Which of Company X and Company Y earned the greater gross...

[KarlS319]

Which of Company X and Company Y earned the greater gross profit last year?

(1) Last year the expenses of Company X were 5/6 of the expenses of Company Y.

(2) Last year the revenues of Company X were $6 million less than the revenues of Company Y.

Thought process went as follows... Is Co. X GP > Co. Y GP? ---> GP = revenue - costs ---> need info to determine revenue and costs for each Co.

(1) Co. X costs = 5/6 of Co. Y costs ---> in other words, Co. X costs will always be less than Co. Y costs...no info about revenue so NOT SUFFICIENT

(2) Co. X revenue = Co.Y revenue - $6M ---> in other words, Co.X revenue will always be less than Co.Y revenue...no info about costs so NOT SUFFICIENT

(1 & 2) Have a relationship for costs and relationship for revenue but Co. X GP > Co. Y GP could be yes or no depending on the constants....tested extreme cases to confirm this such as Co. Y doing $100M of revenue means Co.X did $96M of revenue and if costs were very small (high GM) then Co.Y would have > GP vs. if costs were massive (low GM) then Co. X would > GP. In other words, Co. X's revenue will be always be $6M less than Co. Y but it's cost can technically be any amount since it is 5/6 of an unknown # (Co. Y costs). Therefore, NOT SUFFICIENT.

ANSWER = E

Question: answered correctly but killed too much time on this one. Could you confirm that my above thinking was correct and perhaps, offer a more efficient way to progress through this problem? In particular, I'm wondering if there are any general rules of thumbs that can be drawn from this type of question? For example, when we have two linear equations with two variables, we instantly know we have sufficient info to solve...is there any similar types of rules (like do we always need a constant to solve) for these types of DS questions?

[Sage Pearce-Higgins]

It looks like you're good at testing cases, but you're overusing it a bit. Thinking of rules such as "This equation has 2 variables and therefore I can't solve it" (although watch out for those cunning situations in which one variable cancels out for some reason) is what you need to do.

When I see the question here, I think "I need some information about the comparative revenues, and comparative costs of these two companies to answer this question". Therefore I can eliminate answers A, D, and B pretty quickly. Spending some time checking between C and E is okay here. Perhaps the clue you're looking for is that there is no number fixed to 'expenses'. Without actually picking numbers, you can just think of extremes: if the companies have enormous expenses, then the gap between the companies expenses will be big; alternatively, if the revenues are tiny, then the gap will also be tiny. Correspondingly, the $6 million in revenue that company Y has will be either not important or significant.