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22 Apr 2026, 19:00
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
54% (02:44) correct
46%
(02:16)
wrong
based on 28
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A community theater sold tickets for the same show in January and in February. In January, every ticket was sold at the same fixed price, whereas in February, the ticket price increased, and every ticket was sold at the same higher fixed price. If fewer tickets were sold in February than in January, was the revenue from ticket sales in February greater than the revenue from ticket sales in January?
(1) The percent increase in the ticket price from January to February was equal to the percent decrease in the number of tickets sold from January to February.
(2) If the percent increase in the ticket price from January to February had been 8 percentage points greater than it actually was, while the percent decrease in the number of tickets sold remained the same, then the revenue from ticket sales in February would have been equal to the revenue from ticket sales in January.
(1) The percent increase in the ticket price from January to February was equal to the percent decrease in the number of tickets sold from January to February.
(2) If the percent increase in the ticket price from January to February had been 8 percentage points greater than it actually was, while the percent decrease in the number of tickets sold remained the same, then the revenue from ticket sales in February would have been equal to the revenue from ticket sales in January.
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30 Apr 2026, 02:45
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GMAT Club Official Solution:
A community theater sold tickets for the same show in January and in February. In January, every ticket was sold at the same fixed price, whereas in February, the ticket price increased, and every ticket was sold at the same higher fixed price. If fewer tickets were sold in February than in January, was the revenue from ticket sales in February greater than the revenue from ticket sales in January?
(1) The percent increase in the ticket price from January to February was equal to the percent decrease in the number of tickets sold from January to February.
Let the January ticket price be 100 and the number of tickets sold in January be 100. Then January revenue is 100 * 100 = 10,000.
Let the percent increase in the ticket price and the percent decrease in the number of tickets be p.
If the price increased by p%, the February price is 100 + p, because p% of 100 is p.
If the number of tickets sold decreased by p%, the February number sold is 100 - p.
So February revenue is (100 + p)(100 - p) = 10,000 - p^2.
The question asks:
Is 10,000 - p^2 > 10,000?
Is -p^2 > 0?
Since p must be positive, the answer to the question is NO. So the February revenue was not greater than the January revenue. Sufficient.
(2) If the percent increase in the ticket price from January to February had been 8 percentage points greater than it actually was, while the percent decrease in the number of tickets sold remained the same, then the revenue from ticket sales in February would have been equal to the revenue from ticket sales in January.
This statement says that if the price increase had been even larger, while the drop in tickets sold stayed the same, then the February revenue would have been equal to the January revenue. This implies that, with the smaller actual price increase, the February revenue must have been smaller than the January revenue. Sufficient.
Answer: D.
A community theater sold tickets for the same show in January and in February. In January, every ticket was sold at the same fixed price, whereas in February, the ticket price increased, and every ticket was sold at the same higher fixed price. If fewer tickets were sold in February than in January, was the revenue from ticket sales in February greater than the revenue from ticket sales in January?
(1) The percent increase in the ticket price from January to February was equal to the percent decrease in the number of tickets sold from January to February.
Let the January ticket price be 100 and the number of tickets sold in January be 100. Then January revenue is 100 * 100 = 10,000.
Let the percent increase in the ticket price and the percent decrease in the number of tickets be p.
If the price increased by p%, the February price is 100 + p, because p% of 100 is p.
If the number of tickets sold decreased by p%, the February number sold is 100 - p.
So February revenue is (100 + p)(100 - p) = 10,000 - p^2.
The question asks:
Is 10,000 - p^2 > 10,000?
Is -p^2 > 0?
Since p must be positive, the answer to the question is NO. So the February revenue was not greater than the January revenue. Sufficient.
(2) If the percent increase in the ticket price from January to February had been 8 percentage points greater than it actually was, while the percent decrease in the number of tickets sold remained the same, then the revenue from ticket sales in February would have been equal to the revenue from ticket sales in January.
This statement says that if the price increase had been even larger, while the drop in tickets sold stayed the same, then the February revenue would have been equal to the January revenue. This implies that, with the smaller actual price increase, the February revenue must have been smaller than the January revenue. Sufficient.
Answer: D.
General Discussion
22 Apr 2026, 22:47
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Wording is too big and vast so break it down:
Statement 1:
Form equations for any percent related DS always helps avoid miscalculations or or wrong assumptions.
a[1+z/100] = z
b[1-z/100] = y.
Where Jan = ab and Feb = xy.
Now when you multiple both equations you get that ab[1-z^2/100^2] = xy.
ab>xy always because z is positive.
Also a logical way to look at it is:
When you have 10% profit and 10% loss = 1.1*0.9x = 0.99x.
You will always have a loss when increase and decrease percent is same.
SUFFICIENT.
Statement 2:
No need to solve for this, its just pure logic.
At present you have a certain increase in percent in ticket price and decrease in number of tickets.
Now they say that keeping decrease constant, when you increase ticket price by 8% then you get back to Jan's revenue.
You get back Jan's revenue when u increase ticket prices alone but not make any decrease in prices.
So naturally Jan's revenue was larger than Feb's.
Mathematically:
So basically, think of it like you have a*[xy] = z. Now you have a*[(x+8)y] = a.
(x+8)y = 1 -> y = 1/(x+8)
-> a*[x*1/(x+8)] = z
-> x/(x+8) is <1
Thus a*[Less than 1] = z.
Or z<a.
SUFFICIENT.
Answer: Option D
Statement 1:
Form equations for any percent related DS always helps avoid miscalculations or or wrong assumptions.
a[1+z/100] = z
b[1-z/100] = y.
Where Jan = ab and Feb = xy.
Now when you multiple both equations you get that ab[1-z^2/100^2] = xy.
ab>xy always because z is positive.
Also a logical way to look at it is:
When you have 10% profit and 10% loss = 1.1*0.9x = 0.99x.
You will always have a loss when increase and decrease percent is same.
SUFFICIENT.
Statement 2:
No need to solve for this, its just pure logic.
At present you have a certain increase in percent in ticket price and decrease in number of tickets.
Now they say that keeping decrease constant, when you increase ticket price by 8% then you get back to Jan's revenue.
You get back Jan's revenue when u increase ticket prices alone but not make any decrease in prices.
So naturally Jan's revenue was larger than Feb's.
Mathematically:
So basically, think of it like you have a*[xy] = z. Now you have a*[(x+8)y] = a.
(x+8)y = 1 -> y = 1/(x+8)
-> a*[x*1/(x+8)] = z
-> x/(x+8) is <1
Thus a*[Less than 1] = z.
Or z<a.
SUFFICIENT.
Answer: Option D
Bunuel
