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

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by BTGmoderatorDC » Sat Jul 27, 2019 5:22 pm

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A

B

C

D

E

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Difficulty—

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

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by Ian Stewart » Tue Jul 30, 2019 2:23 pm
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.
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