a and b are integers, is a factor of b?

[M7MBA]

a and b are integers, is a factor of b?

(1) a is a factor of 2b
(2) 2a is a factor of b

The OA is the option B.

Why is not sufficient the first statement? Can any expert clarify this for me? Please.

[GMATinsight]

a and b are integers, is a factor of b?

(1) a is a factor of 2b
(2) 2a is a factor of b

The OA is the option B.

Why is not sufficient the first statement? Can any expert clarify this for me? Please.

Question : Is a factor of b?

Statement 1: a is factor of 2b
Case 1: a = 2 and b = 3, a is factor of 2b but a is NOT a factor of b
Case 2: a = 3 and b = 3, a is factor of 2b and a is also a factor of b

NOT SUFFICIENT

Statement 2: 2a is factor of b

i.e. b is divisible by 2a
i.e. b must also be divisible by a
(any factor of a divisor of a number is always a factor of the primary number)
i.g. if 6 is factor of 12 then every factor of 6(1, 2, 3, 6) will also be a factor of 12

SUFFICIENT
Answer: Option B