\(\frac{M}{P} > \frac{N}{P}\)

Quantity A	Quantity B
M	N

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Hi All,

I found this question in Manhattan book but I am not confident regarding the solution provided. This is how I solved this question.

Algebraic Solution:

Since M / P > N / P
Step 1: M / P - N/P > 0
Step 2: M - N / P > 0
Step 3: M - N > 0 (Multiplying P with 0 - doesn't matter if p is positive or negative since it is being multiplied with 0 and the end product will be 0 anyways)
Step 4: M > N

So as per my solution, Quantity A is greater than Quantity B. However, as per Manhattan, the original answer is D. Their solution is " Without knowing the signs of any of the variables, you cannot assume that m is larger. While it certainly could be (for instance, m = 4, n = 2, and p = 1), if p is negative, the reverse will be true (for instance, m = 2, n = 4, and p = -1)"

I don't know how my solution is not correct. Any comments?

I appreciate your feedback!

Regards,
H.