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GMAT695
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01 Oct 2024, 02:20
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At a history museum, the price of each regular admission ticket sold last Sunday was 30 percent less than the price of each regular admission ticket sold last Saturday. If the museum’s total revenue from the sale of regular admission tickets last Saturday and Sunday was $6,150, what was its revenue from the sale of regular admission tickets last Saturday alone?
(1) The number of regular admission tickets sold by the museum last Sunday was 50 percent greater than the number of regular admission tickets sold by the museum last Saturday.
(2) The price of each regular admission ticket sold by the museum last Saturday was $10.
GMAT-Club-Forum-v1qjuzq6.png [ 124.09 KiB | Viewed 3494 times ]
(1) The number of regular admission tickets sold by the museum last Sunday was 50 percent greater than the number of regular admission tickets sold by the museum last Saturday.
(2) The price of each regular admission ticket sold by the museum last Saturday was $10.
Attachment:
GMAT-Club-Forum-v1qjuzq6.png [ 124.09 KiB | Viewed 3494 times ]
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24 Nov 2024, 02:06
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Jake7Wimmer
At a history museum, the price of each regular admission ticket sold last Sunday was 30 percent less than the price of each regular admission ticket sold last Saturday. If the museum’s total revenue from the sale of regular admission tickets last Saturday and Sunday was $6,150, what was its revenue from the sale of regular admission tickets last Saturday alone?
Assuming the price on Saturday was p, the price on Sunday would be 0.7p. If m tickets were sold on Saturday and n tickets were sold on Sunday, we are given:
pm + 0.7pn = 6,150.
Notice that we need to find the value of pm.
(1) The number of regular admission tickets sold by the museum last Sunday was 50 percent greater than the number of regular admission tickets sold by the museum last Saturday.
This implies n = 1.5m. Substituting this into the equation gives: pm + 0.7p * 1.5m = 6,150, which simplifies to (pm) + 1.05(pm) = 6,150. Solving for pm gives pm = 3,000. Sufficient.
(2) The price of each regular admission ticket sold by the museum last Saturday was $10.
This implies p = 10. However, this alone does not provide information about the number of tickets sold (m) and is therefore insufficient to determine pm.
Answer: A
General Discussion
02 Oct 2024, 02:18
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I have a very messy variable intensive approach to solve this but since no one has given a solution, I thought I'd share mine.
"the price of each regular admission ticket sold last Sunday was 30 percent less than the price of each regular admission ticket sold last Saturday"
Let us assume that the price on Saturday was 'x'. This makes the price on Sunday '0.7x'
We need to find the revenue (Sales*Price)
Let us assume the number of tickets sold on Saturday as 'b' and Sunday as 'a'
Statement - 1
This statement basically tells that if the number of tickets sold on Saturday is 'b' then the number of tickets sold on Sunday would be '1.5b'
If we form an equation, it would look something like:
(0.7x)1.5b + xb = 6150
1.05xb + xb = 6150
2.05xb = 6150
This a point where I did get stuck because it got a bit messy and there were two unknowns. But if you take into account what we have to find, it all makes sense. Revenue (sales*price) is represented by 'xb' in our case. If you find for 'xb', you will get $3,000 as the answer. This exactly what the question asks.
Statement - 2
This seems like the easier statement to work with but without knowledge of the number of tickets sold, we hit a roadblock. If the price is $10 on Saturday, the price is $7 on Sunday. Even if we form an equation, we are stuck with 7a+10b = 6150.
Therefore, we can easily conclude that option A is the correct answer.
"the price of each regular admission ticket sold last Sunday was 30 percent less than the price of each regular admission ticket sold last Saturday"
Let us assume that the price on Saturday was 'x'. This makes the price on Sunday '0.7x'
We need to find the revenue (Sales*Price)
Let us assume the number of tickets sold on Saturday as 'b' and Sunday as 'a'
Statement - 1
This statement basically tells that if the number of tickets sold on Saturday is 'b' then the number of tickets sold on Sunday would be '1.5b'
If we form an equation, it would look something like:
(0.7x)1.5b + xb = 6150
1.05xb + xb = 6150
2.05xb = 6150
This a point where I did get stuck because it got a bit messy and there were two unknowns. But if you take into account what we have to find, it all makes sense. Revenue (sales*price) is represented by 'xb' in our case. If you find for 'xb', you will get $3,000 as the answer. This exactly what the question asks.
Statement - 2
This seems like the easier statement to work with but without knowledge of the number of tickets sold, we hit a roadblock. If the price is $10 on Saturday, the price is $7 on Sunday. Even if we form an equation, we are stuck with 7a+10b = 6150.
Therefore, we can easily conclude that option A is the correct answer.
