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r and s are nonzero integers

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Source: — Data Sufficiency |
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by Patrick_GMATFix » Fri Dec 20, 2013 6:40 pm
This solution is taken from the GMATFix App. My signature below has more info.

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by Brent@GMATPrepNow » Fri Dec 20, 2013 9:41 pm
kobel51 wrote:If r and s are nonzero integers, is r/s an integer?

1) r - 1 = (s + 1)(s - 1)
2) r - s = 20
Target question: Is r/s an integer?

Statement 1: r-1 = (s+1)(s-1)
Expand right side to get: r - 1 = s² - 1
Add 1 to both sides: r = s²
The target question asks, Is r/s an integer?
So we can now replace r with s² to get: Is s²/s an integer?
Simplify to get: Is s an integer?
Well, we're actually told that s is an integer, so we can answer the target question with certainty, which means statement 1 is SUFFICIENT

Statement 2: r - s = 20
There are several values of r and s that satisfy this condition. Here are two:
Case a: r = 21 and s = 1, in which case r/s IS an integer
Case b: r = 23 and s = 3, in which case r/s is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

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by sanju09 » Fri Dec 20, 2013 9:57 pm
kobel51 wrote:If r and s are nonzero integers, is r/s an integer?

1) r-1 = (s+1)(s-1)

2) r-s = 20
(1) This translates to r - 1 = s^2 - 1, which implies that r = s^2 or r/s = s (a non zero integer); hence YES. Sufficient. AD On BCE Gone.

(2) If r = 40 and s = 20, then YES, r/s is an integer, but if r = 39 and s = 19, then NO, r/s is NOT an integer. [spoiler]Insufficient.

Hence A[/spoiler]
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