Bunuel wrote:
If √k is not an integer, then is k a prime number?
(1) k < 10
(2) k < 5
Given: √k is not an integer Target question: Is k a prime number? Statement 1: k < 10 Let's TEST some values.
There are several values of k that satisfy statement 1. Here are two:
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is
NO, k is NOT a prime numberCase b: k = 3 (√3 is not an integer). In this case, the answer to the target question is
YES, k IS a prime numberSince we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: k < 5 Let's TEST some values.
There are several values of k that satisfy statement 2. Here are two:
Case a: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is
NO, k is NOT a prime numberCase b: k = 3 (√3 is not an integer). In this case, the answer to the target question is
YES, k IS a prime numberSince we cannot 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: k = 1.3 (√1.3 is not an integer). In this case, the answer to the target question is
NO, k is NOT a prime numberCase b: k = 3 (√3 is not an integer). In this case, the answer to the target question is
YES, k IS a prime numberSince we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent