Many students will see \(\frac{m}{p} > \frac{n}{p}\) and conclude (incorrectly) that \(m > n\).
However, this is true ONLY IF p is POSITIVE.
If p is NEGATIVE, we have a different story.

Let's test some values

case i:\(p = 1\), \(m = 2\) and \(n = 1\)
This satisfies the condition that \(\frac{m}{p} > \frac{n}{p}\), which becomes\(\frac{2}{1} > \frac{1}{1}\), which is true.
We get:
Quantity A: 2
Quantity B: 1
So, Quantity A is greater


case ii:\(p = -1\), \(m = 1\) and \(n = 2\)
This satisfies the condition that \(\frac{m}{p} > \frac{n}{p}\), which becomes\(\frac{1}{-1} > \frac{2}{-1}\), which is true.
We get:
Quantity A: 1
Quantity B: 2
So, Quantity B is greater

Answer: D

Cheers,
Brent