Problem Solving

Given that P and Q are non-zero integers. Is P/Q > (PQ) ^2 ?

Stmt1: P/Q >0
Stmt2: Q<0

OA: D

Please post this in DS section.

Hey vaibhavjha,


Great question - and I'll admit that I was on the verge of a completely incorrect explanation (quoted below, in progress) so let me explain that!

It's incredibly easy to read questions the way that you would have written them or the way that you have seen them before. Here, the direction of inequality makes all the difference. If the question reversed the inequality (is P/Q < (PQ)^2) then everything I write here would be relevant:

Interesting...what's the source on this one? The way it's written, the answer is definitely NOT D.

Statement 1 allows for both integers to be 1 (or -1), which would make P/Q equal to 1 and PQ^2 = 1, so they would be equal. Or they could be 10 and 1, in which case the squared term would be much, much bigger. So we can prove that we get both "YES" and "NO" here.

As a strategic takeaway with > and < questions, remember that = provides a "no" to either, and often you can find a way to get to equality especially if 1 is a possibility.

Statement 2 still allows for the possibility of both being -1 as discussed above, but then obviously if Q or P has a large absolute value then the squared term would be much bigger.

But it's actually the other way around, and I was initially tricked by assuming that they'd ask whether the squared term would always be bigger than the fractional term. That's just how I figured they "must be" asking it.

The opposite way, the best I could do to have the squared term not greater than the other was to have them "tie". But as it is written, we simply cannot get the answer "YES".


A big takeaway - train yourself to ask "what if they flipped the sign" in practice so that you're thinking both ways on the test. Subtle differences like that can make all the difference in the world on questions like these. Flip the sign on this one and the answer is E, and not D.