Last visit was: 18 Nov 2025, 22:58 It is currently 18 Nov 2025, 22:58
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ Level|   Math Related|         
User avatar
parkhydel
User avatar
Joined: 03 Jun 2019
Last visit: 27 Mar 2025
Posts: 273
Own Kudos:
20,388
 [85]
Given Kudos: 60
Posts: 273
Kudos: 20,388
 [85]
A certain theater has 500 seats. Some are on the main floor and sell f 28 Feb 2024, 22:09
7
Kudos
Add Kudos
78
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide Answer
Hide
Show
History
First balcony: 190 Second balcony: 210
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

56% (03:26) correct 44% (03:53) wrong based on 1078 sessions

History

Date
Time
Result
Not Attempted Yet
­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.­

Show Spoiler
ID: 700232­
First balcony Second balcony
100
150
190
210
250
300
Submit Answer
Start the Timer above, select the radio buttons, and click "Submit" to add this question to your Error log.
ShowHide Answer
Official Answer
First balcony: 190 Second balcony: 210
Most Helpful Reply
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 15 Nov 2025
Posts: 11,238
Own Kudos:
43,697
 [16]
Given Kudos: 335
Status:Math and DI Expert
Location: India
Concentration: Human Resources, General Management
GMAT Focus 1: 735 Q90 V89 DI81
Products:
My Reviews
Expert
Expert reply
GMAT Focus 1: 735 Q90 V89 DI81
Posts: 11,238
Kudos: 43,697
 [16]
A certain theater has 500 seats. Some are on the main floor and sell f 02 Mar 2024, 02:05
13
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
parkhydel
­

­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.
Show more
­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
User avatar
egmat
User avatar
e-GMAT Representative
Joined: 02 Nov 2011
Last visit: 18 Nov 2025
Posts: 5,108
Own Kudos:
32,884
 [15]
Given Kudos: 700
GMAT Date: 08-19-2020
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 5,108
Kudos: 32,884
 [15]
A certain theater has 500 seats. Some are on the main floor and sell f 15 Mar 2024, 04:30
15
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­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
­
General Discussion
User avatar
Oppenheimer1945
User avatar
Joined: 16 Jul 2019
Last visit: 14 Nov 2025
Posts: 784
Own Kudos:
639
 [1]
Given Kudos: 223
Location: India
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
GPA: 7.81
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
Posts: 784
Kudos: 639
 [1]
A certain theater has 500 seats. Some are on the main floor and sell f 07 Mar 2024, 08:00
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,266
Own Kudos:
76,983
 [11]
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,266
Kudos: 76,983
 [11]
A certain theater has 500 seats. Some are on the main floor and sell f 21 Mar 2024, 02:36
9
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
parkhydel
­
­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.
Show more
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 ­
User avatar
Ayushi0002
User avatar
Joined: 07 May 2023
Last visit: 10 Oct 2025
Posts: 51
Own Kudos:
23
 [1]
Given Kudos: 21
Posts: 51
Kudos: 23
 [1]
A certain theater has 500 seats. Some are on the main floor and sell f 19 Apr 2024, 23:24
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
User avatar
Gemmie
User avatar
Joined: 19 Dec 2021
Last visit: 18 Nov 2025
Posts: 491
Own Kudos:
427
 [1]
Given Kudos: 76
Location: Viet Nam
Concentration: Technology, Economics
GMAT Focus 1: 695 Q87 V84 DI83
GPA: 3.55
GMAT Focus 1: 695 Q87 V84 DI83
Posts: 491
Kudos: 427
 [1]
A certain theater has 500 seats. Some are on the main floor and sell f 09 Jun 2024, 23:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­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

 ­
User avatar
AugmentAdInf
User avatar
Joined: 10 Jan 2023
Last visit: 01 Nov 2025
Posts: 10
Given Kudos: 48
Posts: 10
Kudos: 0
A certain theater has 500 seats. Some are on the main floor and sell f 02 Feb 2025, 00:39
Kudos
Add Kudos
Bookmarks
Bookmark this Post
@ KarishmaB In GMAT-speak, 'most' or 'majority' implies more than 50% (or more than half) - why is the same not applicable here?
User avatar
MartyMurray
User avatar
Joined: 11 Aug 2023
Last visit: 18 Nov 2025
Posts: 1,630
Own Kudos:
6,120
 [1]
Given Kudos: 173
GMAT 1: 800 Q51 V51
Expert
Expert reply
GMAT 1: 800 Q51 V51
Posts: 1,630
Kudos: 6,120
 [1]
A certain theater has 500 seats. Some are on the main floor and sell f 13 Feb 2025, 21:25
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AugmentAdInf
In GMAT-speak, 'most' or 'majority' implies more than 50% (or more than half) - why is the same not applicable here?
Show more
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.
User avatar
Sijojohnn
User avatar
Joined: 19 Aug 2024
Last visit: 03 Aug 2025
Posts: 3
Given Kudos: 18
Posts: 3
Kudos: 0
A certain theater has 500 seats. Some are on the main floor and sell f 03 Jul 2025, 05:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
to do it faster should go for non 3 multiples as first flor then only to option to equate .

chetan2u
­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.­

Show Spoiler
ID: 700232­
Show more
Moderators:
Bunuel
Math Expert
105362 posts
kingbucky
496 posts