Data Sufficiency

If k and m are positive integers, does k/m = 3/13?

(1) k is a prime number greater than 10.
(2) m is divisible by 3

Source: www.gmatprepnow.com
Answer: A

[email protected] wrote: ↑

Mon Aug 01, 2022 8:18 am

If k and m are positive integers, does k/m = 3/13?

(1) k is a prime number greater than 10.
(2) m is divisible by 3

Source: www.gmatprepnow.com
Answer: A

Given: k and m are positive integers

Target question: Does k/m = 3/13?
Key concept: If k/m = 3/13, then k must be a positive multiple of 3, and m must be a positive multiple of 13.
So, for example, it could be the case that k = 3 & m = 13, or k = 6 & m = 26, or k = 9 & m = 39, and so on . . .

Statement 1: k is a prime number greater than 10
If k is a prime number greater than 10, then k cannot be a positive multiple of 3, which means k/m cannot equal 3/13.
So, the answer to the target question is NO, k/m does not equal 3/13
Statement 1 is SUFFICIENT

Statement 2: m is divisible by 3
There are several values of k and m that satisfy statement 2. Here are two:
Case a: k = 1 and m = 3, in which case, the answer to the target question is NO, k/m does not equal 3/13
Case b: k = 9 and m = 39, in which case, the answer to the target question is YES, k/m = 3/13
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A