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The number of passengers on a certain bus at any given time is given

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The number of passengers on a certain bus at any given time is given  [#permalink]

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New post 03 Nov 2014, 08:36
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Tough and Tricky questions: Word Problems.



The number of passengers on a certain bus at any given time is given by the equation P = -2(S – 4)^2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?

A. 32
B. 30
C. 24
D. 14
E. 0

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Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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New post 03 Nov 2014, 20:45
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



The number of passengers on a certain bus at any given time is given by the equation P = -2(S – 4)^2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?

A. 32
B. 30
C. 24
D. 14
E. 0

Kudos for a correct solution.


\(P = -2(S – 4)^2 + 32\)

P = 32 - 2(s-4)^2

Value of P can be maximum = 32 when s = 4

2 stops after that means s = 6

\(p = 32 - (2^2)*2 = 32 - 8 = 24\)

Answer = C
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Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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New post 03 Nov 2014, 15:46
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Bunuel wrote:

Tough and Tricky questions: Word Problems.



The number of passengers on a certain bus at any given time is given by the equation P = -2(S – 4)^2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?

A. 32
B. 30
C. 24
D. 14
E. 0

Kudos for a correct solution.


Maximize P = -2*(S – 4)^2 + 32 ---> S=4

Two stops after ---> S = 6

P = -2*(6 – 4)^2 + 32
P = -8 + 32
P = 24

Correct answer is C

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Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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New post 23 Nov 2015, 04:06
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Bunuel wrote:

The number of passengers on a certain bus at any given time is given by the equation P = -2(S – 4)^2 + 32, where P is the number of passengers and S is the number of stops the bus has made since beginning its route. If the bus begins its route with no passengers, how many passengers will be on the bus two stops after the stop where it has its greatest number of passengers?

A. 32
B. 30
C. 24
D. 14
E. 0



Given: P = -2(S – 4)^2 + 32, P is the number of passengers and S is the number of stops. Bus begins with 0 passengers.
Required: How many passengers will be on the bus two stops after the stop where it has its greatest number of passengers

-2(S – 4)^2 + 32 is an expression that is a square + a positive number.
The first part of the expression will always be negative as the square is multiplied with a negative number.
So, to maximize P, we need to have (S-4)^2 = 0


Hence S = 4

We need the passengers 2 stops after this.
So, S = 6

Substituting the value of S in the equation:
-2(6-4)^2 + 32 = -8 + 32 = 24
Option C
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Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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New post 17 Jan 2019, 00:08
If the bus begins its route with no passengers

So this is just a distractor?
I tried using -b/2a but it gave 0
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Re: The number of passengers on a certain bus at any given time is given   [#permalink] 17 Jan 2019, 00:08
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