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

Question

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

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

PareshGmat · Accepted Answer

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

TehMoUsE · Answer

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 :-D

TeamGMATIFY · Answer

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

philipssonicare · Answer

If the bus begins its route with no passengers

So this is just a distractor?
I tried using -b/2a but it gave 0

PolarisTestPrep · Answer

Hey,

Hopefully you see that because the parentheses is squared and then that number is multiplied by -2, resulting in a negative number being added to 32. Therefore, the largest number of passengers will come when the number in the parentheses is equal to 0, as any other S will lead to a number being subtracted from 32

If you didn't see that right away, plugging in 1 for S and then 2 and then 3, etc. would be fairly quick and should reveal the pattern to you

When in doubt, try plugging in logical numbers for the variables

In order to get the parentheses to 0, S must be 4:

-2(4 - 4)^2 + 32 = -2(0)^2 + 32 = -2(0) + 32 = 0 + 32 = 32 = P

This tells us that the highest number of passengers occurs at S = 4 or at stop 4

The question asks for the number of passengers two stops after the stop with the highest number of passengers, or two stops after 4

It is asking for the number of passengers on stop 6

Simply plug in 6 for S:

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

The answer is C

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

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