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

Question

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.

ID: 700232

chetan2u · Accepted Answer

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

egmat · Answer

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:
 
 You saw 3 variables and 2 equations and you gave up.
 
 Corrective action: Build your WP skills.   
 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.   
 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.

https://www.youtube.com/watch?v=w-tzvAfxlvc

Let us know which step you faltered on.
Happy Learning!
Regards,
Payal

Oppenheimer1945 · Answer

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

KarishmaB · Answer

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

Ayushi0002 · Answer

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

Gemmie · Answer

50M + 45F + 35S = 20900
10M + 9F + 7S = 4180 (1)

M + F + S = 500
10M + 10F + 10S = 5000 (2)

(2) - (1)
=> F + 3S = 820

820 leaves a remaind of 1 when being divided by 3
3S is divisible by 3
=> F leaves a remaind of 1 when being divided by 3
=> F is either 100, 190 or 250 
F cannot be 250 because S has the most seats

=> F is either 100 or 190

F = 100 =>  S = \frac{820 - 100}{3} = 240 
F = 190 =>  S = \frac{820 - 190}{3} = 210

F = 190; S = 210

AugmentAdInf · Answer

@  KarishmaB   In GMAT-speak, 'most' or 'majority' implies more than 50% (or more than half) - why is the same not applicable here?

MartyMurray · Answer

In this case, the wording is not "the second balcony has most seats."

The wording is "the second balcony has THE most seats."

With the word "the" before "most," the statement conveys that, among the three balconies, the second balcony has the greatest number of seats.

Sijojohnn · Answer

to do it faster should go for non 3 multiples as first flor then only to option to equate .

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

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GMAT Two-part Analysis (TPA) Questions

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

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