A car dealership has 40 cars on the lot, 30% of which are

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A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percentage of total number of cars are silver?

A. 35%
B. 37.5%
C. 45%
D. 47.5%
E. 50%

The OA is E.

I solve this PS question as follows,

Number of silver cars before shipment = 30% of 40 = 12

Number of silver cars after shipment = 60% of 80 = 48

Total number of silver cars out of 120 = 48 + 12 = 60, which is 50%. Option E.

Please, can anyone explain another way to solve this question? Thanks in advance!
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by [email protected] » Tue Apr 17, 2018 7:15 pm
Hi All,

We're told that a car dealership has 40 cars on the lot, 30% of which are silver and the dealership receives a new shipment of 80 cars, 40% of which are NOT silver. We're asked for the percentage of the total cars are silver. Since we're given percentages - and asked a question in percentage terms - we can actually ignore the number of cars altogether and focus on the percentages. This is essentially a 'Weighted Average' question.

We know that 30% of 40 cars and 60% of the next 80 cars are silver. Since there are TWICE as many cars in the second group, we essentially have 3 groups of 40 cars - and we have to 'weigh' that second percentage twice as much as we weigh the first percentage:

(30% + 60% + 60%)/3 = 150%/3 = 50% of the cars are silver.

Final Answer: E

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by Jeff@TargetTestPrep » Thu Apr 19, 2018 4:42 pm
BTGmoderatorLU wrote:A car dealership has 40 cars on the lot, 30% of which are silver. If the dealership receives a new shipment of 80 cars, 40% of which are not silver, what percentage of total number of cars are silver?

A. 35%
B. 37.5%
C. 45%
D. 47.5%
E. 50%
Before the shipment, the car dealership has 0.3 x 40 = 12 silver cars. The shipment has 0.6 x 80 = 48 silver cars. Thus, after the shipment, the dealership has 12 + 48 = 60 silver cars out of a total of 40 + 80 = 120 cars. We see that the percentage of cars that are silver is 60/120 = 1/2 = 50%.

Answer: E

Jeffrey Miller
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