? [#permalink] New post 27 Feb 2012, 06:17
Expert's post
carcass wrote:
Is N/2 an odd integer?
(1) 2N is even.
(2) N is even.

Here the answer is E, but for me is D. here my explanation.

N/2= Odd ??

N= 2 x Odd= Even....so : N is Even ??

1) 2N= even Yes

2) N= Even

Or should I consider also the case where N/2 is even ??


Yes, N must be even in order N/2 to be an odd integer but, N being even doesn't guarantee that N/2 is odd (so converse is not true).

For example:
If N=4, which satisfies both statements, then N/2=2=even, not odd;
If N=2, which satisfies both statements, then N/2=1=odd;
Two different answers not sufficient.

Answer: E.

Hope it's clear.
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Re: Is N/2 an odd integer? [#permalink] New post 27 Feb 2012, 06:22
Consider the case where N is 6. N/2 is odd.
What about when N is 4. N/2 is even.
(1) is not sufficient.

You can use the same examples above to evaluate statement 2.
(2) is not sufficient.

Combining the information in both statements is also insufficient.
N could be 4 or 6 and result in N/2 being odd or even.

carcass wrote:
Is N/2 an odd integer?
(1) 2N is even.
(2) N is even.

Here the answer is E, but for me is D. here my explanation.

N/2= Odd ??

N= 2 x Odd= Even....so : N is Even ??

1) 2N= even Yes

2) N= Even

Or should I consider also the case where N/2 is even ??
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Re: Is N/2 an odd integer? [#permalink] New post 27 Feb 2012, 06:37
The answer should be (E)
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Re: Is N/2 an odd integer? (1) 2N is even (2) N is even [#permalink] New post 28 Mar 2014, 08:34
Let's try this one by plugging some numbers so as to make solution more practicals. 2N is even, for statement 1 we have that if n is 1 then the answer is no, in fact n/2 is not even an integer. But if answer is N=2 then we have that N/2 is in fact odd hence insufficient.

Statement 2 we have that N is even same here. If N =2 then we have that N/2 is an odd integer but if N=4 then N/2 is even integer hence insufficient. Both statements together, we could try similar cases. Say N=2 then answer is yes, say N equals 4 then answer becomes no.

Therefore correct answer choice is E.
Hope this helps

Cheers
J
Re: Is N/2 an odd integer? (1) 2N is even (2) N is even   [#permalink] 28 Mar 2014, 08:34
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