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16 Sep 2014, 00:21
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A car dealership sold two cars: Car A at a 10% profit and Car B at a 10% loss, resulting into an overall profit of 5% from the two sales. If the dealership's profit from these two cars was $1,000, what was the initial cost of cars A and B?
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
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
16 Sep 2014, 00:21
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Official Solution:
A car dealership sold two cars: Car A at a 10% profit and Car B at a 10% loss, resulting into an overall profit of 5% from the two sales. If the dealership's profit from these two cars was $1,000, what was the initial cost of cars A and B?
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
Since the dealership had an overall profit of 5% and that equals to $1,000, we can determine that the total cost price of the two cars was $20,000 (0.05*x = 1,000 giving x = 20,000).
Among the options, only options C and D give the total cost price of the two cars as $20,000. Let's check one of them:
C. Cost prices of the two cars are given as $11,000 and $9,000. The profit from the first car would be \(0.1*$11,000=$1,100\) and the loss from the second car would be \(0.1*$9,000=$900\). So, the overall profit would be \($1,100-$900=$200\), which is not equal to the total profit of $1,000. Therefore, option C is incorrect.
So, we are left with only option D, which must be correct.
Answer: D
A car dealership sold two cars: Car A at a 10% profit and Car B at a 10% loss, resulting into an overall profit of 5% from the two sales. If the dealership's profit from these two cars was $1,000, what was the initial cost of cars A and B?
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
Since the dealership had an overall profit of 5% and that equals to $1,000, we can determine that the total cost price of the two cars was $20,000 (0.05*x = 1,000 giving x = 20,000).
Among the options, only options C and D give the total cost price of the two cars as $20,000. Let's check one of them:
C. Cost prices of the two cars are given as $11,000 and $9,000. The profit from the first car would be \(0.1*$11,000=$1,100\) and the loss from the second car would be \(0.1*$9,000=$900\). So, the overall profit would be \($1,100-$900=$200\), which is not equal to the total profit of $1,000. Therefore, option C is incorrect.
So, we are left with only option D, which must be correct.
Answer: D
shasadou
Joined: 12 Aug 2015
Last visit: 24 Nov 2022
Posts: 219
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Concentration: General Management, Operations
Schools: Johnson '18 (WL) Duke '18 (M) Tuck '18 (D)
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE:Management Consulting (Consulting)
josegf1987
Hi
this shortcut looks the following way: please the pic.
1. Draw a number line and place values (5 is midpoint, Y is 15 points from the midpoint because it is a loss)
2. The closer to average the greater the weight (X is greater that Y)
3. Configure a proportion where X gets the corresponding value (greater value because weight is greater)
4. X relates to Y just the same way as 15 relates to 5, because X weighs more than Y.
5. Only answer D matches our fraction 15:5
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