Data Sufficiency

dferm wrote: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.

Please Explain....


I got it correct but would like to see the equation setup for this problem...

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

answer = c

Hi peter456,

The 'issue' with your work is more about the note-taking you did than about any particular math that you would have to do.

From the original prompt, we're told that when ALL the seats are sold, total revenue would be $34,600. Given the information on the number of seats, we can construct the following equation:

500X + 334Y = 34,600 where X is the PRICE of an orchestra seat and Y is the PRICE of a balcony seat.

The question asks for the total revenue from LAST NIGHT'S show. Thus, we need to know X and Y AND we need to know how many of each type of ticket was sold. That means we need information on ALL 4 variables!!! From what you described, I don't think that you noted that when you originally faced this question.

Fact 2 gives us enough information to figure out how many of each ticket were sold, but we still know NOTHING about X and Y (the prices of the two tickets). Thus, we cannot determine the total revenue from last night's show.

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