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# PS: Number Properties

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Intern
Joined: 03 Feb 2009
Posts: 27
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
PS: Number Properties [#permalink]

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02 Mar 2009, 09:28
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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

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Intern
Joined: 03 Feb 2009
Posts: 27
Schools: Duke, UNC, Emory, Ga Tech, Vanderbilt, Indiana, Wash U, Texas, Rollins
Re: PS: Number Properties [#permalink]

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02 Mar 2009, 09:35
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.
Manager
Joined: 16 Feb 2009
Posts: 57
Schools: Anderson FEMBA
Re: PS: Number Properties [#permalink]

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02 Mar 2009, 16:48
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.
Director
Joined: 01 Apr 2008
Posts: 827
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: PS: Number Properties [#permalink]

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08 Mar 2009, 04:30
Didnt get this..please explain.
CEO
Joined: 17 Nov 2007
Posts: 3484
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Re: PS: Number Properties [#permalink]

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08 Mar 2009, 04:48
Economist wrote:
Didnt get this..please explain.

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, 04:48
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# PS: Number Properties

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