It is basically asking if r is divisible by s, in another words is r a multiple of s?

r - 1 = s^2 - 1
r = s^2

r/s = s^2/s = s which is an integer.

Sufficient

r - s = 20

If r = 25 and s = 5 then yes 25/5 = 5 integer

But if r = 26 and s = 6 we get no 26/6 = 13/3 not integer.

insufficient.

A is the answer choice.

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From statement 1:

r-1 = \(s^2\) - \(1^2\)

r = \(s^2\) or s = +r or -r.

So r/s is an integer.
Sufficient.

From statement 2:
r-s = 20.

Insufficient.

A is the answer.

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

Answer: A

Cheers,
Brent
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