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# Is n/12 an integer?

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Math Expert
Joined: 02 Sep 2009
Posts: 55236

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28 Jul 2017, 01:44
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Difficulty:

75% (hard)

Question Stats:

22% (01:39) correct 78% (00:54) wrong based on 36 sessions

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Is n/12 an integer?

(1) n^2/144 is an integer.
(2) n/6 is an integer.

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Re: Is n/12 an integer?  [#permalink]

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28 Jul 2017, 02:22
Bunuel wrote:
Is n/12 an integer?

(1) n^2/144 is an integer.
(2) n/6 is an integer.

(1) n could be 12 or any multiple of 12 in all cases n/12 will be an integer
Sufficient

(2) n/6 is an integer then 2n/12 will also be integer

2 * n/12 is an integer
n/12 can be 1/2

Not sufficient

A
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Luckisnoexcuse
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Re: Is n/12 an integer?  [#permalink]

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28 Jul 2017, 02:33
1
mynamegoeson wrote:
Bunuel wrote:
Is n/12 an integer?

(1) n^2/144 is an integer.
(2) n/6 is an integer.

(1) n could be 12 or any multiple of 12in all cases n/12 will be an integer
Sufficient

A

Hi,

always be careful when ever a variable is given..

(1) $$\frac{n^2}{144}$$ is an integer.
EASY to falter..
if n = 12...ans is YES
say n=$$\sqrt{288}$$, so 288/144 is an integer..
but $$n/12=\sqrt{288}/12=12\sqrt{2}/12=\sqrt{2}$$... ans NO
Insuff

(2) $$\frac{n}{6}$$ is an integer.
n=6...ans NO
n=12...ans YES

insuff

combined..
statement II tells u that n=6k, where k is an integer... so n is an INTEGER..
statement I now tells us that $$\frac{n^2}{144}$$ is an integer. so if n is an integer, n has to be a multiple of 12
ans YES
suff
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Re: Is n/12 an integer?   [#permalink] 28 Jul 2017, 02:33
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