thinkpad18 wrote:

Bunuel wrote:

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

(1) Every factor of s is also a factor of r. If every factor of s is also factor of r, then in fraction r/s, s will just be reduced and we get an integer. Sufficient.

(2) Every prime factor of s is also a prime factor of r. The powers of prime factors of s could be higher than powers of prime factors of r. eg 25/125=1/5 not an integer. Not sufficient.

Answer: A.

Hope it's clear.

For statement 1, how do we know that we won't run into a similar problem with statement two in which we could have 2^2*3^2/2^3*3^3?

Hello

We CANNOT take your example, where r = 2^2 * 3^2 and s = 2^3 * 3^3, as this will violate the condition in statement 1.

Statement 1 says that every factor of s is also a factor of r. But if s has more powers of 2 and/or 3 than r, then s will have some factors which are not factors of r. Eg, in your example, 2^3, 3^3, 2^3 * 3^2 .. etc.. are factors of s but they are not factors of r.

So if we go by statement 1 condition, if all factors of s have to be factors of r also, then all powers of all prime numbers contained in s, will also be contained in r. Hence r/s has to be an integer.