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prime number, multiple question from GMAT prep 1

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prime number, multiple question from GMAT prep 1

by LFalken » Tue Aug 25, 2009 5:42 am
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

The answer is D, and I have not been able to satisfy myself completely on how this is exactly done. If anyone could shed some light I would greatly appreciate it. Thanks.
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by kaulnikhil » Tue Aug 25, 2009 6:54 am
since n is s multiple pf 5 so product of p and q should end in 5 or 0
let p =3 and q = 5
we can eliminate p^2,pq and p^3q
now put p =5 and q =3
we can eliminate q^2

Only D is remaining.
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This is how

by enniguy » Tue Aug 25, 2009 7:35 am
Question says that (p^2)q is a multiple of 5. Check which of the following answer choices has (p^2)q. Only D has.

{(p^2)q}{q}.

Why? Because we know that {(p^2)q} is a multiple of 5 and anything you multiply to this number will still be a multiple of 5.
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by Ian Stewart » Tue Aug 25, 2009 8:23 am
If n is divisible by 5, then a 5 must appear in the prime factorization of n. We know the prime factorization of n is (p^2)(q), so either p = 5 or q = 5. Thus, either p^2 = 25 or q^2 = 25. We can't be sure which, but we can be sure that (p^2)(q^2) is a multiple of 25.
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