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# DS - GMATPrep (is positive integer divisible by ....)

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Director
Joined: 19 Mar 2007
Posts: 522
DS - GMATPrep (is positive integer divisible by ....) [#permalink]

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05 May 2007, 10:01
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Manager
Joined: 02 May 2007
Posts: 152

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05 May 2007, 10:23
(A) it is

(1) n^2/36 = (n x n)/(6 x 6) = interger
=> n is divisible by 6
=> n is divisible by 3
=> suff

(2) 144/n^2 = (12 x 12)/(n x n)
=> 12 is divisible by n
=> n can be 12, 6, 3, 4, 1 (4 & 1 are not divisible by 3)
=> insuff

Hence, (A)
Senior Manager
Joined: 03 May 2007
Posts: 270

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05 May 2007, 10:28
kirakira wrote:
(A) it is

(1) n^2/36 = (n x n)/(6 x 6) = interger
=> n is divisible by 6
=> n is divisible by 3
=> suff

(2) 144/n^2 = (12 x 12)/(n x n)
=> 12 is divisible by n
=> n can be 12, 6, 3, 4, 1 (4 & 1 are not divisible by 3)
=> insuff

Hence, (A)

Thanks kirakira
Intern
Joined: 01 May 2007
Posts: 18

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05 May 2007, 10:35
kirakira, can you explain why from "(n x n)/(a x a) = int" follows that n is divisible by a?
Manager
Joined: 02 May 2007
Posts: 152

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05 May 2007, 11:11
kekc wrote:
kirakira, can you explain why from "(n x n)/(a x a) = int" follows that n is divisible by a?

If a square is divisible by a square, the quotient is always a square. Hence:

(n x n)/(a x a) = b x b
=> n x n = (a x a)(b x b)
=> n = a x b
=> n is divisible by a
Director
Joined: 19 Mar 2007
Posts: 522
DS - GMATPrep - OG10 (different conclusions?) [#permalink]

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06 May 2007, 22:21
IMHO, the conclusions made from st (1) and st (2) are different however both are sufficient. Could anybody explain why it is so?
DS - GMATPrep - OG10 (different conclusions?)   [#permalink] 06 May 2007, 22:21
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