Manhattan Prep Inequality Drill Exercise

[yo4561]

Apologies, I put this in the CAT form and moving it to this form.
If ab ≠ 0 and ax – by < 0 , is x < y ?
1) a = b
2) a^3 > 0

I am not sure if this a CAT problem, but it was written by Manhattan Prep. I am confused as to why statement 1 is not sufficient. If you know that ax<by and a=b, isn't that the same as saying a and b are basically constants and that is enough to know x<y? I am just not sure why you would need to divide the constants, as the answer mentions below.

"Problem 14 Solution: C
It makes sense to manipulate the inequality in the question stem before addressing the statements. Adding by to both sides, this inequality becomes ax <
by.

Statement 1: If a = b, then the inequality from the question stem becomes ax< ay. However, dividing by a yields two potential outcomes: either x < y or x > y, depending on the sign of a. Statement 1 is not sufficient.

Statement 2: If a^3 > 0, then a > 0. However, this indicates nothing about b, so depending on the value b takes on we could get two different answers to the question in the stem. Statement 2 is not sufficient. Together: Combining the information allows us to rewrite the inequality in
the question stem as ax < ay, and then to divide by a (which is positive). The result is x < y, and together the statements are sufficient'

[esledge]

Basically I can't prepare for my LSTAT exam due to many reasons. One of the reasons is that I need to graduate this year from college and I do not know how to I will try to find someone who can help me resolve this issue while I am trying to prepare for the most important exam for me. Reading comprehention is the most difficult part of exam for me, that is why I need a lot of time to revise materials and be prepared for this year exam.

Hi rehan, I think you might have intended to post this elsewhere (this is a GMAT math thread). Just notifying in case you want to move/repost it.