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

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26 Apr 2007, 06:53

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A store purchased a Brand C computer for the same amount that it paid for a Brand D computer and then sold them both at higher prices. The storeтАЩs 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 percent greater than the price at which the store sold the Brand D computer.
(2) The storeтАЩs gross profit on the Brand D computer was $300.

The question asks us to determine what percent greater is Brand C's gross profit than Brand D's gross profit.

Here's how I figured this out....

Sc=selling price of Brand C
Sd=selling price of Brand D
Pc=price/cost of C
Pd=price/cost of D
Gc=gross profit of C
Gd=gross profit of D

The equation that needs to be solved is:
(Gc-Gd)/Gc

[1] this tells us that Sc=1.15(Sd)

plug this into the equation for gross profit for C:
Sc-Pc=Gc --> 1.15(Sd)-Pc=Gc --> we can sustitute Pd for Pc because we know from the question stem that they are equal.
Therefore, 1.15(Sd)-Pd=Gc

Cost price of the computers are the same.
Statement 1

Implies that the SP of C = 1.15 SP of D
the equation is reduced to G.P of C- G.P of D/ G.P of D
= 1.15 x- CP -x+CP/ x- CP , where x= Selling price of D, 1.15x= SP of C, CP= cost price of computers ( CP of C= CP of D)

Equation is reduced to 0.15x/ x- CP * 100

Insufficient

Statement 2
GP of D = 300
doesnt not tell us anything about the SP , insufficuent data

Combing statement 1 &2

300= x- CP,
adding this to the previous reduced equation we get
( 0.15x/ x-x+300) *100= ).05 x
the value again depends on x.
so insufficient

The question asks Pc/Pd = (price C - cost)/(price D - cost)

cost C = cost D = cost

From S1: price C = 1.15 price D ; we don't know the 'cost' -> Insuff
From S2: Pd = 300 = price D - cost; when we plug this information into the formula Pc/Pd we still have 'cost' as a variable ---> Insuff

S1 and S2: the 'cost' is still unknown ---> Insuff

the question is asking for gross profit...which means I need to know the total number of units sold for each brand..we have no such info given...

for all i know the store sold 1 brand C computer..and 10 brand B computer etc..the gross profit would be different if the store sold 10 brand C computers and 10 brand D computers...