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# A store purchased a Brand C computer for the same amount

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SVP
Joined: 21 Jul 2006
Posts: 1510
A store purchased a Brand C computer for the same amount [#permalink]

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18 Jul 2008, 04:36
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A store purchased a Brand C computer for the same amount that is paid for a Brand D computer then sold them both at higher prices. The store's gross profit on the Brand C computer was what percent greater than its gross profit on the Brand D computer?

(1) The price at which the store sold the Brand C computer was 15% greater than the price at which the store sold the Brand D computer.

(2) The store's gross profit on the Brand D computer was $300. Director Joined: 01 Jan 2008 Posts: 622 Re: DS: Gross Profit [#permalink] ### Show Tags 18 Jul 2008, 05:21 tarek99 wrote: A store purchased a Brand C computer for the same amount that is paid for a Brand D computer then sold them both at higher prices. The store's gross profit on the Brand C computer was what percent greater than its gross profit on the Brand D computer? (1) The price at which the store sold the Brand C computer was 15% greater than the price at which the store sold the Brand D computer. (2) The store's gross profit on the Brand D computer was$300.

intuitive solution -> E because the purchase price is not known.

formal solution: x - purchase price of computers, y - gross profit on C, z - gross profit on D.
question: what is (y-z)/x?

1: (y+x) = 1.5*(z+x)
2: z = 300

1&2: calculate (y-300)/x

x = 700 -> y = 1.5*(700+300)-700 = 800 -> (y-300)/x = 500/700
x = 200 -> y = 1.5*(200+300)-200=550 -> (y-300)/x = 250/200 = 500/400

obviously those two numbers are different -> E
SVP
Joined: 28 Dec 2005
Posts: 1559

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18 Jul 2008, 05:28
maratikus, dont you mean that we need to find y-z/z , and not y-z/x ? we are looking for the percentage difference in profit, so i dont think we need the purchase price as the denominator.

all we need to know is the purchase price of the PCs, and the profit relationship between C and D, which we are given
Director
Joined: 01 Jan 2008
Posts: 622

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18 Jul 2008, 05:52
pmenon wrote:
maratikus, dont you mean that we need to find y-z/z , and not y-z/x ? we are looking for the percentage difference in profit, so i dont think we need the purchase price as the denominator.

all we need to know is the purchase price of the PCs, and the profit relationship between C and D, which we are given

you are right, it is (y-z)/z but my examples still work:

x = 700 -> y = 1.5*(700+300)-700 = 800 -> (y-300)/300 = 500/300
x = 200 -> y = 1.5*(200+300)-200=550 -> (y-300)/300 = 250/300
Manager
Joined: 15 Jul 2008
Posts: 206

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18 Jul 2008, 05:56
I think what maratikus is trying to say is that, using everything given, u still end up with one unknown in the equation. So the answer should be E.

Here is how i go about it..

St 1. You know neither the selling price, nor the purchase price. It is grossly inadequate. Certainly not option A.
let CP = x. Let SP be y and 1.15y. What u r trying to find out is (y-x)/(1.15y-x). You need atleast two equations to solve this. and u dont have even one.

St 2. From this u get nothing on brand c computer SP. Certainly not option B either.
let CP=x, then SP for brand D is x+300. Still nothing on brand C.

So certainly not option D.

Now combining one and two, put y=x+300 in the expression from st 1. That gives you 300 / (0.15x + 345). Still nothing unless u know x.
Not option C either

SVP
Joined: 21 Jul 2006
Posts: 1510

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18 Jul 2008, 06:07
You guys are right, the OA is E, but there is a simpler way of writing your equations:

Let p be the purchase price for Brand C and Brand D
Let c be the selling price for brand C
Let d be the selling price for brand D

Now, the question here is asking: what is $$(c-p)/(d-p)$$?

(1) c=1.15d

(2) d-p=300

even if you try both these equations, you will still be left with one variable, which makes it not eff. so answer choice is E.
Re: DS: Gross Profit   [#permalink] 18 Jul 2008, 06:07
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