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

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Senior Manager
Joined: 14 Jul 2006
Posts: 281

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

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24 Aug 2006, 10:43
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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.

Kudos [?]: 3 [0], given: 0

Senior Manager
Joined: 14 Aug 2006
Posts: 362

Kudos [?]: 49 [0], given: 0

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24 Aug 2006, 13:53
k/6 + m/4 = t/12

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

1) if k is a multiple of 3 => 3(2*f + m) = t SUFF
12 and t have a common factor 3

2) m is a mulitple of 3 we do not know if there is a common factor so INSUFF

ans : A

Kudos [?]: 49 [0], given: 0

Senior Manager
Joined: 14 Jul 2006
Posts: 281

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24 Aug 2006, 21:25
Yup A is the right answer thanks

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Director
Joined: 28 Dec 2005
Posts: 750

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26 Aug 2006, 11:55
A it is....

From the original eqn.

t=2k+3m

from 1 k=3k1

t=3[2k+m]

3 is a factor of t, its also a factor of 12, suff

from 2
t=2k+9m....INSUFF

Kudos [?]: 18 [0], given: 0

26 Aug 2006, 11:55
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