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OG2016 DS What was the total

This topic has 5 expert replies and 0 member replies
lionsshare Senior | Next Rank: 100 Posts
Joined
09 Aug 2017
Posted:
62 messages

OG2016 DS What was the total

Post Mon Aug 28, 2017 4:11 pm
What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price?

(1) x = 50
(2) Full-price tickets sold for $20 each.

OA: E

Anyone, please, could share the process of solving this problem.

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Post Mon Sep 11, 2017 10:31 am
lionsshare wrote:
What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price?

(1) x = 50
(2) Full-price tickets sold for $20 each.

OA: E
We need to determine the revenue from the sale of 400 tickets. Some of the tickets were sold at the full price and the remainder of the tickets were sold at a reduced price. We can let f = the number tickets sold at full price and r = the number of tickets sold at the reduced price.

Statement One Alone:

x = 50

Without knowing how many tickets are sold at discount, we can’t determine the total revenue. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

The full-price ticket was $20.

Knowing only the price for a full-price ticket is not enough information to determine the total revenue of all tickets sold. Statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statements one and two, we know that the discounted tickets are sold at $10 each. However, without knowing the number of discounted tickets, we cannot determine the total revenue.

Answer: E

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Post Fri Sep 01, 2017 5:25 pm
Hi lionsshare,

We're told that a theater sold 400 tickets - some at X percent of full price and the rest at full price. We're asked for the total revenue from the sale of the tickets. To answer this question, we will need to know a LOT of different things: the number of tickets sold at each price and each of the two prices.

1) X = 50

Fact 1 tells us that the discount price was HALF of the full price, but it does not tell us anything else.
Fact 1 is INSUFFICIENT

2) Full-price tickets sold for $20 each.

Fact 2 tells us the cost of a full-price ticket, but nothing else.
Fact 2 is INSUFFICIENT

Combined, we know the two prices (full-price = $20/each, discount-price = $10/each), but we still don't know the number of each type that were sold.
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

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Last edited by Rich.C@EMPOWERgmat.com on Tue Oct 10, 2017 4:43 pm; edited 1 time in total

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Post Tue Aug 29, 2017 8:49 am
This question is very similar in structure to another OG question: http://www.beatthegmat.com/og2016-ds-what-was-the-revenue-t296244.html#797219
(You'll note similarities in the solution).

Total revenue can be defined as:
Revenue = (# 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)

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 are also given that r (the price of reduced-price tickets) is x% of f (price of full-priced tickets). We would need the value of x and the value of either f or r to infer the price of each.

Target question: what are the values of F, f, R, and r?

(1) x = 50
The reduced-price tickets are half the price of the full-priced ones, but what are those prices? $5 and $10? Or $100 and $200? We also don't know anything about F and R. Insufficient.

(2) Full-price tickets sold for $20 each.
By itself, this gives us only 1 of the 4 values we need to solve. Insufficient.

(1) & (2) together
We can infer that f = $20 and r = $10. However, we still don't know how many of each were sold. If the theater sold mostly full-price tickets (if F is close to 400), the total revenue could be close to $8000. If they sold almost all reduced-price tickets (if R is close to 400), the total revenue would be closer to $4000.

Since we still don't know the values of F and R, we cannot answer the question. The answer is E.

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Post Tue Aug 29, 2017 10:12 pm
lionsshare wrote:
What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price?

(1)
(2) Full-price tickets sold for $20 each.

OA: E

Anyone, please, could share the process of solving this problem.
Say the number of tickets sold at full-price = a, thus the number of tickets sold at x percent of full-price = 400 - a

Say the full price = b, thus, x percent of full-price = x% of b = bx/100

Total revenue = Revenue from the sale of tickets at full-price + Revenue from the sale of tickets at x% of full-price

= ab + (400 - a)bx/100

If we get the value of a, b and x, we get the answer.

Statement 1: x = 50

We do not yet know the values of a and b, we cannot get the value of Total revenue. Insufficient.

Statement 2: Full-price tickets sold for $20 each.

=> b = $20.

We do not yet know the values of a and x, we cannot get the value of Total revenue. Insufficient.

Statement 1 & 2:

We still do not have the value of a, we cannot get the value of Total revenue. Insufficient.

The correct answer: E

Hope this helps!

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GMAT/MBA Expert

Post Wed Aug 30, 2017 2:44 am
lionsshare wrote:
What was the total amount of revenue that a theater received from the sale of 400 tickets, some of which were sold at x percent of full price and the rest of which were sold at full price?

(1) x = 50
(2) Full-price tickets sold for $20 each.
Prompt: Total number of tickets = 400.
Statement 1: Some tickets were sold at 50% of full-price.
Statement 2: Full-price tickets were sold for $20 each.

Even when we combine the statements, we don't know how many of the 400 tickets were sold at full price and how many were sold at 50% of full price.
Thus, the total amount of revenue cannot be determined.
INSUFFICIENT.

The correct answer is E.

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