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A certain theater has 500 seats. Some are on the main floor and sell f

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chetan2u
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A certain theater has 500 seats. Some are on the main floor and sell f [#permalink] New post   28 Feb 2024, 22:09
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95% (hard)

Question Stats:

48% (03:42) correct 52% (04:03) wrong based on 174 sessions
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­A certain theater has 500 seats. Some are on the main floor and sell for $50 each; some are in the first balcony and sell for $45 each; and the rest are in the second balcony and sell for $35 each. When all of the seats are sold for a performance, the gross revenue for that performance is $20,900. Of the three seating areas, the second balcony has the most seats.

Select for First balcony a number of seats in this theater’s first balcony and select for Second balcony a number of seats in this theater’s second balcony such that the selections are jointly consistent with the information provided. Make only two selections, one in each column.
First balcony Second balcony
100
150
190
210
250
300
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First balcony: 190 Second balcony: 210
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Re: A certain theater has 500 seats. Some are on the main floor and sell f [#permalink] New post   15 Mar 2024, 04:30
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­This is a quant TPA question type of “find the values that fit”. Such questions add a definite layer of complexity since the set up is such that we do not get unique set of values. The dataset essentially provides a set of constraints using which we need to find the values among the choices.

Watch the solution and understand which step you faltered on. As such, apart from the obvious translation that is needed to solve this question, here are some faltering points and corrective actions:
  1. You saw 3 variables and 2 equations and you gave up.
    • Corrective action: Build your WP skills.
  2. You processed all 6 choices since you could not draw inference about F not being a multiple of 3.
    • Corrective action: Build your NP inference skills.
  3. You selected F as 250 and S as 190 because you failed to consider the constraints about S being the greatest of all three
    • Corrective action: Make a note of all constraints given in the dataset.



Let us know which step you faltered on.
Happy Learning!
Regards,
Payal
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chetan2u
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Re: A certain theater has 500 seats. Some are on the main floor and sell f [#permalink] New post   02 Mar 2024, 02:05
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chetan2u wrote:
­­
­A certain theater has 500 seats. Some are on the main floor and sell for $50 each; some are in the first balcony and sell for $45 each; and the rest are in the second balcony and sell for $35 each. When all of the seats are sold for a performance, the gross revenue for that performance is $20,900. Of the three seating areas, the second balcony has the most seats.

Select for First balcony a number of seats in this theater’s first balcony and select for Second balcony a number of seats in this theater’s second balcony such that the selections are jointly consistent with the information provided. Make only two selections, one in each column.

­Let the number of seats on the main floor, first bacony and second balcony be m,f and s respectively.

m+f+s = 500
50m+45f+35s = 20,900......50(500-f-s)+45f+35s = 20900.......25000-5f-15s=20900.......5f+15s=4100.....f+3s=820

f cannot be a multiple of 3, otherwise f+3s would also be a multiple of 3.
so f can be 
100: 100+3s = 820......3s=720 or s=240...Not in options
190: 190+3s = 820......3s=630 or s=210....Yes, possible
250: 250+3s = 820......3s=570 or s=190.....Yes, possible but this will make f>s

Solution: f = 190 and s = 210
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Re: A certain theater has 500 seats. Some are on the main floor and sell f [#permalink] New post   07 Mar 2024, 08:00
a+b+c=500 ...(1)

10a+9b+7c=4180 ...(2)

(2)-10*(1)

=>b+3c=820

c>b

rej options for b which are multiple of 3

b=100, c=140 (ok)
b=190, c=210 (ok)
b=250 onwards, c<b
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Re: A certain theater has 500 seats. Some are on the main floor and sell f [#permalink] New post   21 Mar 2024, 02:36
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chetan2u wrote:
­
All Data Insight question: TPA [ Official Guide DI Review 2023-24] 

­A certain theater has 500 seats. Some are on the main floor and sell for $50 each; some are in the first balcony and sell for $45 each; and the rest are in the second balcony and sell for $35 each. When all of the seats are sold for a performance, the gross revenue for that performance is $20,900. Of the three seating areas, the second balcony has the most seats.

Select for First balcony a number of seats in this theater’s first balcony and select for Second balcony a number of seats in this theater’s second balcony such that the selections are jointly consistent with the information provided. Make only two selections, one in each column.
 

Here is what we know:

a + b + c = 500 (Total number of seats)

50a + 45b + 35c = 20,900

We have 3 unknowns and 2 equations. We will get many solutions. The question is interested in first balcony and second balcony seats so we should eliminate "a".

50 (500 - b - c) + 45b + 35c = 20,900
b + 3c = 820

Since c is greater than both a and b, we know it must be greater than 166 (1/3rd of 500).
If b and c were equal, c would be 205 (1/4th of 820). Hence c must be greater than 205. 

Try c = 210
b = 190
Both options are available in table. Hence select 190 and 210. ANSWER ­
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Re: A certain theater has 500 seats. Some are on the main floor and sell f [#permalink] New post   19 Apr 2024, 23:24
I have just changed the variables e.g for me 35(500-x-y) is the second balcony but I am not getting the correct answer, the equation is

3x+2y=680
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Re: A certain theater has 500 seats. Some are on the main floor and sell f [#permalink]
19 Apr 2024, 23:24
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