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# PS: Number Properties

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Joined: 03 Feb 2009
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Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
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PS: Number Properties [#permalink]  02 Mar 2009, 08:28
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If n is a multiple of 5 and n=(p^2)*q, where p and q are prime numbers, which of the following must be a multiple of 25?
a) p^2
b) q^2
c) pq
d) (p^2)*(q^2)
e) (p^3)*q
Intern
Joined: 03 Feb 2009
Posts: 27
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
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Re: PS: Number Properties [#permalink]  02 Mar 2009, 08:35
My thought process what if n is a multiple of 5 and n = (p^2)*q, where p and q are prime numbers, then q has to be 5 because no prime number squared = 5. So if the question wants to know what number is a multiple of 25? .... then you have to square q. So if q^2 equals 25, then (p^2)*(q^2) has to be a multiple of 25.

The correct answer is D....(p^2)*(q^2), but I wanted to make sure my thought process was correct.

Additionally, one of the answers was q^2. Is 25 technically a multiple of 25? (i.e. 1X25 = 25) Or does a multiple, technically, have to be greater than the number itself?

Thanks.
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Re: PS: Number Properties [#permalink]  02 Mar 2009, 15:48
i believe the answer is D: (p^2)*(q^2).

We know that n = 5i (where i is some integer)
we know that n = (p^2)*q (where p and q are prime numbers).
Therefore either p or q is 5.

Which must be a multiple of 25? Since we don't know which (p or q) is 5, only P^2)*(q^2) solves the issue.
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Re: PS: Number Properties [#permalink]  08 Mar 2009, 03:30
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Re: PS: Number Properties [#permalink]  08 Mar 2009, 03:48
Expert's post
Economist wrote:

1) n is divisible by 5, so p OR q must be 5 (as p and q are prime numbers).

2) to be divisible by 5 a new number must contain p^2 AND q^2. Otherwise, there would be possibility for a new number to be not divisible by 25.
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Re: PS: Number Properties   [#permalink] 08 Mar 2009, 03:48
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