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QOTD#14 A car dealer received a shipment of cars, half of

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QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 19 Aug 2016, 16:03
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Question Stats:

85% (02:08) correct 14% (03:23) wrong based on 21 sessions
A car dealer received a shipment of cars, half of which were black, with the remainder consisting of equal numbers of blue, silver, and white cars. During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold. What percent of the cars in the shipment were sold during that month?

A. 36%
B. 50%
C. 55%
D. 60%
E. 72%

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Question: 16
Page: 153
[Reveal] Spoiler: OA

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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 19 Aug 2016, 16:09
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Explanation

In the shipment, \(\frac{1}{2}\) f the cars were black. Since the remainder of the cars consisted of equal numbers of blue, silver, and white cars, it follows that \(\frac{1}{2}*\frac{1}{3}\), or \(\frac{1}{6}\), of the cars were blue, \(\frac{1}{6}\) were silver, and \(\frac{1}{6}\) were white. Based on the percents of the cars of each color that were sold during the next month, the percent of the cars in the shipment that were sold during that month was

\(\frac{1}{2}*70%+\frac{1}{6}*80%+\frac{1}{6}*30%+\frac{1}{6}*40%\)

= \(60%\).

The correct answer is Choice D.
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 23 Aug 2016, 14:22
Expert's post
sandy wrote:
A car dealer received a shipment of cars, half of which were black, with the remainder consisting of equal numbers of blue, silver, and white cars. During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold. What percent of the cars in the shipment were sold during that month?

A. 36%
B. 50%
C. 55%
D. 60%
E. 72%


Another approach is to assign some initial values that match the given information.

Half of the cars were black, with the remainder consisting of equal numbers of blue, silver, and white cars
Let's say we have:
30 black cars
10 blue cars
10 silver cars
10 white cars
TOTAL CAR INITIALLY = 30 + 10 + 10 + 10 = 60

Aside: The above values satisfy the given conditions. HOWEVER, we can also use different values (like 6 black cars, 2 blue cars, 2 silver cars and 2 white cars) and get the same correct answer. I like using the above values because they're easy to use with percents.

During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold
Black cars sold = 70% of 30 = 21
Blue cars sold = 80% of 10 = 8
Silver cars sold = 30% of 10 = 3
White cars sold = 40% of 10 = 4
TOTAL CAR SOLD = 21 + 8 + 3 + 4 = 36

What percent of the cars in the shipment were sold during that month?
36/60 = 3/5 = 60%

Answer: D

Cheers,
Brent
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 25 Apr 2018, 08:06
GreenlightTestPrep wrote:
sandy wrote:
A car dealer received a shipment of cars, half of which were black, with the remainder consisting of equal numbers of blue, silver, and white cars. During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold. What percent of the cars in the shipment were sold during that month?

A. 36%
B. 50%
C. 55%
D. 60%
E. 72%


Another approach is to assign some initial values that match the given information.

Half of the cars were black, with the remainder consisting of equal numbers of blue, silver, and white cars
Let's say we have:
30 black cars
10 blue cars
10 silver cars
10 white cars
TOTAL CAR INITIALLY = 30 + 10 + 10 + 10 = 60

Aside: The above values satisfy the given conditions. HOWEVER, we can also use different values (like 6 black cars, 2 blue cars, 2 silver cars and 2 white cars) and get the same correct answer. I like using the above values because they're easy to use with percents.

During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold
Black cars sold = 70% of 30 = 21
Blue cars sold = 80% of 10 = 8
Silver cars sold = 30% of 10 = 3
White cars sold = 40% of 10 = 4
TOTAL CAR SOLD = 21 + 8 + 3 + 4 = 36

What percent of the cars in the shipment were sold during that month?
36/60 = 3/5 = 60%

Answer: D

Cheers,
Brent



How do I even come up with this approach, I was unable to think of it.
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 01 May 2018, 06:07
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Just assume 100 cars so 50 are black and other three colors are \(\frac{50}{3}\). You can see better to assume 120 cars. Then you have nice whole numbers. 60 black and 20 of the remaining colors.

With experience you will find you can get the right number of cars to assume.

In this case the critial number was \(\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}\). So pick a number divisible by 6.
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 01 May 2018, 21:30
sandy wrote:
Just assume 100 cars so 50 are black and other three colors are \(\frac{50}{3}\). You can see better to assume 120 cars. Then you have nice whole numbers. 60 black and 20 of the remaining colors.

With experience you will find you can get the right number of cars to assume.

In this case the critial number was \(\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}\). So pick a number divisible by 6.



I like the way you changed the assumption from 100 to 120 so to have easily divisible whole numbers ..Thanks mate :) Kudos.
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 02 May 2018, 04:05
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As entire question is about percentage. Assuming initial number as 100 and further solving as per inputs will give the solution.
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 10 May 2018, 06:44
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sandy wrote:
A car dealer received a shipment of cars, half of which were black, with the remainder consisting of equal numbers of blue, silver, and white cars. During the next month, 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold. What percent of the cars in the shipment were sold during that month?

A. 36%
B. 50%
C. 55%
D. 60%
E. 72%


We can let the total number of cars in the shipment = 120.

So 1/2(120) = 60 are black and 60/3 = 20 = blue = silver = white.

Since 70 percent of the black cars, 80 percent of the blue cars, 30 percent of the silver cars, and 40 percent of the white cars were sold, we have:

0.7 x 60 + 0.8 x 20 + 0.3 x 20 + 0.4 x 20 = 42 + 16 + 6 + 8 = 72.

Thus, the percentage of cars sold was 72/120 = 6/10 = 60% of the cars in the shipment.

Answer: D
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Re: QOTD#14 A car dealer received a shipment of cars, half of [#permalink] New post 23 Sep 2018, 23:16
Consider total cars = 60

so Black cars = 30, Blue cars= Silver cars=White cars = 10

Black sold cars (70% of 30)= 21, Blue sold cars = 8, Silver sold cars = 3, White sold cars = 4

Total sold cars = 21+8+3+4=36

So % of total cars sold= 36/60*100= 60%

Answer D
Re: QOTD#14 A car dealer received a shipment of cars, half of   [#permalink] 23 Sep 2018, 23:16
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