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

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Manager
Joined: 29 May 2007
Posts: 96

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If N is a positive integer and N^2 is divisible by 72, then [#permalink]

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09 Aug 2007, 18:17
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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Director
Joined: 12 Jul 2007
Posts: 857

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09 Aug 2007, 19:50
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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Director
Joined: 03 May 2007
Posts: 867

Kudos [?]: 264 [0], given: 7

Schools: University of Chicago, Wharton School

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09 Aug 2007, 19:53
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

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.

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Director
Joined: 09 Aug 2006
Posts: 754

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10 Aug 2007, 01:34
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

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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Intern
Joined: 03 Aug 2007
Posts: 3

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10 Aug 2007, 01:53
I think that the answer is d (36),
because 36^2 = 1296, it divides 72!
If that is not correct, please tell

it cannot be E, because 48, as 42^2 =1764, does not divide 72...

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10 Aug 2007, 01:53
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