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# If k, m, and t are positive integers and k/6+m/4 = t/12, do

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If k, m, and t are positive integers and k/6+m/4 = t/12, do [#permalink]

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30 Apr 2006, 07:55
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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.

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30 Apr 2006, 07:59
t = 2k+3m

hence A is sufficient while B is not

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01 May 2006, 14:29
M8 wrote:
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.

k/6+m/4 = t/12
2k+3m = t
if k is a multiple of 3, then t and 12 both have at least 3 as common factor.

statement (i) is suff...
statement (ii) is not suff cuz it doesnot matter whether m is a multiple of 3.

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01 May 2006, 22:51
k/6 + m/4 = (4k + 6m)/24 = t/12 = 2t/24

So 4K + 6m = 2t --> t = 2k+3m

St1:
K is a multiple of 3. 2(3x) = 3(2x)
t = 3(2x+m)

Since t is a multiple of 3, it will always have 3 as a factor. 12 will also have 3 as a factor. Sufficient.

St2:
m is a multiple of 3. 3(3m)
t = 2x + 3(3m)

Depending on x, t might or might not have a common factor with 12 other than 1.

Insufficient.

Ans A

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03 May 2006, 04:47
Yeah.. asnwer is A...

Time to retire... dazed!

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03 May 2006, 06:59
A it is

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03 May 2006, 06:59
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