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Difficulty:
85%
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Question Stats:
36% (01:59) correct
64%
(02:03)
wrong
based on 80
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A concert hall sold only two types of tickets for a show: Premium and Standard. Was the revenue from Premium tickets greater than 75 percent of the concert hall’s total ticket revenue?
(1) Each Premium ticket cost more than twice as much as each Standard ticket cost.
(2) The hall sold 4 Premium tickets for every 3 Standard tickets.
(1) Each Premium ticket cost more than twice as much as each Standard ticket cost.
(2) The hall sold 4 Premium tickets for every 3 Standard tickets.
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11 Mar 2026, 02:45
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GMAT Club Official Solution:
A concert hall sold only two types of tickets for a show: Premium and Standard. Was the revenue from Premium tickets greater than 75 percent of the concert hall’s total ticket revenue?
Let p be the price of a Premium ticket and s be the price of a Standard ticket.
Let m be the number of Premium tickets sold and n be the number of Standard tickets sold.
We are asked whether Premium revenue is greater than 75 percent of total revenue:
m * p > 0.75(m * p + n * s)
mp > 3ns
So we need to know whether (mp)/(ns) > 3.
(1) Each Premium ticket cost more than twice as much as each Standard ticket cost.
This gives p/s > 2, but m/n is unknown, so (mp)/(ns) is unknown. Not sufficient.
(2) The hall sold 4 Premium tickets for every 3 Standard tickets.
This gives m/n = 4/3, but p/s is unknown, so (mp)/(ns) is unknown. Not sufficient.
(1) + (2) From (2), m/n = 4/3, so the question becomes:
Is (mp)/(ns) > 3
Is (p/s)(m/n) > 3
Is (p/s)(4/3) > 3
Is p/s > 9/4
So the question becomes: do we know that p/s > 9/4?
From (1), we only know p/s > 2. If p/s is between 2 and 9/4, the answer is No, but if p/s is greater than 9/4, the answer is Yes. Not sufficient.
Answer: E.
A concert hall sold only two types of tickets for a show: Premium and Standard. Was the revenue from Premium tickets greater than 75 percent of the concert hall’s total ticket revenue?
Let p be the price of a Premium ticket and s be the price of a Standard ticket.
Let m be the number of Premium tickets sold and n be the number of Standard tickets sold.
We are asked whether Premium revenue is greater than 75 percent of total revenue:
m * p > 0.75(m * p + n * s)
mp > 3ns
So we need to know whether (mp)/(ns) > 3.
(1) Each Premium ticket cost more than twice as much as each Standard ticket cost.
This gives p/s > 2, but m/n is unknown, so (mp)/(ns) is unknown. Not sufficient.
(2) The hall sold 4 Premium tickets for every 3 Standard tickets.
This gives m/n = 4/3, but p/s is unknown, so (mp)/(ns) is unknown. Not sufficient.
(1) + (2) From (2), m/n = 4/3, so the question becomes:
Is (mp)/(ns) > 3
Is (p/s)(m/n) > 3
Is (p/s)(4/3) > 3
Is p/s > 9/4
So the question becomes: do we know that p/s > 9/4?
From (1), we only know p/s > 2. If p/s is between 2 and 9/4, the answer is No, but if p/s is greater than 9/4, the answer is Yes. Not sufficient.
Answer: E.
General Discussion
Theeldertwin
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03 Mar 2026, 09:14
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Revenue= Number of tickets sold * Cost of ticket
Now let's analyse each option:
A. Statement 1 alone: We do not know the number or proportion of tickets sold. We cannot calculate revenue. Hence, not sufficient.
B. Statement 2 alone: Even though we know the proportion of tickets sold, we do not know the prices, hence we cannot calculate the revenue. Thus, insufficient.
C. Combine statement 1 and statement 2:
Cost of standard ticket = P
Cost of premium ticket = 2P + m
Number of standard tickets sold = 3k
Number of premium tickets sold = 4k
Total Revenue = Revenue from premium ticket + revenue from standard ticket
= ((2P+m)*4k) + (P*3k) = 11Pk + 4mk = k(11P+4m)
Revenue from premium ticket = 8Pk + 4mk = k(8P +4m)
Ratio= (8P +4m)/ (11P+4m)
Now, to decide whether this is less than or greater than 75% or 3/4:
[ (8P +4m)/ (11P+4m) ] ◻ [3/4]
=> (32 P +16m) ◻ (33P+12m)
=> 4m ◻ P
=> m ◻ (P/4)
Hence, depending on whether m is less than or greater than P/4, it will determine whether premium tickets contribute to 75% of the revenue or not. If m > P/4 (that is, cost of premium tickets is more than 2.25 times the cost of standard tickets) then it would contribute to more than 75%. If m< P/4 ( that is, cost of premium tickets is between 2-2.25 times the cost of standard tickets) then it would contribute less than 75%.Therefore, E is the answer.
Hope this helps!
Now let's analyse each option:
A. Statement 1 alone: We do not know the number or proportion of tickets sold. We cannot calculate revenue. Hence, not sufficient.
B. Statement 2 alone: Even though we know the proportion of tickets sold, we do not know the prices, hence we cannot calculate the revenue. Thus, insufficient.
C. Combine statement 1 and statement 2:
Cost of standard ticket = P
Cost of premium ticket = 2P + m
Number of standard tickets sold = 3k
Number of premium tickets sold = 4k
Total Revenue = Revenue from premium ticket + revenue from standard ticket
= ((2P+m)*4k) + (P*3k) = 11Pk + 4mk = k(11P+4m)
Revenue from premium ticket = 8Pk + 4mk = k(8P +4m)
Ratio= (8P +4m)/ (11P+4m)
Now, to decide whether this is less than or greater than 75% or 3/4:
[ (8P +4m)/ (11P+4m) ] ◻ [3/4]
=> (32 P +16m) ◻ (33P+12m)
=> 4m ◻ P
=> m ◻ (P/4)
Hence, depending on whether m is less than or greater than P/4, it will determine whether premium tickets contribute to 75% of the revenue or not. If m > P/4 (that is, cost of premium tickets is more than 2.25 times the cost of standard tickets) then it would contribute to more than 75%. If m< P/4 ( that is, cost of premium tickets is between 2-2.25 times the cost of standard tickets) then it would contribute less than 75%.Therefore, E is the answer.
Hope this helps!
