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Which of Company X and Company Y earned the greater gross [#permalink]

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23 Jul 2012, 06:09

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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.

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

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23 Jul 2012, 07:15

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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 _________________

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

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23 Jul 2012, 08:12

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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.

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.

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

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26 Jul 2012, 06:30

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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) _________________

" Make more efforts " Press Kudos if you liked my post

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

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18 Apr 2014, 03:11

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

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10 May 2014, 12:01

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

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

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12 Sep 2014, 23:45

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

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

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08 Dec 2014, 16:03

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.

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

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14 Aug 2015, 09:54

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

Which of Company X and Company Y earned the greater gross [#permalink]

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14 Aug 2015, 10:08

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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.

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