Data Sufficiency

aditya67 wrote: ↑

Wed Mar 25, 2020 10:36 am

Is b<0?
(1) Integer b is a multiple of 13
(2) ^{b^3}< 13

Target question: Is b less than 0?

Statement 1: Integer b is a multiple of 13
There are several values of b that satisfy statement 1. Here are two:
Case a: b = -13, in which case x IS less than 0
Case b: b = 0, in which case x is NOT less than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b³ < 13
There are several values of b that satisfy statement 2. Here are two:
Case a: b = -13, in which case x IS less than 0
Case b: b = 0, in which case x is NOT less than 0
Since 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: b = -13, in which case x IS less than 0
Case b: b = 0, in which case x is NOT less than 0
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent