Given: n and p are integers
Target question: Is p > 0?
Statement 1: n + 1 > 0
No information about p.
Statement 1 is NOT SUFFICIENT
Statement 2: np > 0
There are several values of n and p that satisfy statement 2. Here are two:
Case a: n = 1 and p = 1. In this case, the answer to the target question is YES, p is greater than 0
Case b: n = -1 and p = -1. In this case, the answer to the target question is NO, p is NOT greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that n + 1 > 0
This means n > -1
Since n is an integer, we know that the possible values of n are: 0, 1, 2, 3, 4, 5, 6, . . .
Statement 2 tells us that np > 0
Since np is greater than 0, we know that n ≠ 0. So, now the possible values of n are: 1, 2, 3, 4, 5, 6, . . .
In other words, we can be certain that n is POSITIVE
If n is POSITIVE AND np > 0, we can be certain that p is POSITIVE
So, the answer to the target question is YES, p is greater than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
