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A car dealer received a shipment of c new cars from the car

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A car dealer received a shipment of c new cars from the car

by BTGmoderatorAT » Sun Jan 21, 2018 6:38 am
A car dealer received a shipment of c new cars from the car company at a base price of p dollars per car. If the dealer was able to sell d cars at a profit for f dollars each, but had to sell the rest of the cars at a loss for m dollars each, which of the following represents the total profit generated on the sales of the automobiles?

A. df - cp - mp
B. df + f(d - m) - cp
C. d(f - m) + c(m - p)
D. cp - df - f(c - d)
E. df - m(c - d) - cm

I'm confused how to set up the formulas here. Can any experts assist?
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by Jay@ManhattanReview » Tue Jan 23, 2018 12:57 am
ardz24 wrote:A car dealer received a shipment of c new cars from the car company at a base price of p dollars per car. If the dealer was able to sell d cars at a profit for f dollars each, but had to sell the rest of the cars at a loss for m dollars each, which of the following represents the total profit generated on the sales of the automobiles?

A. df - cp - mp
B. df + f(d - m) - cp
C. d(f - m) + c(m - p)
D. cp - df - f(c - d)
E. df - m(c - d) - cm

I'm confused how to set up the formulas here. Can any experts assist?
Profit from the sale of d cars = $d(f -p)
Loss from the sale of the remaining cars (= c -d) cars = $(p - m)(c -d)

The total profit generated on the sales of the automobiles = Total Profit - Total Loss = $[d(f -p) - (p - m)(c -d)].

We see that there is no option as d(f -p) - (p - m)(c -d). Let's manipulate this and see which option would match.

$d(f -p) - (p - m)(c -d) = $[df - dp -pc + pd + mc - md] = $[df -pc + mc - md] = $[d(f -m) + c (m - p)]

The correct answer: C

Hope this helps!

-Jay
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by Jeff@TargetTestPrep » Wed Jan 24, 2018 9:42 am
ardz24 wrote:A car dealer received a shipment of c new cars from the car company at a base price of p dollars per car. If the dealer was able to sell d cars at a profit for f dollars each, but had to sell the rest of the cars at a loss for m dollars each, which of the following represents the total profit generated on the sales of the automobiles?

A. df - cp - mp
B. df + f(d - m) - cp
C. d(f - m) + c(m - p)
D. cp - df - f(c - d)
E. df - m(c - d) - cm
The total cost of the c cars was cp dollars.

The revenue made on d cars was df dollars, and the revenue made on the remaining (c - d) cars was (c - d)m = cm - dm dollars. Thus, the total revenue for the c cars was df + cm - dm dollars.

Therefore, the total profit made on selling the c cars was:

(df + cm - dm) - cp = d(f - m) + c(m - p) dollars

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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