Number Properties

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ftaslimi
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Topic: Number Properties
PostSat Nov 07, 2009 9:27 pm
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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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xcusemeplz2009
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PostSat Nov 07, 2009 9:53 pm
imo d

oa pls
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ftaslimi
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PostSat Nov 07, 2009 10:42 pm
The answer is not D.
Pls. show your work.
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okigbo
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PostTue Nov 10, 2009 12:55 am
Is it 12?

72=2^3 * 3^2

So n must have 2 2's and a 3
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vivek.kapoor83
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PostTue Nov 10, 2009 11:07 am
taking n = 12, n^2 = 144 which is divisible by 72
so, 12 is the largest no. thru which n divides.another eg doesnt satisfy
IMO B
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PostTue Nov 10, 2009 1:15 pm
Note you are not looking for n. You are looking for the largest positive integer that must divide n.

The smallest n = 12, so n^2 = 144, like you said. 144 is divisible by every answer choice. Since (e) is the greatest....

Note that 12 = 2*2*3, so 12^2 = 2*2*2*2*3*3.

72 = 6*6*2 = 3*3*2*2*2. You MUST have one more factor of 2 in order to get a perfect square (two 3s and four 2s).
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ftaslimi
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PostTue Nov 10, 2009 11:48 pm
Yes, the correct answer is B.
Thanks,
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