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?
Common factor?
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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.
(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.