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n = Multiple of 5. Also, n = p^2q. which means either p = 5 or q = 5. We cannot assume either of it. Option D squares off both the variables, hence leaving no room. We can safely say that D will be definitely a multiple of 25. _________________

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Plug in these numbers and you will find that only D satisfies the condition.

if n has to be a multiple of 5, and p and q are prime numbers ( prime numbers are not divisible by any other number except 1 and themselves) then, p or q must contain 5 as a factor).

We can not say that only p or q will have 5 as a factor.

N= is a factor of 5 Therefore we know that either P or Q must have 5 as prime factor.

We know want to know which equation is a multiple of 25. Which means when broken into it's primes there must be 5x5.

A. p^2 - doesn't guarantee as Q could have contained the 5 B. q^2 - doesn't guarantee as P could have contained the 5 C. pq - doesn't guarantee as 1 and not both might have contained the 5 D. p^2q^2 - with n equation we know 1 variable contained a 5 now we can guarantee one contains 2 5's E. p^3q - doesn't guarantee as Q could have contain the 5

If n is a multiple of 5 and n = p^2q, then obviously p should be a multiple of 5, as p and q are prime numbers. So p^2 and p^2q^2 will both be multiples of 25. What is the source for this question?

If n is a multiple of 5 and n = p^2q, then obviously p should be a multiple of 5, as p and q are prime numbers. So p^2 and p^2q^2 will both be multiples of 25. What is the source for this question?

Based on the answer choices, it is not n=p^{2q} but n={p^2} \times q. If it was n=p^{2q}, then like you said both choices must be multiples of 25. By the way, that what I thought too. But then I screened the answer choices and figured out there must be something wrong with my reading of the formula

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If n is a multiple of 5, n=p^2q, where p and q are prime num [#permalink]
06 Apr 2014, 09:49

3

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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.