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Number Properties - multiples of 5 (gmat prep)

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by kshin78 » Sat Aug 09, 2008 1:13 pm
If n is a multiple of 5 and n = p^2q where p & q are prime numbers, 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

Please provide an explanation. Thanks in advance!!
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by parallel_chase » Sat Aug 09, 2008 2:13 pm
n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

25=5*5

Therefore, p^2q^2 will ensure that we have two 5's i.e. multiple of 25, irrespective of whether p is 5 or q is 5.

Hence D is the answer.
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by drizzle » Sun Aug 10, 2008 7:16 am
parallel_chase wrote:n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

Hence D is the answer.
here p should be 5 right...or else n can't be mulitple of 5...hope i'm not missing anything...
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by parallel_chase » Sun Aug 10, 2008 8:40 am
drizzle wrote:
parallel_chase wrote:n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

Hence D is the answer.
here p should be 5 right...or else n can't be mulitple of 5...hope i'm not missing anything...
q can also be 5. If q is 5 n would still be a multiple of 5
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by pepeprepa » Sun Aug 10, 2008 8:41 am
Agree with D)
p^2q^2 is p^2 * q^2
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by kshin78 » Sun Aug 10, 2008 12:27 pm
parallel_chase wrote:n=p^2q

we know that n is a multiple of 5.
p and q are different prime numbers and one of them has to be 5, then only we can be assured that n is a multiple of 5.

25=5*5

Therefore, p^2q^2 will ensure that we have two 5's i.e. multiple of 25, irrespective of whether p is 5 or q is 5.

Hence D is the answer.
Thanks! I should have realized p or q had to be 5....
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by ritubahl » Tue Apr 07, 2009 10:08 am
I am sorry I still don't get it - how can n be a multiple of 5 if p is not a multiple of 5?
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by pakaskwa » Tue Apr 07, 2009 12:56 pm
The original question was not clear:
n=p^2q

Is it n=(p^2)*q, or n=p^(2q)?
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by aj5105 » Mon May 04, 2009 2:09 am
n=(p^2)*q
pakaskwa wrote:The original question was not clear:
n=p^2q

Is it n=(p^2)*q, or n=p^(2q)?
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