m and n are both positive integers

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

by uptowngirl92 » Sat Jul 18, 2009 12:32 am

If m and n are both positive integers and m>n is 6 a factor of the product mn?
1. m+n=188
2. m is 150% of n

[spoiler=]Ans:B[/spoiler]

How is b sufficient guys?

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Source: Beat The GMAT — Data Sufficiency | Sat Jul 18, 2009 12:32 am

tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

by tohellandback » Sat Jul 18, 2009 6:08 am

since you already know why 1 is not sufficient, I will just explain why B is sufficient

m is 150% of n
so m=1.5n=n+.5n, now for m to be an integer, n has to be even because of the term n/2
so n must have atleast 2 as a prime factor
mn=1.5n*n=1.5n^2 , so when we square n, the 2 in n become 2^2 that is 4 and
4*1.5=6. so 6 is a factor of mn

The powers of two are bloody impolite!!

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