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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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