OG2016 DS What was the revenue

[lionsshare]

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.

[ceilidh.erickson]

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.

[Jay@ManhattanReview]

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 number of tickets sold at full-price = a, thus the number of tickets sold at reduced price = 400 - a

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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-Jay
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[ceilidh.erickson]

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!

[kapstone1996]

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.