BTGmoderatorLU wrote:If m and n are positive integers, and p and q are different prime numbers, do p/q and n/m represents different numbers?

(1) Neither n nor m is a prime number.
(2) m is not divisible by q.

The OA is B.

I'm confused by this DS question. Please, can someone help? Thanks in advance!

Given: (1) m and n are positive integers, and (2) p and q are different prime numbers

Question: Is p/q ≠ n/m?

Let's take each statement one by one.

(1) Neither n nor m is a prime number.

Case 1: Say p/q = 2/3 and n/m = 4/9, then p/q ≠ n/m. The answer is Yes.
Case 2: Say p/q = 2/3 and n/m = 4/6 (= 2/3), then p/q = n/m. The answer is No. No unique answer. Insufficient.

(2) m is not divisible by q.

For p/q to be equal to n/m, n must be a multiple of p and m must be a multiple of q. Since it is given that m is not divisible by q, the answer is yes, p/q ≠ n/m. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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