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Number Properties from GMATPrep

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Number Properties from GMATPrep [#permalink] New post 27 Sep 2009, 23:34
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

82% (01:57) correct 18% (00:00) wrong based on 13 sessions
Please help me to solve that problem.
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Re: Number Properties from GMATPrep [#permalink] New post 27 Sep 2009, 23:50
The answer is D: p^2*q^2.

You are given that n = p^2 * q, which is a multiple of 5. Therefore p^2 * q is a multiple of 5. Since 5 is a prime number, p OR q must be a multiple of 5. Therefore, in order to be a multiple of 25, you must have a MINIMUM of p^2 * q^2 in the answer, since you don't know whether p or q is the multiple of 5. The only answer which satisfies this condition is D.
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Re: Number Properties from GMATPrep [#permalink] New post 02 May 2011, 19:32
n = 5k = 20,45 etc.

20 = 2^2 * 5; 45 = 3^2 * 5

hence min solution possible is p^2 * q^2.
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Re: Number Properties from GMATPrep [#permalink] New post 02 May 2011, 21:29
It is given that
n = p^2 (q)
n = 5(...)

We do not know whether p = 5 OR q = 5. There are 2 possibilities.

n = 5^2 (q)
OR
n = p^2 (5)

Since, we do not know whether p or q is 5 then. (A) and (B) could be eliminated.

(D) on the other hand raises both p and q to a power of 2. This guarantees 5 to be raised to 2 which is equivalent to 25.

Hence, D.
Re: Number Properties from GMATPrep   [#permalink] 02 May 2011, 21:29
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Number Properties from GMATPrep

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