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Math Expert V
Joined: 02 Sep 2009
Posts: 53792
The number of passengers on a certain bus at any given time is given  [#permalink]

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2
8 00:00

Difficulty:   15% (low)

Question Stats: 79% (01:50) correct 21% (01:53) wrong based on 185 sessions

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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

Kudos for a correct solution.

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Joined: 27 Dec 2012
Posts: 1817
Location: India
Concentration: General Management, Technology
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Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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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

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

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Intern  Joined: 12 May 2013
Posts: 27
Concentration: Finance, Economics
GMAT 1: 700 Q49 V36 Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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2
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 _________________

Feel free to message if you have any questions :D

Senior Manager  Joined: 20 Aug 2015
Posts: 388
Location: India
GMAT 1: 760 Q50 V44 Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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1
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
Senior Manager  P
Joined: 15 Feb 2018
Posts: 257
Re: The number of passengers on a certain bus at any given time is given  [#permalink]

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If the bus begins its route with no passengers

So this is just a distractor?
I tried using -b/2a but it gave 0 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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# The number of passengers on a certain bus at any given time is given

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