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If n is a multiple of 5 and n = p^2q, where p and q are....

by galinaphillips » Sun Jun 03, 2007 6:25 pm

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

p^2
q^2
pq
p^2q^2
p^3q

The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
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Re: If n is a multiple of 5 and n = p^2q, where p and q are.

by jayhawk2001 » Sun Jun 03, 2007 6:53 pm
galinaphillips wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?

p^2
q^2
pq
p^2q^2
p^3q

The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.

Since the question asks for "must be a multiple of 25", we have to find
the answer that we know WILL match

p^2 alone cannot be the answer since it could be q that is the multiple of
5. Same story for q^2.

pq we know will yield a multiple of 25, only when p and q are multiples
of 5 or when either of p or q is a multiple of 25. We don't know this
for sure as well. Discard. Same story for p^3*q.

p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5.
We know that n is a multiple of 5, so either p or q SHOULD be a multiple
of 5 and hence p^2*q^2 will be a multiple of 25.
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Thanks

by galinaphillips » Mon Jun 04, 2007 5:30 am
Thanks a lot!!! :)
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Re: Thanks

by alexdallas » Sun Jun 28, 2009 3:05 pm
"p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5. "

why is this?
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by AymanMath » Sun Jun 28, 2009 11:35 pm
I think these type of question you cannot solve it without assuming real figures

So I assume that P=2 and q=5 which is coincide with forth answer

Am I correct guys ?? :)
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by alexdallas » Mon Jun 29, 2009 5:14 pm
anyone?
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by abcdefg » Mon Jun 29, 2009 6:43 pm
does p^2q^2 = p^(4q)?
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by pallavisingh12 » Tue Jun 30, 2009 3:15 am
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.

Im sorry but this dsn make sense.. For the above..Should'nt "p" HAVE to be 5.
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by alexdallas » Wed Jul 01, 2009 4:12 am
i think he meant to say "mult. of 25", not mult. of 5. then it makes sense.
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by uptowngirl92 » Wed Aug 26, 2009 3:27 am
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.

Please explain the above..i dnt understand the logic.
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by sranga » Thu Nov 26, 2009 5:27 am
For N to be a multiple of 5 [which is as per the question] then either P or Q must be 5 because both P and Q are prime numbers.

eg,

N being a multiple of 5 can take values 10 , 15, 20 and so on

which is 5*2 or 2*5 = 10 [here either p or q is 5]

similarly 5*3 or 3*5 = 15 [here either p or q is 5]

and so on...

so in order to be a multiple of 25 we need one of the number to be 25, which can be obtained by squaring either P or Q, since we do not know which of the both is 5 ,we are better off squaring both

hence the answer is (p^2)(q^2)

HTH
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by greentealeaf » Sat Apr 24, 2010 5:42 pm
jayhawk2001 wrote:
galinaphillips wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?

p^2
q^2
pq
p^2q^2
p^3q

The answer is p^2q^2 on this problem from mba.com but I'm not sure how to solve?
Thanks!
If n is a multiple of 5, then either p is a multiple of 5 or q is a multiple of 5
or both.

Since the question asks for "must be a multiple of 25", we have to find
the answer that we know WILL match

p^2 alone cannot be the answer since it could be q that is the multiple of
5. Same story for q^2.

pq we know will yield a multiple of 25, only when p and q are multiples
of 5 or when either of p or q is a multiple of 25. We don't know this
for sure as well. Discard. Same story for p^3*q.

p^2*q^2 will be a multiple of 25 if either p or q is a multiple of 5.
We know that n is a multiple of 5, so either p or q SHOULD be a multiple
of 5 and hence p^2*q^2 will be a multiple of 25.
very nice explaination!
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by crisro » Wed May 25, 2011 6:58 pm
if p^2q^2 is a multiple of 5, with p and q prime numbers then we can have only three possible options
1) p=5, when p^2=25
2) q=5, when q^2=25
3) p=q=5, when pq=25

the only answer choise that has all three options is answer d)
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by Scott@TargetTestPrep » Wed Jul 04, 2018 6:07 pm
jayhawk2001 wrote:
galinaphillips wrote:If n is a multiple of 5 and n = p^2q, where p and q are prime numbers, which of the following must be a multiple of 25?

p^2
q^2
pq
p^2q^2
p^3q
A common phrase that is used on the GMAT is the word must. In this question, we are asked which of the following must be a multiple of 25. This means that one of our answer choices will always be a multiple of 25, no matter what. It is our job to determine which one, based on the given information.

We are given that n is a multiple of 5, n = (p^2)q, and that p and q are prime numbers.

Because n is a multiple of 5, a prime number, we know that either p or q is 5. Let's now analyze each answer choice to determine which one MUST (in all cases) be a multiple of 25.

A) p^2

If p = 3, then p^2 = 9 is not a multiple of 25. Answer choice A is not correct.

B) q^2

If q = 3, then q^2 = 9 is not a multiple of 25. Answer choice B is not correct.

C) pq

If p = 5 and q = 3 (or vice versa), pq = 15 is not a multiple of 25. Answer choice C is not correct.

D) (p^2)(q^2)

Regardless of which values we select for p and q, since we know that either p or q is 5, (p^2)(q^2) will always be a multiple of 25. If this is difficult to see, let's use numbers.

If p = 5 and q = 3, (p^2)(q^2) = (25)(9) is a multiple of 25.

If p = 3 and q = 5, (p^2)(q^2) = (9)(25) is also a multiple of 25.

Answer choice D is correct.

For practice, let's analyze answer choice E.

E) (p^3)q

If p = 3 and q = 5, then (p^3)q = 135 is not a multiple of 25. Answer choice E is not correct.

Answer: D

Scott Woodbury-Stewart
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