What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price?
(1) The number of tickets sold at the full price was 1/4 of the total number of tickets sold.
(2) The full price of a ticket was $25.
OA: E
Hello, Experts. Can you please share how to solve this problem.
OG2016 DS What was the revenue
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- lionsshare
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If we want to know the total revenue that the theater received, we need to know:
(# of full-price tickets)x(full-ticket price) + (# of reduced-price tickets)x(reduced-ticket price)
I'll assign the following variables for clarity:
number of full-price tickets = F
price of each full-ticket = f
number of reduced-price tickets = R
price of each reduced-ticket = r
Revenue = (F)(f) + (R)(r)
In order to answer the question, we'd need values for each of these variables: F, f, R, and r.
We're given the total # of tickets, so we know that F + R = 400. If we knew a proportion between F and R, we could infer the values. We would still need actual values for f and r.
Target question: what are the values of F, f, R, and r?
(1) The number of tickets sold at the full price was 1/4 of the total number of tickets sold.
This allows us to infer that F = 100 and R = 300. We still don't know the prices of each ticket, so we don't know total revenue. Insufficient.
(2) The full price of a ticket was $25.
With this statement alone, we know that f = 25, but we do not know how many of each ticket was sold, or the price of reduced tickets. Insufficient.
(1) & (2) together
We know that F = 100, f = 25, and R = 300. However, we still don't know anything about the price of reduced tickets, so we don't know the total revenue. Insufficient.
The answer is E.
(# of full-price tickets)x(full-ticket price) + (# of reduced-price tickets)x(reduced-ticket price)
I'll assign the following variables for clarity:
number of full-price tickets = F
price of each full-ticket = f
number of reduced-price tickets = R
price of each reduced-ticket = r
Revenue = (F)(f) + (R)(r)
In order to answer the question, we'd need values for each of these variables: F, f, R, and r.
We're given the total # of tickets, so we know that F + R = 400. If we knew a proportion between F and R, we could infer the values. We would still need actual values for f and r.
Target question: what are the values of F, f, R, and r?
(1) The number of tickets sold at the full price was 1/4 of the total number of tickets sold.
This allows us to infer that F = 100 and R = 300. We still don't know the prices of each ticket, so we don't know total revenue. Insufficient.
(2) The full price of a ticket was $25.
With this statement alone, we know that f = 25, but we do not know how many of each ticket was sold, or the price of reduced tickets. Insufficient.
(1) & (2) together
We know that F = 100, f = 25, and R = 300. However, we still don't know anything about the price of reduced tickets, so we don't know the total revenue. Insufficient.
The answer is E.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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- Jay@ManhattanReview
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Say the number of tickets sold at full-price = a, thus the number of tickets sold at reduced price = 400 - alionsshare wrote:What was the revenue that a theater received from the sale of 400 tickets, some of which were sold at the full price and the remainder of which were sold at a reduced price?
(1) The number of tickets sold at the full price was 1/4 of the total number of tickets sold.
(2) The full price of a ticket was $25.
OA: E
Hello, Experts. Can you please share how to solve this problem.
Say the full price = b and the price of the tickets sold at reduced price = c
Total revenue = Revenue from the sale of tickets at full-price + Revenue from the sale of tickets sold at reduced price
= ab + (400 - a)c
If we get the value of a, b and c, we get the answer.
Statement 1: The number of tickets sold at the full price was 1/4 of the total number of tickets sold.
This gives 400 - a = 1/4 of 400 = 100
Thus, a = 300.
We do not yet know the values of b and c, we cannot get the value of Total revenue. Insufficient.
Statement 2: The full price of a ticket was $25.
=> b = $25.
We do not yet know the values of a and c, we cannot get the value of Total revenue. Insufficient.
Statement 1 & 2:
We still do not have the value of c, we cannot get the value of Total revenue. Insufficient.
The correct answer: E
Hope this helps!
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Compare to a similar OG question posted here: https://www.beatthegmat.com/og2016-ds-wh ... tml#797220
It's worth noting that the GMAT often writes variations on the same prompt!
It's worth noting that the GMAT often writes variations on the same prompt!
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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X =Full Price ticket
Y = Reduced Price ticket
FP = cost of full price
RP = Cost of reduced price
X + Y = 400
1) (1/4) of total = (1/4) of 400 so 3/4 (400) = x = 100 & Y = 300
100 + 300 = 400
FP + RP = ? (revenue)
Insufficient since we do not know the cost per ticket
2) FP = $25
Insufficient since we do not know RP, X, and Y
Combined (1) & (2)
100 + 300 = 400
$25 + RP = ? (revenue)
Insufficient since we do not know RP.
Y = Reduced Price ticket
FP = cost of full price
RP = Cost of reduced price
X + Y = 400
1) (1/4) of total = (1/4) of 400 so 3/4 (400) = x = 100 & Y = 300
100 + 300 = 400
FP + RP = ? (revenue)
Insufficient since we do not know the cost per ticket
2) FP = $25
Insufficient since we do not know RP, X, and Y
Combined (1) & (2)
100 + 300 = 400
$25 + RP = ? (revenue)
Insufficient since we do not know RP.