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A certain company sells only cars and trucks, and the average selling

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A certain company sells only cars and trucks, and the average selling [#permalink]

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A certain company sells only cars and trucks, and the average selling price of all the cars and trucks combined is $18,000. If the average selling price of each car is $15,500, did the company sell more trucks than cars?

1) The number of sold cars is 100.

2) The average price of trucks sold was $21,500.
[Reveal] Spoiler: OA

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Re: A certain company sells only cars and trucks, and the average selling [#permalink]

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New post 24 Sep 2017, 10:24
A certain company sells only cars and trucks, and the average selling price of all the cars and trucks combined is $18,000.
=> Let no. of cars = C and No. of trucks = T
=> ( total selling price of all cars + total selling price of all trucks)/(C+T) = 18000
=> total selling price of all cars + total selling price of all trucks = 18000(C+T)
=>TSPC +TSPT =18000(C+T)

If the average selling price of each car is $15,500,
=> Average selling price of cars = 15500 = Total selling price of all cars/C
=> TSPC= C* 15500

Put given value in previous equation => 15500*C+TSPT = 18000*C+18000*T => TSPT = 2500*C+18000*T ---------- eq(1)

did the company sell more trucks than cars? => Find is T > C ?


1) The number of sold cars is 100.
C = 100
=> Total selling price of all cars = 15500* C = 15500* 100

If we put this value in derived equation (1). We will not get any additional information.
Here we don't know about total selling price of all trucks(TSPT) or T.
Insufficient

2) The average price of trucks sold was $21,500.
=> Average selling price of Trucks = 21500 = Total selling price of all Trucks/T
=> Total selling price of trucks = TSPT = T* 21500

Lets put this value in derived equation (1)
=> 15500*C+TSPT = 18000*C+18000*T
=> 15500*C + 21500*T = 18000*C+18000*T
=> 3500*T = 2500* C
=> 35/25 * T = C
=> C>T .... definite answer
Sufficient


Answer: B

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Re: A certain company sells only cars and trucks, and the average selling [#permalink]

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New post 24 Sep 2017, 10:45
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hazelnut wrote:
A certain company sells only cars and trucks, and the average selling price of all the cars and trucks combined is $18,000. If the average selling price of each car is $15,500, did the company sell more trucks than cars?

1) The number of sold cars is 100.

2) The average price of trucks sold was $21,500.


No need for equations here!

question: This looks like a weighted average problem. Cars have one average price, trucks have another average price. It looks like the average price of cars is $15,500. That's lower than the overall average, so the average price of trucks must be higher than the overall average - higher than $18,000.

If there are more cars, the average will be closer to the price of the cars. If there are more trucks, the average will be closer to the price of the trucks. If we have exactly the same number of cars and trucks, then the average will be right in the middle. The price of cars is $2,500 below the overall average. So, if there were the same number of cars and trucks, the price of trucks would be $2,500 above the average, or $20,500.

In summary:

same number of trucks and cars = average price of trucks is $20,500

more trucks than cars = average price of trucks is lower than $20,500 (since the average would have to be less than $2,500 away from the truck price, in order for the average to be closer to trucks than to cars)

more cars than trucks = average price of trucks is higher than $20,500 (since the average would have to be more than $2,500 away from the truck price, so the average could be closer to cars than to trucks)

Statement 1: This isn't useful, since it doesn't pin down the number of trucks. You could easily have 100 cars and 1 truck, or 100 cars and 1000 trucks. Not sufficient.

Statement 2: This tells us that the average price of trucks is higher than $20,500. So, there must be more cars than trucks, as described above. Sufficient.

The correct answer is B.
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Re: A certain company sells only cars and trucks, and the average selling   [#permalink] 24 Sep 2017, 10:45
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