DS 6

kanishka12 wrote: ↑

Sun Aug 30, 2020 5:59 am

Is x an integer?

1) x^2 is not an integer
2) x/2 is not an integer

Target question: Is x an integer?

Statement 1: x² is an integer.
Let's TEST some values.
There are several values of x that satisfy statement 1. Here are two:
Case a: x = 1. In this case, the answer to the target question is YES, x IS an integer
Case b: x = √2. In this case, the answer to the target question is NO, x is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x/2 is not an integer.
NOTE: Notice that we can re-use the same counterexamples from statement 1.
Case a: x = 1. In this case, the answer to the target question is YES, x IS an integer
Case b: x = √2. In this case, the answer to the target question is NO, x is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Since I was able to use the same counter-examples to show that each statement ALONE is not sufficient, the same counter-examples will satisfy the two statements COMBINED.
So, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent