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# If m/n=7/15, mn=? 1). M and n are positive integers 2). The

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Manager
Joined: 04 Sep 2006
Posts: 113
If m/n=7/15, mn=? 1). M and n are positive integers 2). The [#permalink]

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24 May 2009, 09:10
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If m/n=7/15, mn=?
1). M and n are positive integers
2). The greatest common factor of m and n is 3
Intern
Joined: 02 Mar 2009
Posts: 43
Location: Austin

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24 May 2009, 09:20
B

I. Insuff. M can be 7 * 6, N can be 15*6 or M = 7*8, N= 15*8
II. Suff. M = 7*(-3), N =15*(-3) or M = 7*(-5), N=15*(-5)
Either way the product is always positive.

Last edited by packem on 24 May 2009, 10:11, edited 1 time in total.
Manager
Joined: 30 Mar 2009
Posts: 242

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24 May 2009, 09:26
IMO B (1'14'')

If m/n=7/15, mn=?
1). M and n are positive integers
not sufficient

2). The greatest common factor of m and n is 3
from this, we can find that at least m is (7*3)=21, then n must be 45 --> calculate the outcome of m.n
Because m/n=7/15, so if we want to find another greater couples, we should multiply each m & n with a same integer --> their greatest common factor will be greater than 3 --> eliminate this possibility
If N=-21 and M=-45, then the outcome of m.n is still the same

Therefore, B alone is sufficient
Intern
Joined: 02 Mar 2009
Posts: 43
Location: Austin

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24 May 2009, 10:10
Yup agreed.

B alone is sufficient.
Re: GCD   [#permalink] 24 May 2009, 10:10
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