Dreams25 wrote:

I'm very confused why both statement are not sufficient

From statement 1 we know that company x had less expenses than y let say y's expenses are 6m and x are 5m now if I were to tell you in the 2nd statement that their revenues are the same there's no doubt I would be able to tell who had a higher GP since I know for sure that x had less expenses than y

Now the 2nd statement tells us that x earned 6m less than y, now if we say for example that x earned 24m and y 30 m revenue minus expenses would be as following, x revenue - 5/6 of y's expenses or 24m -5m =19m which would be less than y's revenue - 6•x's expenses or 30m- 6m= 24m and that would hold true for any numbers as 60 44 etc

I know I'm making a mistake

Am I wrong because I'm comparing GP of 2 companies with 2 different revenues?

So how do you compare GP of 2 companies they never earned the same exact revenue?

The bottom line of my question is why "logically" [not algebraically] isn't statement 1 and 2 together sufficient to say that y earns more since I know that x earns 6m less than y and x's expenses is just 5/6 of y so automatically x is making less money

Thanks

The mistake you are doing is to neglect the case when gross profits will become equal. As the question is asking whether the difference Px-Py > or < 0, the equality of the profits will end up providing 1 more solution leading to E.

Ex, Ey are expenses of x,y respectively, Rx, Ry are revenues of X and Y respectively while Px and Py are profits of x and Y respectively.

Assume Ey = 36, Ex=30. Now for any value of Ry = a , Rx =a-6

Px - Py = a-6-30-(a-36) = a-36-a+36 = 0.

Thus both Px and Py are equal in this scenario while in all other cases you have shown that Px < Py.

Thus we get a "yes" and a "no" at the same time making E the correct answer. Sometimes, algebra helps you to look at cases that you might miss by using pure numbers. Algebra helped me in figuring out the 'limiting case' for these 2 statements that turned out to be Ex=30, Ey=36.

Hope this helps.