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If N is a positive integer and N^2 is divisible by 72, then

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If N is a positive integer and N^2 is divisible by 72, then [#permalink] New post 09 Aug 2007, 17:17
If N is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is:

a)6
b)12
c)24
d)36
e)48

PLEASE REPLY WITH EXPLANATIONS
Director
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 [#permalink] New post 09 Aug 2007, 18:50
search through the first 1 or 2 pages, this question was just asked recently.

if I remember correctly the answer is B. 12 and they had plenty of explanation to go along with it.
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Re: GMAT Review [#permalink] New post 09 Aug 2007, 18:53
r0m3416 wrote:
If N is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is:

a)6
b)12
c)24
d)36
e)48

PLEASE REPLY WITH EXPLANATIONS


B. 12

n^2 = 72k
n^2 = 2x2x2x3x3 (k)

since n is a +ve integer and n^2 is a square, 72k has to be a squre. if so, then k should be at least 2. in that case n = 2x2x3 = 12.
Director
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Re: GMAT Review [#permalink] New post 10 Aug 2007, 00:34
r0m3416 wrote:
If N is a positive integer and N^2 is divisible by 72, then the largest positive integer that must divide N is:

a)6
b)12
c)24
d)36
e)48

PLEASE REPLY WITH EXPLANATIONS


Since N^2 is divisible by 72, N^2 is atleast 72*2=144 implying that N has to be atleast 12. Answer B.
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 [#permalink] New post 10 Aug 2007, 00:53
I think that the answer is d (36),
because 36^2 = 1296, it divides 72!
If that is not correct, please tell :oops:

it cannot be E, because 48, as 42^2 =1764, does not divide 72...
  [#permalink] 10 Aug 2007, 00:53
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