Data Sufficiency

If r and s are integers, is r/s an integer?

1.Every factor of s is also a factor of r.
2.Every prime factor of s is also prime factor of r

OA is A
Its nowhere stated that r>s, then how can we conclude this from statement 1?

tapanmittal wrote:If r and s are integers, is r/s an integer?

1.Every factor of s is also a factor of r.
2.Every prime factor of s is also prime factor of r

Statement 1: Every factor of s is also a factor of r.
The greatest factor of s is S ITSELF.
Since EVERY factor of s is a factor of r, S ITSELF must be a factor of r.
Since s is factor of r, r/s must be an integer.
SUFFICIENT.

Statement 2: Every prime factor of s is also a prime factor of r.
Case 1: r=18 and s=6.
The prime factors of r=18 are 2 and 3.
The prime factors of s=6 are 2 and 3.
Thus, every prime factor of s is also a prime factor of r.
In this case, r/s = 18/6 = 3, which is an integer.

Case 2: r=6 and s=18.
The prime factors of r=6 are 2 and 3.
The prime factors of s=18 are 2 and 3.
Thus, every prime factor of s is also a prime factor of r.
In this case, r/s = 6/18 = 1/3, which is NOT an integer.
INSUFFICIENT.

The correct answer is A.