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if n is an integer,is n even?

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by emina1992 » Wed Feb 05, 2014 6:51 pm
I am giving the question here:(2)3n+4 is an even integer , but this sentence has two possibilities,if 3n+4=12 then the n will be the 8/3,which is neither even nor odd; if 3n+4=16 then the n will be the 4 ,which is an even now. So the outcome of sentence(2) is uncertain . why OG choose the D? thx
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by emina1992 » Wed Feb 05, 2014 6:53 pm
this is OG13 27
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by Brent@GMATPrepNow » Wed Feb 05, 2014 7:18 pm
First, let's deal with the entire question:
If n is an integer, is n even?
(1) n² − 1 is an odd integer.
(2) 3n + 4 is an even integer.
Target question: Is n even?

Statement 1: n² − 1 is an odd integer.
If n² −1 is an odd integer, then n² must be an even integer.
If n² is an even integer, then n must be even.
Rationale: (odd)² = odd, but (even)² = even
As such, statement 1 is SUFFICIENT

Statement 2: 3n + 4 is an even integer.
If 3n + 4 is an even integer, then 3n must be an even integer (since Even + Even = Even).
If 3n must be an even integer, then n must be even.
Rationale: (odd)(even) = even and
As such, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent
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by Brent@GMATPrepNow » Wed Feb 05, 2014 7:25 pm
emina1992 wrote:I am giving the question here:(2)3n+4 is an even integer, but this sentence has two possibilities,if 3n+4=12 then the n will be the 8/3,which is neither even nor odd; if 3n+4=16 then the n will be the 4 ,which is an even now. So the outcome of sentence(2) is uncertain . why OG choose the D? thx
The statement does not say that 3n+4 = 12. It says that 3n+4 is an even integer.
The fact of the matter is that we don't know the actual value of n. Likewise, we don't know the actual value of 3n+4. So, we can't just assign it some value.
I believe that you're reading statement 2 as "3n+4 is any even integer" when this is not the case.

Cheers,
Brent
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by emina1992 » Wed Feb 05, 2014 7:51 pm
Brent@GMATPrepNow wrote:
emina1992 wrote:I am giving the question here:(2)3n+4 is an even integer, but this sentence has two possibilities,if 3n+4=12 then the n will be the 8/3,which is neither even nor odd; if 3n+4=16 then the n will be the 4 ,which is an even now. So the outcome of sentence(2) is uncertain . why OG choose the D? thx
The statement does not say that 3n+4 = 12. It says that 3n+4 is an even integer.
The fact of the matter is that we don't know the actual value of n. Likewise, we don't know the actual value of 3n+4. So, we can't just assign it some value.
I believe that you're reading statement 2 as "3n+4 is any even integer" when this is not the case.

Cheers,
Brent


it means that we just need to make qualitative evaluation for this type of question rather than put some definite numbers in the statement? thanks
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