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Common factor?

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by cartera » Sun Nov 23, 2008 7:40 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.


OA A

Any explanation on this?
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Source: — Data Sufficiency |
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by mals24 » Sun Nov 23, 2008 8:04 am
k/6+m/4 = t/12

(2k+3m)/12 = t/12

2k+3m = t

3m is a multiple of 3, we only need information about k.

St 1: K is a multiple of 3

k = 3*a, where 'a' is an integer which when multiplied by 3 gives a product of k.

2(3*a) + 3m = t

3*[2a + 3m] = t

So t is also a multiple of 3. Hence the answer to the question is yes
St 1: SUFF

St 2: m is a multiple of 3.

3m is anyways a multiple of 3. We don't know if 2k is a multiple of 3 or not.

If k=1, m=5; t = 17, the only common factor between 17 and 12 is 1. Hence answer to the question is No.
k=2, m=4; t = 16, the answer to the question is Yes.

So answer is A.
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by cramya » Sun Nov 23, 2008 11:59 am
Excellent solution Mals24! :-)
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by mals24 » Sun Nov 23, 2008 12:09 pm
Thank you cramya :D
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by logitech » Sun Nov 23, 2008 2:08 pm
I think I should leave the love birds alone :D
LGTCH
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"DON'T LET ANYONE STEAL YOUR DREAM!"
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by mals24 » Sun Nov 23, 2008 2:28 pm
I think I should leave the love birds alone Very Happy
Yes please Get Out!!!

PS: When someone appreciates your effort, thanking that person is considered POLITE.
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