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

Question

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

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

niks18 · Answer

Total cost  = c*p=cp

total selling price for 1st lot  = d*f=df

Total selling price for 2nd lot  = (c-d)*m=cm-dm

Hence Total selling price  = df+cm-dm

Hence Net Profit  = df+cm-dm-cp=d(f-m)+c(m-p)

Option  C

KarishmaB · Answer

Too many variables so plugging in will be too confusing.

Focus on what you need.

Total profit = Revenue - Cost 
Revenue = df + (c - d)m = df + cm - dm
Cost = cp

Total profit = df + cm - dm - cp

Option (C) matches.

pushpitkc · Answer

Agree this method is quite cumbersome as already suggested, but its an alternate method

Let the car dealer have ordered  c=10  cars each priced at  p=100 
Hence, the cost price that the cars cost the car dealer was  1000(10*100)

It has been given that the dealer was able to sell  d=4  cars with a profit of 25 making  f=125  
The selling price of the 4 cars is  4*(100+25) = 500 
The remaining cars(6 in number) were sold at the a loss of 25 dollars each( m=75 ) 
The selling price of these cars was  6*75 = 450 , making the total selling price  450+500 = 950

The selling of the cars leads to a loss of 50, profit is -50

Plugging the values into the equation, we get 
A. df – cp – mp = 1250 - 1000 - 2500 (need not calculate, can't be -50)
B. df + f(d – m) – cp = 1250 + 25(-21) - 1000 (need not calculate, can't be -50)
C. d(f – m) + c(m – p) = 4(125-75) + 10(75-100) = 200 + 10(-25) = 200 - 250 = -50

Hence,  Option C {d(f – m) + c(m – p)}  is the correct answer

Mo2men · Answer

Hi,
The highlighted part is not correct:

According to your solution, it should be

d(f – m) + c(m – p) = 4(25-75) + 10(75-100) =  -  200 + 10(-25) = -200 - 250 = -450....it does not match the answer you provided above (-50). However, your math is totally correct in example you provided.

I tried many other sets of number which could match choice C.

I wonder where it is wrong in plugging number.

Mo2men · Answer

Hi  niks18 ,

The choices has something incorrect.

If you have d cars and f profit for each, so the revenue is not d * f. It must be d (f+P)...Do you agree???

If I have 1 car with price 100 and profit 20.......So revenue would be 1 (20+100)=120 and i is NOT 1 * 20 =20

What do you think???

chetan2u · Answer

Hi..
The choices are ok..

If the statement read... d cars were sold at a profit OF f dollars meant profit was fd.

But if statement reads ... d cars were sold at a profit FOR f dollars MEANS revenue is fd and f is more than the base price

rahul16singh28 · Answer

Total cost for c Cars =  c∗p

The total selling price for d cars =  d∗f

The total selling price remaining cars =  (c−d)∗m

Hence Total selling price for all cars =  df+cm−dm

Hence Net Profit =  df+cm−dm−cp

Hence, Option C

Mo2men · Answer

Make sense. Thanks for your reply.

pushpitkc · Answer

Make sense. Thanks for your reply.

Hi  Mo2men

I think I was also making the same mistake.
If we change the value of f, we should get Option C as the answer.

Have corrected the solution accordingly

JeffTargetTestPrep · Answer

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

DhanyaAbhirami · Answer

"at a profit  for  f dollars each" is different from "at a profit  of  f dollars each"

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards