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A basketball team plays in a stadium that holds 60,000 people. With ti

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Math Expert
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Joined: 02 Sep 2009
Posts: 60480
A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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New post 02 Dec 2019, 00:44
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A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

64% (03:24) correct 36% (02:59) wrong based on 22 sessions

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A basketball team plays in a stadium that holds 60,000 people. With ticket prices at $28, the average attendance had been 32,000. After ticket prices were lowered to $24, the average attendance rose to 36,000. Assuming that the demand for tickets is a linear function of ticket prices, what price should the team charge for tickets to maximize its revenue?

A. $26
B. $28
C. $30
D. $32
E. $35


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Joined: 13 Feb 2018
Posts: 496
GMAT 1: 640 Q48 V28
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A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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New post 02 Dec 2019, 01:03
1
We can observe that $4 price decrease results in 4000 attendance increase, so $1 increase will result in 1000 attendance decrease

check the options

A) $26*34=884
B) $28*32=896
C) $30*30=900
D) $32*28=896
E) $35*25=875

P.S I dont have a better approach, hope experts will give us a more time-consuming way to solve this problem

IMO
Ans: C
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Joined: 25 Jan 2019
Posts: 6
Location: India
Schools: ISB '21
Re: A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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New post 02 Dec 2019, 01:09
An increase of 4$ in ticket prices results to 4000 decrease in the number of tickets.

As the demand for tickets is a linear function of ticket prices, we get that 1$ change would result in a difference of 1000 tickets.

Therefore, quickly checking the revenue for the options we get the maximum revenue for 30$ per ticket.

Dollar- Tickets- Revenue
24 36000 864000
26 34000 884000
28 32000 896000
30 30000 900000
32 28000 896000
35 25000 875000

Hence Option (c)
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Joined: 05 May 2019
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Re: A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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New post 10 Dec 2019, 06:36
To maximize the product of two numbers, they ought to be equal.
Bunuel would approve.
GMAT Club Bot
Re: A basketball team plays in a stadium that holds 60,000 people. With ti   [#permalink] 10 Dec 2019, 06:36
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