If P, Q, R, and S are positive integers, and P/Q = R/S, is R

[BTGmoderatorDC]

If P, Q, R, and S are positive integers, and P/Q = R/S, is R divisible by 5?

(1) P is divisible by 140

(2) Q = 7^x, where x is a positive integer

OA C

Source: Manhattan Prep

[Ian Stewart]

We can rewrite the equation:

PS = QR

So PS and QR are exactly the same number, and must have the same divisors. Statement 1 tells us PS is divisible by 140, so PS is divisible by 5. So QR must be divisible by 5, but maybe only Q is divisible by 5, and maybe only R is. But Statement 2 tells us Q is not divisible by 5, so R must be, and the answer is C.