BTGModeratorVI wrote: ↑

Wed Jul 29, 2020 2:43 pm

If a and b are positive integers, is a/b an integer?

(1) a > b
(2) a and b share only one factor.

Answer: E
Source: Veritas

Target question: Is a/b an integer?

Given: a and b are positive integers

Statement 1: a > b
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 = 2 and b = 1, in which case a/b = 2/1 = 2, and 2 IS an integer
Case b: a = 3 and b = 2, in which case a/b = 3/2, and 3/2 is NOT an integer
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: a and b share only one factor
There are several values of a and b that satisfy statement 2. Here are two:
Case a: a = 2 and b = 1, in which case a/b = 2/1 = 2, and 2 IS an integer
Case b: a = 3 and b = 2, in which case a/b = 3/2, and 3/2 is NOT an integer
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of a and b that satisfy BOTH statements. Here are two:
Case a: a = 2 and b = 1, in which case a/b = 2/1 = 2, and 2 IS an integer
Case b: a = 3 and b = 2, in which case a/b = 3/2, and 3/2 is NOT an integer
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent