Vincen wrote:Is a positive?
(1) a - b > 0
(2) 2a - b > 0
Target question: Is a positive?
Statement 1: a - b > 0
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 5 and b = 1. In this case,
the answer to the target question is YES, a IS positive
Case b: a = -1 and b = -10. In this case,
the answer to the target question is NO, a is NOT positive
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: 2a - b > 0
Let's TEST some values again.
Case a: a = 5 and b = 1. In this case,
the answer to the target question is YES, a IS positive
Case b: a = -1 and b = -10. In this case,
the answer to the target question is NO, a is NOT positive
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: a = 5 and b = 1. In this case,
the answer to the target question is YES, a IS positive
Case b: a = -1 and b = -10. In this case,
the answer to the target question is NO, a is NOT positive
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer: E
Cheers,
Brent
