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# Sixty-eight people are sitting in 20 cars and each car contains at mos

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Math Expert
Joined: 02 Sep 2009
Posts: 52905
Sixty-eight people are sitting in 20 cars and each car contains at mos  [#permalink]

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06 Feb 2019, 23:53
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Difficulty:

45% (medium)

Question Stats:

62% (01:36) correct 38% (02:04) wrong based on 29 sessions

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Sixty-eight people are sitting in 20 cars and each car contains at most 4 people. What is the maximum possible number of cars that could contain exactly 1 of the 68 people?

A. 2
B. 3
C. 4
D. 8
E. 12

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Re: Sixty-eight people are sitting in 20 cars and each car contains at mos  [#permalink]

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07 Feb 2019, 00:06
Bunuel wrote:
Sixty-eight people are sitting in 20 cars and each car contains at most 4 people. What is the maximum possible number of cars that could contain exactly 1 of the 68 people?

A. 2
B. 3
C. 4
D. 8
E. 12

Max 1 will be when rest of the car is in full capacity

16*4+1+1+1+1=68(in 4 cars )
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Re: Sixty-eight people are sitting in 20 cars and each car contains at mos  [#permalink]

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07 Feb 2019, 00:12
1
Bunuel wrote:
Sixty-eight people are sitting in 20 cars and each car contains at most 4 people. What is the maximum possible number of cars that could contain exactly 1 of the 68 people?

A. 2
B. 3
C. 4
D. 8
E. 12

total 68 people and each car can car 4 people at most
so at max 16 cars can carry 64 people
leaving 4 cars which can carry exactly 1 person .
IMO C ; 4
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Posts: 1
Re: Sixty-eight people are sitting in 20 cars and each car contains at mos  [#permalink]

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07 Feb 2019, 09:37
let, the maximum possible number of cars that could contain exactly 1 be x
so,
(20-x)4+x=68
calculated the equation
we get x=4

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Re: Sixty-eight people are sitting in 20 cars and each car contains at mos  [#permalink]

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11 Feb 2019, 07:05
Bunuel wrote:
Sixty-eight people are sitting in 20 cars and each car contains at most 4 people. What is the maximum possible number of cars that could contain exactly 1 of the 68 people?

A. 2
B. 3
C. 4
D. 8
E. 12

If 8 cars contain 1 person each, then we have 68 - 8 = 60 people for the remaining 20 - 8 = 12 cars. This makes an average of 60/12 = 5 people per car, which is also impossible.

C. 4

If 4 cars contain 1 person each, then we have remaining 68 - 4 = 64 people for remaining 20 - 4 = 16 cars. This makes an average of 64/16 = 4 people per car, which is possible.

So the maximum number of cars that could contain exactly 1 person each is 4.

Alternate Solution:

To maximize the number of cars with only one person, let’s suppose all the remaining cars contain 4 people. Let n denote the number of cars with only one person. Then, the remaining 20 - n cars contain 4(20 - n) people. We are given that the 4(20 - n) people together with the n people each of whom ride alone must add up to 68; therefore we have:

4(20 - n) + n = 68

80 - 4n + n = 68

12 = 3n

n = 4

So the maximum number of cars that could contain exactly 1 person each is 4.

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Re: Sixty-eight people are sitting in 20 cars and each car contains at mos  [#permalink]

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11 Feb 2019, 07:42
Bunuel wrote:
Sixty-eight people are sitting in 20 cars and each car contains at most 4 people. What is the maximum possible number of cars that could contain exactly 1 of the 68 people?

A. 2
B. 3
C. 4
D. 8
E. 12

So each car contains at most 4 people

this means that, y = possible number of cars that could contain exactly 1

y*1 + (20-y) * 4 = 68

We can directly plug in from C

4 + 16 * 4 = 68
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Re: Sixty-eight people are sitting in 20 cars and each car contains at mos   [#permalink] 11 Feb 2019, 07:42
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