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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

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

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06 Apr 2014, 10:49

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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.

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