Bunuel wrote:
If r and s are nonzero integers, is r/s an integer ?
(1) r - 1 = (s + 1)(s - 1)
(2) r - s = 20
Given: r and s are nonzero integers Target question: Is r/s an integer ? Statement 1: r - 1 = (s + 1)(s - 1) Expand to get: r - 1 = s² - 1
Add 1 to both sides of the equation to get: r = s²
The target question becomes:
Is s²/s an integer ? Since s²/s = s, and since we're told s is an integer, the answer to the target question is
YES, r/s is an integerSince we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: r - s = 20There are several values of r and s that satisfy statement 2. Here are two:
Case a: r = 22 and s = 2. In this case, r/s = 22/2 = 11. So, the answer to the target question is
YES, r/s is an integerCase b: r = 23 and s = 3. In this case, r/s = 23/3 = 7 2/3. So, the answer to the target question is
NO, r/s is not an integerSince we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
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