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test-prep companies in New Jersey

by sanju09 » Wed May 02, 2012 2:59 am
There are an even number x of different test-prep companies in New Jersey. Each company is for sale for a price of d dollars. A trader purchases all the companies. After y years, the trader sells half of the companies for 2d dollars each and the other half of the companies for d/2 dollars each. What is the total amount in dollars that the trader receives from the sale of all x companies?
(A) dx
(B) 5dx/4
(C) dx/y
(D) 3dx/2
(E) dxy



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by Anurag@Gurome » Wed May 02, 2012 8:59 pm
sanju09 wrote:There are an even number x of different test-prep companies in New Jersey. Each company is for sale for a price of d dollars. A trader purchases all the companies. After y years, the trader sells half of the companies for 2d dollars each and the other half of the companies for d/2 dollars each. What is the total amount in dollars that the trader receives from the sale of all x companies?
(A) dx
(B) 5dx/4
(C) dx/y
(D) 3dx/2
(E) dxy



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rephrased to comfort
Cost of x companies for the trader = x * d = $xd
After y years, the trader sells half of the companies for 2d dollars each implies selling price of half of the companies for the trader = (x/2) * 2d = $xd
Selling price of the other half of the companies = (x/2) * (d/2) = $(xd/4)

Therefore, the total amount that the trader receives from the sale of all x companies = xd + (xd/4) = [spoiler]$(5xd/4)[/spoiler]

The correct answer is B.
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