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Multiples Question

by Tdot23 » Wed May 23, 2012 4:09 am
Question from the GMAC Practice Test #1:

Q: If n=multiples of 5 and n=p^2q and p and q are both prime, which must be multiples of 5?
A:
(a) p^2
(b) q^2
(c) pq
(d) p^2q^2
(e) p^3q

The answer is (d) p^2q^2 but I am also getting answer choice (c) as the answer... which is what I had initially chosen and was incorrect.

Thanks so much for taking the time to help me with this!
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by Anurag@Gurome » Wed May 23, 2012 4:11 am
NYC23 wrote:Question from the GMAC Practice Test #1:

Q: If n=multiples of 5 and n=p^2q and p and q are both prime, which must be multiples of 5?
A:
(a) p^2
(b) q^2
(c) pq
(d) p^2q^2
(e) p^3q

The answer is (d) p^2q^2 but I am also getting answer choice (c) as the answer... which is what I had initially chosen and was incorrect.

Thanks so much for taking the time to help me with this!
If n is multiple of 5, and n = p²q where p and q are prime, then either p or q or both of them must be equal to 5. Let's analyze each of the cases. (Note that only one of the following can happen at a time)
1. p = 5, p² is multiple of 25, q² not
2. q = 5, q² is multiple of 25, p² not
3. p = q = 5, p² = q² = multiple of 25

We have to find a generalized expression containing p and q such that it becomes multiple of 25. From above analysis we know p² or q² is not that expression as they may or may not be a multiple of 25. But in p²q² both of them are present and simultaneously all the three cases are merged into one! For any of the above cases p²q² will be always a multiple of 25.

The correct answer is D.
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by GMATGuruNY » Wed May 23, 2012 4:24 am
I posted an explanation here:

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