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Profit & Loss

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Profit & Loss

by Akansha » Sat May 14, 2011 8:02 am
Martha bought an armchair and a coffee table at an auction and sold both items at her store. Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?
1) Martha paid 10 percent more for her armchair than for the coffee table.
2) Martha sold the armchair for 20 percent more than she sold the coffee table.

Can anyone explain why the answer for this question is E and not C?
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by pemdas » Sat May 14, 2011 8:18 am
let's call an armchair A and a coffee table B, the gross profit (A-B)/A?
A=PA-SA, B=PB-SB where P is purchase and S is sale
st(1) Martha paid (purchase, P) 10% more for her armchair than for the coffee table -> PA-PB=0.1 Not Sufficient
st(2) Martha sold (sale, S) the armchair for 20% more than she sold the coffee table -> SA-SB=0.2 Not Sufficient

Combined st(1&2): (PA-SA-PB+SB)/(PA-SA) -> (0.1-0.2)/(PA-SA) Not sufficient, as we don't know the purchase price(P) and sales price (S) for an armchair; we know only relative values.
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by abhi0697 » Mon May 16, 2011 6:19 am
Let's call armchair A and coffee table B
Let P be purchase and S be sale
(1) PA=1.1*PB. (IS)
(2) SA=1.2*SB. (IS)

Combined:
((SA-PA)-(SB-PB))/(SA-PA)=((1.2*SB-1.1*PB)-(SB-PB))/(1.2*SB-1.1*PB) now this equation cannot be solved for a value.

Hence, E
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by vinay_mashetty » Thu Jul 14, 2011 11:44 pm
I agree with abhi0697. But, I do have a doubt whether the denominator should contain the profit of armchair or coffee table. In my view it has to be the profit earned over coffee table but not that over armchair.

So,
((SA-PA)-(SB-PB))/(SA-PA)=((1.2*SB-1.1*PB)-(SB-PB))/(SB-PB))
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by gmatdriller » Sat Jul 23, 2011 3:34 pm
Percentage A greater than B ==>
(A-B)/B

In that case denominator is variables for coffee.
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by Ozlemg » Mon Jul 25, 2011 2:30 am
pemdas wrote:let's call an armchair A and a coffee table B, the gross profit (A-B)/A?
A=PA-SA, B=PB-SB where P is purchase and S is sale
st(1) Martha paid (purchase, P) 10% more for her armchair than for the coffee table -> PA-PB=0.1 Not Sufficient
st(2) Martha sold (sale, S) the armchair for 20% more than she sold the coffee table -> SA-SB=0.2 Not Sufficient

Combined st(1&2): (PA-SA-PB+SB)/(PA-SA) -> (0.1-0.2)/(PA-SA) Not sufficient, as we don't know the purchase price(P) and sales price (S) for an armchair; we know only relative values.
The Q asks for percentage, so why cant we solve the problem by plug ın numbers? We do not need actula ones, the Q asks the incremental?

What is the source of the problem? Is it form Official Guide?
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by GMATGuruNY » Mon Jul 25, 2011 3:00 am
Akansha wrote:Martha bought an armchair and a coffee table at an auction and sold both items at her store. Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?
1) Martha paid 10 percent more for her armchair than for the coffee table.
2) Martha sold the armchair for 20 percent more than she sold the coffee table.

Can anyone explain why the answer for this question is E and not C?
The following scenarios satisfy both statements:

Let amount paid for table = 10.
Then amount paid for armchair = (1.1)*10 = 11.

Case 1:
Let selling price of table = 20.
Then selling price of armchair = (1.2)*20 = 24.
(Armchair profit)/(Table profit) = (24-11)/(20-10) = 13/10.

Case 2:
Let selling price of table = 30.
Then selling price of armchair = (1.2)*30 = 36.
(Armchair profit)/(Table profit) = (36-11)/(30-10) = 25/20.

Since 13/10 ≠ 25/20, the ratio of the two profits cannot be determined.

The correct answer is E.
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