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A parking lot contains ten cars. The average age of the cars is seven

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Bunuel
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A parking lot contains ten cars. The average age of the cars is seven [#permalink] New post   13 Feb 2019, 00:48
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A parking lot contains ten cars. The average age of the cars is seven years. If the average age of nine of the cars is six years, what is the age of the remaining car in years?

(A) 3
(B) 7
(C) 10
(D) 16
(E) 20
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D
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Re: A parking lot contains ten cars. The average age of the cars is seven [#permalink] New post   13 Feb 2019, 06:55
Bunuel wrote:
A parking lot contains ten cars. The average age of the cars is seven years. If the average age of nine of the cars is six years, what is the age of the remaining car in years?

(A) 3
(B) 7
(C) 10
(D) 16
(E) 20


age of all cars = 70
and 9 cars age = 54
70-54 = 16
IMO D
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Re: A parking lot contains ten cars. The average age of the cars is seven [#permalink] New post   13 Feb 2019, 07:06
Since average age of 10 cars= 7 years,
Thus,sum of ages of all the 10 cars = 10*7= 70 years
Average age of 9 cars= 6 years
Sum of ages of the 9 cars= 9*6=54 years.
Hence,the age of the 10th car=70-54=16 years

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Re: A parking lot contains ten cars. The average age of the cars is seven [#permalink] New post   13 Feb 2019, 08:06
Bunuel wrote:
A parking lot contains ten cars. The average age of the cars is seven years. If the average age of nine of the cars is six years, what is the age of the remaining car in years?

(A) 3
(B) 7
(C) 10
(D) 16
(E) 20

\(10*7 - 6*9\)

= \(70 - 54\)

= 16, Answer must be \((D) 16\)
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Re: A parking lot contains ten cars. The average age of the cars is seven [#permalink] New post   15 Feb 2019, 18:25
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Bunuel wrote:
A parking lot contains ten cars. The average age of the cars is seven years. If the average age of nine of the cars is six years, what is the age of the remaining car in years?

(A) 3
(B) 7
(C) 10
(D) 16
(E) 20



The total sum of the ages of all 10 cars is 10 x 7 = 70.

The sum of the 9 cars is 9 x 6 = 54

Therefore, the age of the remaining car is 70 - 54 = 16.

Answer: D
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Re: A parking lot contains ten cars. The average age of the cars is seven [#permalink] New post   16 Feb 2019, 16:52
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It's a weighted average problem so you can also use a number line:

--6--7-----------------C---

The ratio of the distances to the middle must be 1 to 9, since that's the ratio of the numbers of cars in each group, and since the smaller distance is 1, the larger distance is 9, and C = 7+9 = 16.

Of course with a problem set up in such a straightforward way, you don't need to use a weighted average method to solve - the methods posted above are just as easy.
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Re: A parking lot contains ten cars. The average age of the cars is seven [#permalink]
16 Feb 2019, 16:52
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