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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

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?

Re: PS: Number Properties [#permalink]
08 Mar 2009, 03:48

Expert's post

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. _________________