Bunuel wrote:
If n is a prime number, does n = 17?
(1) n − 1 = m⁴, where m is an integer.
(2) n² < 300
Given: n is a prime number Target question: Does n = 17? Statement 1: n − 1 = m⁴, where m is an integer. This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of n and m that satisfy statement 1 (and the given information, which says n is prime). Here are two:
Case a: n = 2 and m = 1. In this case, the answer to the target question is
NO, n does not equal 17Case b: n = 17 and m = 2. In this case, the answer to the target question is
YES, n equals 17Since we can’t answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: n² < 300Pro tip: Rather than try to find values of n that satisfy statement 2, we can save some time by checking to see whether we can REUSE any of the values we used for statement 1.
In this case, it turns out that we can reuse both pairs values, since the n-values in both pairs also satisfy statement 2 (i.e., 2² < 300 and 17² < 300) So, we have:
Case a: n = 2. In this case, the answer to the target question is
NO, n does not equal 17Case b: n = 17. In this case, the answer to the target question is
YES, n equals 17Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined IMPORTANT: Notice that 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: n = 2 and m = 1. In this case, the answer to the target question is
NO, n does not equal 17Case b: n = 17 and m = 2. In this case, the answer to the target question is
YES, n equals 17Since we can’t answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
_________________