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Manager  Joined: 07 Dec 2011
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Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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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. Quote: what i did. statement I & II independently insufficient. Taking together, let Y expenses be 6m X expenses= 5m Let Y revenue= 12m X revenue= 12-6=6m y profit= exp*R= 6*12=72m x profit= 5*6= 30 m therefore, Y profit> X profit. Both statement together suff. Now my Q is why is it wrong? _________________ Please press Kudos if you found this post helpful Originally posted by maybeam on 23 Jul 2012, 06:09. Last edited by Bunuel on 05 Jun 2019, 05:03, edited 2 times in total. Edited the question. Most Helpful Expert Reply Math Expert V Joined: 02 Sep 2009 Posts: 58335 Re: Which of Company X and Company Y earned the greater gross profit last [#permalink] Show Tags 5 3 maybeam wrote: 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.

Quote:
what i did.

statement I & II independently insufficient.

Taking together,

let Y expenses be 6m
X expenses= 5m

Let Y revenue= 12m
X revenue= 12-6=6m

y profit= exp*R= 6*12=72m
x profit= 5*6= 30 m

therefore, Y profit> X profit.

Both statement together suff.

Now my Q is why is it wrong?

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. _________________ Most Helpful Community Reply Manager  Joined: 06 Jun 2012 Posts: 119 Re: Which of Company X and Company Y earned the greater gross profit last [#permalink] Show Tags 3 3 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 _________________ Please give Kudos if you like the post General Discussion Senior Manager  B Status: Final Countdown Joined: 17 Mar 2010 Posts: 406 Location: United States (NY) GPA: 3.82 WE: Account Management (Retail Banking) Re: Which of Company X and Company Y earned the greater gross profit last [#permalink] Show Tags 2 1 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)
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Re: Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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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
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Re: Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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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
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Re: Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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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.
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Re: Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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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
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Re: Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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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.
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Re: Which of Company X and Company Y earned the greater gross profit last  [#permalink]

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maybeam wrote:
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.

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

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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Our high-level "quant" preparation starts here: https://gmath.net Re: Which of Company X and Company Y earned the greater gross profit last   [#permalink] 29 Jan 2019, 06:21
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