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# A certain theater has a total of 884 seats, of which 500 are

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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
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thanhnguyen8825
A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600. What was the theater's total revenue from ticket sales for last night's performance?

(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

I think A because all tickets are sold

We know: 500x + 384y = 34600
x = 2y
=> We can find x and y

We are told that when tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600 and are asked to find the revenue from ticket sales for last night's performance.

From (1) we don't know how many tickets were sold for last nigh's performance, thus the first statement is not sufficient.

If we knew that for last night's performance all the tickets were sold, then neither statement is needed to answer the question because the stem itslef says that when tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600.

Hope it's clear.
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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
Hi All,

On DS questions, when a prompt comes with a twist, the GMAT writers usually provide a "hint" about that twist in one or the other of the two Facts.

At first glance, you might not realize that the theater DID NOT NECESSARILY sell all of it's tickets for last night's performance. However, there ARE two clues that should have helped you to realize this possibility:

1) The prompt says that "...when all tickets are sold...the total revenue is \$34,600", but then the question asks what the revenue was from last night's performance. There MUST be a twist of some kind, otherwise you would already have the answer to the question: \$34,600 and the two Facts wouldn't need to be there.

2) Fact 2 tells us that while ALL of the balcony tickets were sold, ONLY 80% of the orchestra seats were sold. Here, you can catch the twist and go back to double check your work.

Since the other explanations in this thread explain the "math", I won't rehash any of that here, but it's worth remembering that DS questions are a test of a variety of your skills, including: organization, accuracy, thoroughness, attention-to-detail, pattern-matching, the ability to PROVE that you're correct....and some basic math skills. When you get a DS question wrong, the real reason probably won't be because of a math mistake. Get in the habit of taking LOTS of notes and doing organized work and you'll find most DS questions are pretty straight-forward.

GMAT assassins aren't born, they're made,
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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
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fozzzy
A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600. What was the theater's total revenue from ticket sales for last night's performance?

(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

We do not have to do any calculation in this question.
from first
500x+ 2x * 384 = 34600
we can find x

from second
400 x+ 384 *2x we know the value of x from 1 we can subsititute to find the value of final collection of last night

so C
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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
fozzzy
A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600. What was the theater's total revenue from ticket sales for last night's performance?

(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

From question stem we know that total orchestra seats are 500 and total balcony seats are 384 (884-500). we also know the total sale if all the tickets are sold.

We are asked to find last nights sale. To find this we need how many Orchestra and Balcony tickets were sold and what is the price of each ticket.

Statement 1 gives us price of each ticket. We can calculate ticket price 500x+ 384 *2x = 34,600. But, we do not get the information that how many tickets were sold.

Statement 2 gives us the information that how many total tickets were sold, but we are not told the price of each ticket.

Both statements together give required information. Hence answer is 'C'
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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
The statements in the prompt tell you that there are 500 orchestra seats and 384 balcony seats. let 'o' be the price of an orchestra seat, and 'b' be the price of a balcony seat.
then the statement in the prompt tells us that
500o + 384b = 36,400

(1)
this tells us that
o = 2b
that's a substitution, which we can use in the equation above, and which will therefore yield a unique solution (o, b) for the prices of the 2 different types of tickets.
however, this statement tells us nothing about last night's performance, so it is insufficient.

(2)
this tells us that all 384 balcony seats, and 400 of the 500 orchestra seats, were sold.
we don't have price points for the two different types of seats, so we can't figure this one out. (the more that the orchestra seats cost, relative to the balcony seats, the farther short of \$34,600 the revenue will fall.)

(together)
from statement (1) we can figure the price of each type of ticket, so we know 'o' and 'b'. using statement (2), we know that the revenue is 384b + 400o. plug in and find out the revenue.
sufficient

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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
fozzzy
A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600. What was the theater's total revenue from ticket sales for last night's performance?

(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

From question stem we know that total orchestra seats are 500 and total balcony seats are 384 (884-500). we also know the total sale if all the tickets are sold.

We are asked to find last nights sale. To find this we need how many Orchestra and Balcony tickets were sold and what is the price of each ticket.

Statement 1 gives us price of each ticket. We can calculate ticket price 500x+ 384 *2x = 34,600. But, we do not get the information that how many tickets were sold.

Statement 2 gives us the information that how many total tickets were sold, but we are not told the price of each ticket.

Both statements together give required information. Hence answer is 'C'

Since the statement says "The price of an orchestra seat ticket is twice the price of a balcony seat ticket." And if we denote orchestra as x and balcony is y then x = 2y
500(2y) + 384 (y), not the other way around? Right? You seem to have 2x paired with 384.... Am i missing something here?
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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
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fozzzy
A certain theater has a total of 884 seats, of which 500 are orchestra seats and the rest are balcony seats. When tickets for all the seats in the theater are sold, the total revenue from ticket sales is \$34,600. What was the theater's total revenue from ticket sales for last night's performance?

(1) The price of an orchestra seat ticket is twice the price of a balcony seat ticket.
(2) For last night's performance, tickets for all the balcony seats were sold, but only 80 percent of the tickets for the orchestra seats were sold.

Let A: Price of Orchestra
Let B: Price of Balcony

500A + 384B = 34600 => Eq 1

Let X: # of Orchestra Tickets Sold
Let Y: # of Balcony Tickets Sold

Need: XA + YB = ? (Need 4 vars)

1) A = 2B
Other vars unknown => Not sufficient

2) Y = 384
X = 400
Other vars unknown => Not sufficient

1+2)
4 equations and 4 unknowns => Sufficient

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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
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Re: A certain theater has a total of 884 seats, of which 500 are [#permalink]
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