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

Cheers,
Brent