Data Sufficiency

BTGModeratorVI wrote: ↑

Wed Oct 07, 2020 7:13 am

Is the positive integer p a prime number?

(1) p is odd.
(2) 2 < p < 17

Answer: E
Source: Official guide

Target question: Is the positive integer p a prime number?

Statement 1: p is odd.
There are several values of p that satisfy statement 1. Here are two:
Case a: p = 3, in which case the answer to the target question is YES, p is prime
Case b: p = 9, in which case the answer to the target question is NO, p is not prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 2 < p < 17
Tip: If you feel that statement to is insufficient, see if you can RE-USE the same counter-examples be used for statement 1.
In this case, we CAN reuse those counterexamples, since they also satisfy statement 2:
Case a: p = 3, in which case the answer to the target question is YES, p is prime
Case b: p = 9, in which case the answer to the target question is NO, p is not prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Since I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: p = 3, in which case the answer to the target question is YES, p is prime
Case b: p = 9, in which case the answer to the target question is NO, p is not prime
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent