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20 Aug 2024, 01:30
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (02:40) correct
39%
(02:27)
wrong
based on 164
sessions
History
Date
Time
Result
Not Attempted Yet
An Opera house has 200 seats of two kinds: Box seats and Stall seats. Each box seat ticket cost $355, and each stall seat cost $150. When the tickets are sold out, the total revenue generated is $36,150. What was the revenue generated last night greater than $30,000?
(1) More than 85% of the tickets for each type of seat were sold last night.
(2) The number of stall seats sold was approximately 5 times the number of box seats sold.
(1) More than 85% of the tickets for each type of seat were sold last night.
(2) The number of stall seats sold was approximately 5 times the number of box seats sold.
20 Aug 2024, 02:51
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(1) More than 85% of the tickets for each type of seat were sold last night.
As more than 85% of the tickets were sold for both categories, one can treat it as 85% sold for both categories to find the value below the lowest possible dollar amount made. In doing this, one simplifies the math. Assigning 85% to both categories means that the revenue will also be 85% of the total possible revenue.
As \(36 150\) is not the prettiest of numbers, treat it as \(36 000\).
85% of \(36 000\) is \(30 600\). Thus, last night's performance has to have brought in more than $30 000.
SUFFICIENT
(2) The number of stall seats sold was approximately 5 times the number of box seats sold.
Without more information, a mere ratio will not allow one to solve the question. Perhaps a single box seat and five stall seats were sold, in which case last night made less than $30 000. While one could solve for the amount of tickets available for each category, Statement 1 provides a clue that it is possible that more than $30 000 was made.
INSUFFICIENT
ANSWER A
As more than 85% of the tickets were sold for both categories, one can treat it as 85% sold for both categories to find the value below the lowest possible dollar amount made. In doing this, one simplifies the math. Assigning 85% to both categories means that the revenue will also be 85% of the total possible revenue.
As \(36 150\) is not the prettiest of numbers, treat it as \(36 000\).
85% of \(36 000\) is \(30 600\). Thus, last night's performance has to have brought in more than $30 000.
SUFFICIENT
(2) The number of stall seats sold was approximately 5 times the number of box seats sold.
Without more information, a mere ratio will not allow one to solve the question. Perhaps a single box seat and five stall seats were sold, in which case last night made less than $30 000. While one could solve for the amount of tickets available for each category, Statement 1 provides a clue that it is possible that more than $30 000 was made.
INSUFFICIENT
ANSWER A
20 Aug 2024, 02:59
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#Box Seats (B) + #Stall Seats (S) = 200
Price of box seats = $355
Price of stall seats = $150
When all seats are sole, revenue = $36,150
355B + 150S = 36,150
B + S = 200
150B + 150S = 30,000
Therefore, B = 30 and S = 170
We have to find whether 355B + 150S > 30,000
St. 1 More than 85% of the tickets for each type of seat were sold last night.
Let us consider what are 85% seats of B and S,
B = 25.5, therefore minimum 26 seats were sold
S = 144.5, therefore minimum 145 seats were sold
355*26 + 150*145 = 30,980 which is > than 30,000 for minimum no. of seats sold as per the statement
Therefore, we have one answer; St.1 is Sufficient
^ Alternate way is to take, 0.85 * 36,150 as both seats are sold above 85% the total revenue will be more than 0.85 * 36,150 => 30,737.5 which is already more than 30,000
St. 2 The number of stall seats sold was approximately 5 times the number of box seats sold.
If 1 box seat was sold, ~5 stall seats were sold; in this case revenue < 30,000
If 30 box seat was sold, ~150 stall seats were sold; in this case revenue > 30,000
We don't have one answer; St.2 is Not Sufficient
Answer is A. St 1. alone is sufficient
Price of box seats = $355
Price of stall seats = $150
When all seats are sole, revenue = $36,150
355B + 150S = 36,150
B + S = 200
150B + 150S = 30,000
Therefore, B = 30 and S = 170
We have to find whether 355B + 150S > 30,000
St. 1 More than 85% of the tickets for each type of seat were sold last night.
Let us consider what are 85% seats of B and S,
B = 25.5, therefore minimum 26 seats were sold
S = 144.5, therefore minimum 145 seats were sold
355*26 + 150*145 = 30,980 which is > than 30,000 for minimum no. of seats sold as per the statement
Therefore, we have one answer; St.1 is Sufficient
^ Alternate way is to take, 0.85 * 36,150 as both seats are sold above 85% the total revenue will be more than 0.85 * 36,150 => 30,737.5 which is already more than 30,000
St. 2 The number of stall seats sold was approximately 5 times the number of box seats sold.
If 1 box seat was sold, ~5 stall seats were sold; in this case revenue < 30,000
If 30 box seat was sold, ~150 stall seats were sold; in this case revenue > 30,000
We don't have one answer; St.2 is Not Sufficient
Answer is A. St 1. alone is sufficient
