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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]
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.

Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]
24 Aug 2014, 15:54

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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]
25 Aug 2014, 03:34

Expert's post

If \(n\) is multiple of \(5\), and \(n = p^2q\) where \(p\) and \(q\) are prime, which of the following must be a multiple of \(25\)?

A \(p^2\) B. \(q^2\) C. \(pq\) D. \(p^2q^2\) E. \(p^3q\)

\(n=5k\) and \(n=p^2p\), (\(p\) and \(q\) are primes). Q: \(25m=?\)

Well obviously either \(p\) or \(q\) is \(5\). As we are asked to determine which choice MUST be multiple of \(25\), right answer choice must have BOTH, \(p\) and \(q\) in power of 2 or higher to guarantee the divisibility by \(25\). Only D offers this.

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