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Is n an integer?

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Is n an integer? [#permalink] New post 08 Apr 2012, 04:51
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Is n an integer?

(1) 2n is an integer.
(2) 3n is an integer.

Please explain your answeres
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Apr 2012, 04:57, edited 1 time in total.
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Re: Is n an integer? [#permalink] New post 08 Apr 2012, 05:01
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Is n an integer?

(1) 2n is an integer --> 2n=integer: if n=1/2 then the answer is NO but if n=1 then the answer is YES. Not sufficient.
(2) 3n is an integer --> 3n=integer: if n=1/3 then the answer is NO but if n=1 then the answer is YES. Not sufficient.

(1)+(2) Subtract (1) from (2): 3n-2n=integer-integer --> n=integer (since integer-integer=integer). Sufficient.

Answer: C.

Hope it's clear.
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Re: Is n an integer? [#permalink] New post 08 Apr 2012, 05:19
+1 C

Bunuel like the shortcut for getting "n" while solving both. I was trying to use a fraction to break the question stem
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Re: Is n an integer? [#permalink] New post 08 Apr 2012, 07:25
thanks Bunuel!!!

i was taking into the realm of LCM's but couldnt get a headway. i.e., 1 and 2 cannot deduce the fact that n is an integer.

combining both of them together 2n and 3n is an integer, it would mean that 6n would be an integer but reached a block there again as it still doesnt prove n is an integer.

ur method is short and easy. thanks!!
Re: Is n an integer?   [#permalink] 08 Apr 2012, 07:25
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