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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Thu Apr 02, 2009 11:40 am

If k, m, and t are positive integers and k/6 + m/4 = t/12, do t and 12 have a common factor greater than 1 ?
(1) k is a multiple of 3.
(2) m is a multiple of 3.

Please tell me how to solve it?
OA: A

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Source: Beat The GMAT — Data Sufficiency | Thu Apr 02, 2009 11:40 am

bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

by bluementor » Fri Apr 03, 2009 2:24 am

k/6 + m/4 = t/12
2k/12 + 3m/12 = t/12
2k + 3m = t

do t and 12 have a common factor greater than 12?

statement 1:
k=3x, where x is some positive integer.

so,

2(3x) + 3m = t
3(2x + m) = t

we know that (2x + m) is an integer, so t is a multiple of 3. therefore, t and 12 have 3 as a common factor, which is greater than 1. sufficient.

statement 2:
m=3y, where y is some positive integer.

so,

2k + 3(3y) = t

we cannot factorize the equation further because we don’t know anything about k or y. insufficient.

Choose A.

-BM-

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ketkoag: Legendary Member; Posts: 876; Joined: Thu Apr 10, 2008 8:14 am; Thanked: 13 times

by ketkoag » Fri Apr 03, 2009 3:52 am

thanks a lot for the reply

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