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the bus begins its route

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by sanju09 » Thu Mar 03, 2011 5:24 am
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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by Night reader » Thu Mar 03, 2011 5:50 am
P is zero when S=0; P is maximized at S=4 --> -2 (4 - 4)^2 + 32= 32 :)
two stops after P was maximized makes S=6 --> P = -2 (6 - 4)^2 + 32= 24

IOM C
sanju09 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
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by rohu27 » Thu Mar 03, 2011 5:52 am
the exp P = -2 (S - 4)^2 + 32, has greatest value only whenthe negative part is = 0,
so P shud be 32. 32=-2 (S - 4)^2 + 32, on sloving, S=4
so 2 stops after having greatest number means no. of pasengers at S=6.
at S=6, P=24.

[spoiler]ans: C[/spoiler]
sanju09 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
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by Anurag@Gurome » Thu Mar 03, 2011 5:53 am
sanju09 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
As P = -2(S - 4)² + 32, the maximum value of P, i.e. number of passengers is 32, when S = 4.

Hence, at the after making 4 stops since beginning its route, the bus will have maximum number of passengers. Therefore, number of passengers after making 2 more stops, i.e. a total of 6 stops, the number of passengers in the bus = -2(6 - 4)² + 32 = 32 - 8 = 24

The correct answer is C.
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