Number properties question from OG 11

[Osirus@VeritasPrep]

If r and s are positive 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 a prime factor of r

OA A










My question is when it states that every prime factor of s is also a prime factor of r does that not mean that all of the prime factors of s is a prime factor of r?

[thephoenix]

try sme no's.

let s=6 ( factors are 1,2,3,6)

to satisfy S1) r(will be)=n8(1*2*3*6)......where n is an int

r/s=n an int

hence suff...

s2)let s=12( prime fastors are 2,3)

so to satisfy s2) r has to be=n(2*3) where n is an int
now for all n<12
r/s is not an int
but for n=multiple of 12
r/s is an int

therefore two ans and hence insuff

A it is