RadiumBall wrote:
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
We can rephrase by rewriting the formula as PS = QR, and writing the question as R = 5K where K is an integer.
(1) If P is divisible by 140, then we know that P = 2*2*5*7. Consequently PS = (2*2*5*7)S. Because PS is divisible by 5 and PS = RQ, then RQ must be divisible by 5 (remember, P, Q, S, and R are integers), but this doesn't mean that R is divisible by 5.
YES Example: P = 140, S = 1, Q = 140, and R = 1. R is not divisible by 5.
NO Example: P = 140, S = 1, Q = 1, and R = 140. R is divisible by 5.
Insufficient
(2) Because Q is a power of 7, QR must be divisible by 7, but since we don't know anything about PS we can't find the value of R. Again we can create a YES example and a NO example.
YES Example: P = 7, S = 1, Q = 7, and R = 1. R is not divisible by 5.
NO Example: P = 7, S = 5, Q = 7, and R = 5. R is divisible by 5.
Insufficient
(1) & (2) Now we have PS = (2*2*5*7)(S) = (7^x)(R) = QR, we know that PS and QR are both divisible by 5. But, since Q is a power of 7, it cannot be divisible by 5. Consequently, in order for QR to be divisible by 5, R must be divisible by 5.
Sufficient.
The correct answer is C
Examples and counter examples are easy ways to evaluate the individual statements, but some more abstract reasoning is required to evaluate the statements together. In the final step it's helpful to have already factored 140 and made some conclusions about PS and QR.
As a general rule, you should factor largish integers when you see them in DS problems.
J
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