Set7 Q5

[arocks]

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.

Explain please. Thanks

[josephcho77]

I will go with "A"

k/6+m/4=t/12 is equal to 2K+3m=t

1) if k is a multiple of 3, no matter what m is, t must have factor of 3.
Therefore, since 12 has a factor of 3, t and 12 have a common factor
greater than 1

2) if m is a multiple of 3, t can be prime numbers or non prime number.
When t is a prime number, t and 12 can't have a common factor
greater than 1 but when t is a non prime number, t and 12 have a
common factor greater than 1.

[arocks]

Thanks. Very clear.