BANON wrote:

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.

it matters which one is greater. if s is greater than r, it's impossible for r/s to be a whole number (it will automatically be a fraction less than 1).

first, rephrase the question: is s a factor of r? or, is r a multiple of s? or, is r divisible by s? etc.

you shouldn't leave the question in its original form; the original form is just sort of ugly.

(1)

here's the easiest way to handle this one:

s is a factor of itself.

therefore, since every factor of s (including s itself) is a factor of r, s is a factor of r.

sufficient.

you can do this part with a whole lot of song and dance involving prime numbers, but i like this argument because it's simple and elegant.

(2)

this just means that r and s are combinations of the same prime factors, but you don't know how many times each of those prime factors appears. for instance, 10 and 1000 are both made up of 2's and 5's. therefore, (r, s) could be (10, 1000), in which case the answer is 'no', or (1000, 10), in which case the answer is 'yes'.

insufficient.

ans = a

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