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# Does 4 divide (n^2 + 2)?? 1. n is even 2. n is odd

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Senior Manager
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Does 4 divide (n^2 + 2)?? 1. n is even 2. n is odd [#permalink]  12 Aug 2004, 17:25
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Does 4 divide (n^2 + 2)??

1. n is even
2. n is odd
GMAT Club Legend
Joined: 15 Dec 2003
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D
1) put in any even number for n^2+ 2 and it will never be divisible by 2
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Best Regards,

Paul

Senior Manager
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Paul wrote:
D
1) put in any even number for n^2+ 2 and it will never be divisible by 2

Wow... I was careless on that one. EEK!
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(n^2+2)/4 = (n^2+2)/(2*2). So if (n^2+2)is even, it can divided evenly
by 4.

1. If n is even, n^2+2 = even
2. If n is odd, n^2+2 = even

Manager
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if n is even (n^2 + 2) will never be divided by 4

n = 2k
(n^2 + 2) = (4k^2 + 2)
Senior Manager
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Paul, OlegC are u saying that, for "n" being even or odd the expression is NOT divisible and hence the question can be answered by either statements???
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Joined: 15 Dec 2003
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cbrf3 wrote:
Paul, OlegC are u saying that, for "n" being even or odd the expression is NOT divisible and hence the question can be answered by either statements???

yes. n, being even or odd, in the given equation, will never be divisible by 4. Only way it is divisible by 4 is if it is not an integer. ie root2, root6, root10 and so on
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Best Regards,

Paul

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