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by BTGmoderatorRO » Wed Dec 13, 2017 5:04 pm
A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

A) $5,000 and $1,000
B) $9,000 and $5,000
C) $11,000 and $9,000
D) $15,000 and $5,000
E) $20,000 and $10,000

OA is D
I'm struggling with the question, can an expert explain why it is D? Thanks a lot.
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by Jay@ManhattanReview » Fri Dec 15, 2017 2:53 am
Roland2rule wrote:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

A) $5,000 and $1,000
B) $9,000 and $5,000
C) $11,000 and $9,000
D) $15,000 and $5,000
E) $20,000 and $10,000

OA is D
I'm struggling with the question, can an expert explain why it is D? Thanks a lot.
Say the price of the first car = $x, and that of the second car = $y.

Thus, the sale price of the first car = (100 + 10)% of x = 1.1x and the sale price of the second car = (100 - 10)% of y = 0.9y

Profit margin from the sale of the two cars = Sale price of the two cars - Cost price of the two cars = (1.1x + 0.9y) - (x + y) = 0.1 (x - y) ---(1)

We know that the profit margin is 5% (of the cost price) = 0.05(x + y) ---(2)

We are given that the dealership's total profit was $1000, thus

0.1 (x - y) = 1000 => x - y = 10,000 ---(3)

Also, 0.05(x + y) = 1000 => x + y = 1000/0.5 = 20,000 ---(4)

From (3) and (4), we get that x= $15000 and y = $5000.

The correct answer: D

Hope this helps!

-Jay
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by GMATWisdom » Fri Dec 15, 2017 7:02 am
Roland2rule wrote:A car dealership sold two cars: the first car at a 10% profit and the second car at a 10% loss, which gave them an overall profit margin of 5% from these two sales. If the dealership's total profit was $1000, what was the sale price of each car?

A) $5,000 and $1,000
B) $9,000 and $5,000
C) $11,000 and $9,000
D) $15,000 and $5,000
E) $20,000 and $10,000

OA is D
I'm struggling with the question, can an expert explain why it is D? Thanks a lot.
let me first tell you that if the given options are correct then
he should have asked the purchase price of each item and not the sale price

ASSUMING HE IS ASKING THE PURCHASE PRICE OF EACH ITEM

overall 5% profit = $1000
therefore total purchase price of the items = (100/5)*1000= $20000

only in options C and D total purchase price becomes $20000

in option C, 10% of 11000 is 1100 and 10% of 9000 is 900
therefore overall profit becomes 1100-900= $200

in option D , 10% 15000 = 1500 and
10% of 5000 = 500 and the overall profit = difference between the two =$ 1000

hence option D is correct
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