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If r and s are nonzero integers, is r/s an integer ?

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Re: If r and s are nonzero integers, is r/s an integer ? [#permalink]
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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 integer
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: r - s = 20
There 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 integer
Case 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 integer
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Cheers,
Brent
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Re: If r and s are nonzero integers, is r/s an integer ? [#permalink]
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Re: If r and s are nonzero integers, is r/s an integer ? [#permalink]
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