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

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Math Expert
Joined: 02 Sep 2009
Posts: 61283
A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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01 Dec 2019, 23:44
00:00

Difficulty:

65% (hard)

Question Stats:

65% (03:21) correct 35% (02:59) wrong based on 23 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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Senior Manager
Joined: 13 Feb 2018
Posts: 498
GMAT 1: 640 Q48 V28
A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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02 Dec 2019, 00:03
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
Intern
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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02 Dec 2019, 00:09
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)
Yale Moderator
Joined: 05 May 2019
Posts: 180
GPA: 3
Re: A basketball team plays in a stadium that holds 60,000 people. With ti  [#permalink]

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10 Dec 2019, 05:36
To maximize the product of two numbers, they ought to be equal.
Bunuel would approve.
Re: A basketball team plays in a stadium that holds 60,000 people. With ti   [#permalink] 10 Dec 2019, 05:36
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# A basketball team plays in a stadium that holds 60,000 people. With ti

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