Source: Eq, Ineq & VIC - Question Bank 17/25

Is p^2q > pq^2?

(1) pq < 0

(2) p < 0

My choice is A but the MGMT sol says C.

What is wrong with my reasoning below:

Rephrase Qs: IS pq(p - q) >0
=> IS pq >0 OR p-q > 0? ----(a)
=> IS pq < 0 OR p-q <0? ----(b)

Since statement 2 is easier, I will use the BD/ ACE grid

1) INSUFF: no information on q
2) if pq <0, THEN p - q<0 could be true as well => p<q --- SUFF-- A

MGMT argues that pq<0 is not enough, since we dont know which one is positive or negative. Why is that important? Because once we have established (b) is the applicable, it is true that the line highlighted by "(b)" above is true.

Could you explain the concept behind why my reasoning may be flawed?

Thank you,

Your rephrase:
IS pq(p - q) >0 this part is fine
BUT
In order for this to be greater than zero, BOTH pq and (p-q) have to have the same sign.
In order for this to be less than zero, pq and (p-q) have to have opposite signs.
If we don't know whether they have the same or opposite signs, then we can only answer the question "maybe." It's not enough to know what COULD be possible - I have to answer the question definitively, ALWAYS.

"if pq <0, THEN p - q<0 could be true as well => p<q --- SUFF-- A"
Yes, it could be, but it could also be that p-q>0. If I get both possibilities, the statement is insufficient.

Remember that to answer a yes/no question, I have to answer it definitively - that is, always yes or always no. Think of it as a "must" question rather than a "could" question.