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At a car dealership, 62% of vehicles on the lot are electric and 48%

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At a car dealership, 62% of vehicles on the lot are electric and 48% [#permalink]

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New post 06 Mar 2017, 03:53
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

64% (02:28) correct 36% (02:11) wrong based on 100 sessions

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At a car dealership, 62% of vehicles on the lot are electric and 48% are autonomous. If at least 15% of the 400 vehicles on the lot are neither electric nor autonomous, the number of electric, autonomous vehicles can be anything from:

A. 62 to 110
B. 100 to 192
C. 110 to 192
D. 100 to 248
E. 110 to 248
Spoiler: OA

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At a car dealership, 62% of vehicles on the lot are electric and 48% [#permalink]

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New post 06 Mar 2017, 13:40
Nice Question.

I generally prefer using double-set matrix for a problem with only two sets of option.

Electric Non- Electric Total
Autonomous 100 92 192 (48%)
Non- Autonomous 60 (Minimum. 15 %)) 208 (400-192)
Total 248 (62%) 152 (400-248) 400



Electric Non- Electric Total
Autonomous 192 0 192 (48%)
Non- Autonomous 152 (Maximum) 208 (400-192)
Total 248 (62%) 152 (400-248) 400


Using the Minimum- Maximum case it is clear that electric, autonomous vehicles can be anything from 100-192. Hence answer choice B.


Ps- I could not draw the above table on my post hence I posted it this way. If someone knows how to draw a table, kindly let me know. Thank you.
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Re: At a car dealership, 62% of vehicles on the lot are electric and 48% [#permalink]

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New post 07 Mar 2017, 17:49
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Bunuel wrote:
At a car dealership, 62% of vehicles on the lot are electric and 48% are autonomous. If at least 15% of the 400 vehicles on the lot are neither electric nor autonomous, the number of electric, autonomous vehicles can be anything from:

A. 62 to 110
B. 100 to 192
C. 110 to 192
D. 100 to 248
E. 110 to 248


We are given that, of 400 cars at a dealership, 62% of the vehicles on the lot are electric, and 48% are autonomous. Thus:

Number of electric cars = 400 x 0.62 = 248. Thus, the number of cars that ARE NOT electric is 400 - 248 = 152.

Number of autonomous cars = 400 x 0.48 = 192. Thus, the number of cars that ARE NOT autonomous is 208.

We are also given that at least 15% or 0.15 x 400 = 60 of the vehicles on the lot are neither electric nor autonomous. Thus, the minimum number of cars that are neither electric nor autonomous is 60.

Since there are 152 cars that are not electric and 208 cars that are not autonomous, the maximum number of cars that could be neither electric nor autonomous is 152.

Finally we can determine the range of “both” using the following formula:

Total cars = total electric + total autonomous - both + neither

When neither is 60, we have:

400 = 248 + 192 - both + 60

400 = -both + 500

both = 100

When neither is 192, we have:

400 = 248 + 192 - both + 152

400 = -both + 592

both = 192

Thus, the range is from 100 to 192.

Answer: B
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Re: At a car dealership, 62% of vehicles on the lot are electric and 48% [#permalink]

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New post 07 Mar 2017, 18:11
Bunuel wrote:
At a car dealership, 62% of vehicles on the lot are electric and 48% are autonomous. If at least 15% of the 400 vehicles on the lot are neither electric nor autonomous, the number of electric, autonomous vehicles can be anything from:

A. 62 to 110
B. 100 to 192
C. 110 to 192
D. 100 to 248
E. 110 to 248


Official solution from Veritas Prep.

In this overlapping sets problem, you can work with the fact that the minimum percentage of "neither" is 15%. If that minimum case is true, then your Venn Diagram equation would look like:

62% + 48% - Both + 15% = 100%

In that case, you'd get to 125% - Both = 100%, so "Both" = 25%. Since there are 400 vehicles total, that sets one of your parameters at 25% of 400, which is 100.

To find the other limit, notice first the role of the "Neither" figure in the equation above. The larger you make what was 15%, the larger you'd need to make the subtracted "Both" to compensate to stay at the 100% figure. So the only direction for the "Both" total to go is up from 100.

From there, recognize that the maximum has to be constrained by the 48%. Why? Because if only 48% are autonomous, you couldn't more than 48% be autonomous AND something else. The maximum you could have for autonomous AND electric is if all autonomous vehicles are electric, and you know that the number of autonomous is capped at 48%. So therefore your maximum value is 48% of 400, which is 192, making B the correct answer.
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Re: At a car dealership, 62% of vehicles on the lot are electric and 48% [#permalink]

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New post 07 Mar 2017, 18:20
JeffTargetTestPrep wrote:
Bunuel wrote:
At a car dealership, 62% of vehicles on the lot are electric and 48% are autonomous. If at least 15% of the 400 vehicles on the lot are neither electric nor autonomous, the number of electric, autonomous vehicles can be anything from:

A. 62 to 110
B. 100 to 192
C. 110 to 192
D. 100 to 248
E. 110 to 248


We are given that, of 400 cars at a dealership, 62% of the vehicles on the lot are electric, and 48% are autonomous. Thus:

Number of electric cars = 400 x 0.62 = 248. Thus, the number of cars that ARE NOT electric is 400 - 248 = 152.

Number of autonomous cars = 400 x 0.48 = 192. Thus, the number of cars that ARE NOT autonomous is 208.

We are also given that at least 15% or 0.15 x 400 = 60 of the vehicles on the lot are neither electric nor autonomous. Thus, the minimum number of cars that are neither electric nor autonomous is 60.

Since there are 152 cars that are not electric and 208 cars that are not autonomous, the maximum number of cars that could be neither electric nor autonomous is 152.

Finally we can determine the range of “both” using the following formula:

Total cars = total electric + total autonomous - both + neither

When neither is 60, we have:

400 = 248 + 192 - both + 60

400 = -both + 500

both = 100

When neither is 192, we have:

400 = 248 + 192 - both + 152

400 = -both + 592

both = 192

Thus, the range is from 100 to 192.

Answer: B


Dear JeffTargetTestPrep, Why the maximum number of cars that could be neither electric nor autonomous is 152 instead of 208?
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Re: At a car dealership, 62% of vehicles on the lot are electric and 48%   [#permalink] 07 Mar 2017, 18:20
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