Data Sufficiency

kushal.adhia wrote:If m is an integer, is 14 a factor of m ?

• (1) 14 is a factor of 15 m.
  (2) 14 is a factor of 16 m.

It took me almost 3.5 to 4 mins to figure out this question and yet i got it wrong

Some help please

Kushal

Given: m is an integer.

Statement 1: 14 is a factor of 15m.
Now, 14 = 2*7 and 15m = (3*5)*m
As 15 doesn't contain 2 or 7 and 14 is a factor of 15m, 2 and 7 must be prime factors of m. Thus 14 is a factor of m.

Sufficient.

Statement 2: 14 is a factor of 16m.
Now, 14 = 2*7 and 16m = (2*2*2*2)*m
Now 16 contains 2 (four times) but doesn't contain 7. Thus m must contain 7 as prime factor to make 16m divisible by 14. But m may or may not contain 2 as prime factor. Thus 14 may or may not be a factor of m.

Not sufficient.

The correct answer is A.