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# If n is an integer, is n even? (1) n^2-1 is an odd integer

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If n is an integer, is n even? (1) n^2-1 is an odd integer [#permalink]

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12 Jul 2003, 16:01
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If n is an integer, is n even?

(1) $$n^2-1$$ is an odd integer
(2) $$3n+4$$ is an even integer

Official Guide 12 Question

 Question: 24 Page: 274 Difficulty: 600

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12 Jul 2003, 23:13
(1) n^2-1=odd

n^2=odd+1=even
n*n=even
thus, n is even ------------OK

(2) 3n+4=even
3n=even - 4=even
3n=even
Thus, n has to be even, since 3 is odd. OK

Finally, it is D.

Remember: ZERO is EVEN but neither positive nor negative.
So, if you take n=0 for (2) set, you will get 4 that is even.

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10 Feb 2010, 13:42
Ekin4112 wrote:
If n is an integer is n even?

1) n^2-1 is an odd integer
2) 3n+4 is an even integer

According to GMAT answer it is D but I disagree and have to say it is E because n can be 0 which is not an even number while satisfying both requirement.

Any thoughts?

Hello Ekin, welcome to the Gmat Club.

First of all I must say that zero IS an even integer, though it's neither positive nor negative.

Even number (even integer) $$n$$ is of the form $$n=2k$$, where $$k$$ is an integer, so for $$k=0$$, $$n=2*0=0$$.

As for the question:

(1) $$n^2-1=(n-1)(n+1)=odd$$ --> both $$n-1$$ and $$n+1$$ must be odd to produce an odd integer when multiplied, hence $$n$$ is be even. Sufficient.

(2) $$3n+4=even$$ --> $$3n$$ must be even --> $$n$$ must even. Sufficient.

Hope it helps.
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10 Feb 2010, 17:21
Thanks for clearing that up.

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14 Mar 2010, 03:12
Ekin4112 wrote:
If n is an integer is n even?

1) n^2-1 is an odd integer
2) 3n+4 is an even integer

According to GMAT answer it is D but I disagree and have to say it is E because n can be 0 which is not an even number while satisfying both requirement.

Any thoughts?

Its D, as said by Bunuel zero is even integer.

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OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 00:27
If n is an integer, is n even?
(1) (n^2) - 1 is an odd integer.
(2) 3n + 4 is an even integer.

I personally think it is E, because putting n as 0, both the condition are insufficient. But the OA does not include 0 as one of the conditions to check.

Please explain or am I missing something here?

Thanks,
Sandeep Nerli (Taking GMAT on 30th of June, 2010)

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 01:30
IMO A.

Why n=0 is not a valid condition?

sandeepnerli wrote:
If n is an integer, is n even?
(1) (n^2) - 1 is an odd integer.
(2) 3n + 4 is an even integer.

I personally think it is E, because putting n as 0, both the condition are insufficient. But the OA does not include 0 as one of the conditions to check.

Please explain or am I missing something here?

Thanks,
Sandeep Nerli (Taking GMAT on 30th of June, 2010)

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 01:41
I think you are forgetting that 0 is even.

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 01:47
Sorry, I want to change my answer to D.
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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 02:09
if n=3( an integer)
n^2-1=3^2-1=8 is not odd integer
3n+4=3*3+4=13 is not even integer.

Both these conditions are insufficient.

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 02:23
IN DS, the two given statement are correct. If you are checking for their correctness then it is wrong.

Here, both statements are true and you need to consider that for which values these 2 statements meeting the criteria.

Let me know if you have some questions.

innersanctum wrote:
if n=3( an integer)
n^2-1=3^2-1=8 is not odd integer
3n+4=3*3+4=13 is not even integer.

Both these conditions are insufficient.

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 02:29
Hi,

The question clearly states that n is an integer, so n can be 0 and I agree that for n= 0 both the statements hold true, but since 0 is neither negative nor positive, I think the answer should be E, not D

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 03:10

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 03:54
Sorry missed it, is O even or odd? I believe it is neither, and its a debatable topic. But how should we answer these kinda questions.

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 03:56
Also what does GMAC consider's 0 as - Even or Odd or Both or Neither?

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Re: OFFICIAL GUIDE 12th Edition DS Q24 [#permalink]

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11 Jun 2010, 22:46
Acoording to GMAT 0 is even but it is neither positive nor negative

Hope this helps
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Re: OFFICIAL GUIDE 12th Edition DS Q24   [#permalink] 11 Jun 2010, 22:46
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# If n is an integer, is n even? (1) n^2-1 is an odd integer

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