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

Two reasons why your solution is wrong:
1. {Profit} = {Revenue} - {Expenses}, not {Profit} = {Revenue}*{Expenses}, as you've written.
2. One example is not enough to conclude that a statement is not sufficient.

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

Since {Profit} = {Revenue} - {Expenses}, then we are asked whether \(R_x-E_x>R_y-E_y\)?

(1) Last year the expenses of Company X were 5/6 of the expenses of Company Y --> \(E_x=\frac{5}{6}*E_y\). Not sufficient, as we know nothing about the revenues.

(2) Last year the revenues of Company X were $6 million less than the revenues of Company Y --> \(R_x=R_y-6,000,000\). Not sufficient, as we know nothing about the expenses.

(1)+(2) So, according to the above the question becomes whether \((R_y-6,000,000)-\frac{5}{6}*E_y>R_y-E_y\) or whether \(E_y>6*6,000,000\). We don't know that, hence even taken together the statements are not sufficient.

Answer: E.

Hope it's clear.
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Individually both are Not Sufficient. So solving for together

Profit X = Revenue X - Expense X

Expense X = 6/5 Expense Y
Revenue X = Revenue Y- 6

Hence Profit X = Revenue Y - 6 - 6/5 Expense Y
Now Profit Y = Revenue Y - Expense Y

Here if 6 + 6/5 Expense Y = Expense Y, than the statement is false as profit becomes equal, and its the case if Expense Y =36. For other examples the statement is true, ex. like the one you took. Hence insufficient and E

it's a DS ;Let's keep it simple
Revenue-Expenses=Profit
(i)expenses of x =5/6 of Y
WE STILL NEED REVENUE-insufficient
(ii)revenue of x= $6mn less than y
we don't know expenses-insufficient
from (i) and (ii)
both details are relative (to each other) not a standard figure, so (E)

From statement 1 and 2 , we have

P(x) = R(y) - 5/6*C(y) -6
P(y) = R(y) - C(y). At first sight it might seem for whatever value of C(y), P(y) would be greater. But for C(y) = 36, we get P(x)=P(y). Hence E is the answer

Done with table method,
1 and 2 alone insufficient
On combining we know expenses of x is 5/6y if y is expenses.
And Y's revenue - 6 million
No data of y's revenue
So E

Just want to provide a cautionary tale...

Had stmt 1 told us that expenses for r were equal to or greater than y, then both statements together would be sufficient. Seems simple enough, but if you get too concerned with trying to apply formulas, you really could waste a good amount of time.

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.
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\(?\,\,\,:\,\,\,X\,\,{\rm{or}}\,\,Y\,\,\,\,\,\,\left[ {{\rm{max}}\,\left( {{\rm{rev}} - {\rm{exp}}} \right)} \right]\)

The monetary unit will be millions of dollars.

\(\left( {1 + 2} \right)\,\,\left\{ \matrix{\\
\,\,{{{{\exp }_X}} \over {{{\exp }_Y}}} = {5 \over 6} \hfill \cr \\
\,\,{\rm{re}}{{\rm{v}}_Y}\,\, = \,\,{\rm{re}}{{\rm{v}}_X} + 6 \hfill \cr} \right.\)

\(\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {{\rm{re}}{{\rm{v}}_X}\,\,;\,\,{{\exp }_X}\,\,;\,\,{\rm{re}}{{\rm{v}}_Y}\,\,;\,\,{{\exp }_Y}} \right) = \left( {6\,;\,5\,;\,12\,;\,6} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,{\rm{Y}} \hfill \cr \\
\,{\rm{Take}}\,\,\left( {{\rm{re}}{{\rm{v}}_X}\,\,;\,\,{{\exp }_X}\,\,;\,\,{\rm{re}}{{\rm{v}}_Y}\,\,;\,\,{{\exp }_Y}} \right) = \left( {55\,;\,50\,;\,61\,;\,60} \right)\,\,\,\, \Rightarrow \,\,\,{\rm{?}}\,\,{\rm{ = }}\,\,X \hfill \cr} \right.\)


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Hi, people, just a few thoughts.

When it comes to questions such as this, I think a conceptual approach helps you more than anything else.

Statement 1 tells you that company X has less expenses than company Y; but it doesn't really tell you anything more than that. Fundamentally, you have to realize that the actual amount could be small or large. Indeed, who is to say expenses of both companies did not exceed their revenues!

Statement 2 doesn't give you much more to play around with either. Six million lower than what? should be running through your mind. In many ways the same concepts we're are looking at in the first statement are at play here again.

When you look at both statements a part of you should recognize that if you played around with the figures enough, you could make the statement True or False depending.
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logic solution:

1) (X)costs = 5/6 (Y)costs ---> (X)costs < (Y)costs ---> (X) in a better position

2) (X)rev = (Y)rev - 6million ---> (X)rev < (Y)rev ---> (Y) in a better position

we still don't know which company is in a better position = ANSWER E

this can be solved mostly by logic. Of course, a mathematical route can be taken, however, i find this one more efficient.
Firstly, Profit = Revenue- Expenses

Stmt 1: No hard numbers, this is just a ratio. Moreover, no clue about revenue. Not sufficient
Stmt 2: To calculate Profit, we need hard numbers. Here y can literally be anything and x 6 million less than that. Plus no information on expenses. Not sufficient

combined evaluation: not a lot of new information is added. We are still clueless as to what revenue of X and Y is, and in the name of expenses, we merely have a ratio. Hence, E stands.

Hope that's helpful.

The question is Which of Company X and Company Y earned the greater gross profit last year, so we could have 3 different answers:
a) X earned the greater profit.
b) Y earned the greater profit.
c) Neither, they both earned the same.

And there could be another one: d) Both earned negative, which would be = 0 profit, and it becomes the same as c), but we can compare negative numbers even though they make no sense in the context. But nevertheless, stick with the 3 first.

Using both information, we could determine which of a), b) or c) is. And which is it? c) they both earned the same.

Anyone doing the same thinking as me?

What do I have wrong?

Can someone give an example of negative scenario where X profit is greater than Y profit?

nikitathegreat


We definitely don't want to dive into negatives here. If the GMAT is asking us to compare profits, they will be non-negative. Otherwise, the question would be more precise and talk about profits or losses. The issue here is that even with 1+2 together, all we know is that X had both lower costs and lower revenues. But we don't know enough to determine whether profits were lower because one statement is about proportion and the other is about actual quantities. It's like saying "This year I worked 10% less, but I made $2 more per hour. Did I earn more or less?" You can't tell, because you don't know whether that $2 raise was enough to offset my 10% reduction in hours.
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Hi
I meant the scenario where X profit is greater than Y profit.
I could deduce the scenario where Y profit is greater and couldnt find the other scenario. Else, should I consider this a blanket statement that when is expressed in percent and the other in amount, we cannt find the final answer?

Posted from my mobile device

nikitam

Ah, I see. Yes, we can more or less make that blanket statement, but the particulars can matter. For instance, if we knew that someone were making a smaller percent profit and also that the sale price were lower, then of course we'd know the overall profit was lower.

As for making X's profit greater than Y's, there's a good general principle we can apply here: the larger the numbers we work with, the less difference a fixed quantity (such as $6 million) makes. We can also flip this around for the the 5/6 part. The larger the numbers, the more money 1/6 will be. So for both revenue and expenses, we want big numbers.

Y revenue: 100.006 billion
X revenue: 100 billion

Y expenses: 60 billion
X expenses: 50 billion

Y profits = 100.006 - 60 = 40.006 billion
X profits = 100 - 50 = 50 billion
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