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# A car dealership orders 80 automobiles from the factory and wants to

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A car dealership orders 80 automobiles from the factory and wants to  [#permalink]

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17 May 2017, 23:15
1
10
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:35) correct 34% (02:45) wrong based on 125 sessions

A car dealership orders 80 automobiles from the factory and wants to sell each for $22,275. 60 of the cars are sold at this price, which represented an 8% profit above the dealership’s cost from the factory. To sell the remaining 20 cars, the dealership has to substantially discount the retail price, and each is sold at a price that represents a 4% loss below the dealership’s cost. What was the dealership’s profit or loss as a percent of the dealership’s initial cost for the 80 automobiles? A. 5% loss B. 4% loss C. 2% profit D. 4% profit E. 5% profit _________________ Manager Joined: 04 Apr 2015 Posts: 107 Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink] ### Show Tags 18 May 2017, 03:35 2 1 IMO E Thought first solving it with conventional took me 5.5 minutes then I managed to get a shortcut 60*+8 =480 20*-4=-80 total=+400 per car 400/80 =+5 Intern Joined: 20 Jul 2015 Posts: 15 Re: A car dealership orders 80 automobiles from the factory and wants to [#permalink] ### Show Tags 18 May 2017, 03:46 Bunuel wrote: A car dealership orders 80 automobiles from the factory and wants to sell each for$22,275. 60 of the cars are sold at this price, which represented an 8% profit above the dealership’s cost from the factory. To sell the remaining 20 cars, the dealership has to substantially discount the retail price, and each is sold at a price that represents a 4% loss below the dealership’s cost. What was the dealership’s profit or loss as a percent of the dealership’s initial cost for the 80 automobiles?

A. 5% loss
B. 4% loss
C. 2% profit
D. 4% profit
E. 5% profit

weighted avg. is rather much faster method for above such problems

Let x be avg. profit/loss

then

60/20= (-4-x)/x-8

3x-24= -4-x

4x = 20

x=5

ans E
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A car dealership orders 80 automobiles from the factory and wants to  [#permalink]

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18 May 2017, 04:41
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I'd plug in a number, let say 100 as the CP of the cars.

Given data is
60 sold at 8% more than CP
20 sold at 4% less than SP

Total CP: $$80*100 = 8000$$
Total SP: $$60*1.08*100 + 20*.96*100 = 60*108 + 20*96 = 6480+1920 = 8400$$

Profit is SP - CP, which is $$400(8400-8000)$$

Therefore, the profit percentage is $$\frac{400}{8000}*100$$ or 5%(Option E)

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Re: A car dealership orders 80 automobiles from the factory and wants to  [#permalink]

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18 May 2017, 04:48
Bunuel wrote:
A car dealership orders 80 automobiles from the factory and wants to sell each for $22,275. 60 of the cars are sold at this price, which represented an 8% profit above the dealership’s cost from the factory. To sell the remaining 20 cars, the dealership has to substantially discount the retail price, and each is sold at a price that represents a 4% loss below the dealership’s cost. What was the dealership’s profit or loss as a percent of the dealership’s initial cost for the 80 automobiles? A. 5% loss B. 4% loss C. 2% profit D. 4% profit E. 5% profit$22,275 represented 8% profit, so the cost is $$\frac{22,275}{1.08}=20,625$$

Sell remaining 20 cars at price: $$20,625 \times 0.96 = 19,800$$

The total revenue: $$60 \times 22,275 + 20 \times 19,800$$
The total cost: $$80 \times 20,625$$

The profit/loss ratio: $$\frac{(60 \times 22,275 + 20 \times 19,800) - 80 \times 20,625}{80 \times 20,625}$$
$$=\frac{6 \times 22,275 + 2 \times 19,800}{8 \times 20,625} - 1 \\ = \frac{3 \times 22,275 + 19,800}{4 \times 20,625} - 1 \\ = 1.05 - 1 = 0.05 = 5 \%$$

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Re: A car dealership orders 80 automobiles from the factory and wants to  [#permalink]

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22 May 2017, 17:27
Bunuel wrote:
A car dealership orders 80 automobiles from the factory and wants to sell each for $22,275. 60 of the cars are sold at this price, which represented an 8% profit above the dealership’s cost from the factory. To sell the remaining 20 cars, the dealership has to substantially discount the retail price, and each is sold at a price that represents a 4% loss below the dealership’s cost. What was the dealership’s profit or loss as a percent of the dealership’s initial cost for the 80 automobiles? A. 5% loss B. 4% loss C. 2% profit D. 4% profit E. 5% profit We are given that 60 cars were sold for$22,275 at a profit of 8%. Thus:

Profit = 0.08(cost)

Revenue - cost = 0.08(cost)

22,275 - c = 0.08c

22,275 = 1.08c

22,275/1.08 = c

20,625 = c

Thus, the dealership’s cost for each car was 20,625 dollars.

We are also given that 20 cars were sold at a loss of 4%. Thus, each of the remaining 20 cars was sold at 96% of the dealership’s cost.

Thus, each of the remaining 20 cars was sold for 0.96(20,625) = $19,800. In total, the dealership spent 20,625 x 80 = 1,650,000 on the cars and earned: 22,275 x 60 + 19,800 x 20 = 1,336,500 + 396,000 = 1,732,500 Thus, the dealership made a profit on the sale of 80 cars and the profit is: [(1,732,000 - 1,650,000)/1,650,000] x 100 = (82,000/1,650,000) x 100 = 0.05 x 100 = 5%. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Senior Manager Joined: 02 Apr 2014 Posts: 474 GMAT 1: 700 Q50 V34 A car dealership orders 80 automobiles from the factory and wants to [#permalink] ### Show Tags 20 Nov 2017, 19:19 Can be solved quickly using weighted average concept. 96 (4% loss, 20 cars(weightage) ) <------------------------------------------> 108 (8% profit, 60 cars (weightage)) 60:20 = 3 : 1 96 <--------------3------------------->|<--------1-------->108 so the diff between 108 - 96 , must be divided in 3:1 ratio (60:20) according to weightage so weighted average = $$96 + (12 * 3/4) = 105$$ = 5% profit, Answer (E) Thanks Manager Joined: 14 Jul 2014 Posts: 96 Location: India Concentration: Social Entrepreneurship, Strategy GMAT 1: 620 Q41 V34 WE: Information Technology (Computer Software) A car dealership orders 80 automobiles from the factory and wants to [#permalink] ### Show Tags 22 Sep 2018, 11:21 The awkward numbers in this problem and the seemingly tedious calculations required to solve it are a hint to look for a faster approach. While you could calculate the total profit on the 60 cars and the total loss on the 20 cars, combine, and divide by the total cost to the dealership, this would take a very, very long time Since the problem is about percentage profit or loss, the values of the cars are not important. The answer will be the same if it is a$10,000 car, a $15,000 car or a$22,275 car. This is really just a good old-fashioned weighted average problem. ¾ of the cars were sold at an 8% profit and ¼ were sold at a 4% loss. This means the ratio of cars with a profit to cars with a loss is 3:1 and this controls the weighting between +8% and -4%. Using the mapping strategy, see that the combined profit would be 5%:

-4% ------------------------------5%-------8%
----------------9%----------------------3%-----
The ratio of 8% profit to 4% loss is the correct 3:1.

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Re: A car dealership orders 80 automobiles from the factory and wants to  [#permalink]

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22 Sep 2018, 12:37
I just did 8*(3/4) + (-4)*(1/4) = 6 - 1 = +5%.
Re: A car dealership orders 80 automobiles from the factory and wants to &nbs [#permalink] 22 Sep 2018, 12:37
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