For a certain concert, the price of balcony tickets was exactly half

Question

For a certain concert, the price of balcony tickets was exactly half the price of orchestra tickets. The ratio of balcony to orchestra tickets sold was 3:2. What was the price of one orchestra ticket?

(1) the total revenue taken in from tickets of both kinds was $4200

(2) the difference between the number of balcony tickets sold and the number of orchestra tickets sold was 40

Kudos for a correct  solution .

kunal555 · Answer

Let x be the price of balcony tickets, then the price of orchestra ticket will be 2x.
Let y be the common multiplier for the ratio of number of tickets sold. So the ratio is 3y:2y or the number of balcony tickets is 3y and the number of orchestra ticket is 2y.

Statement 1:
Total revenue is 4200
or 3xy+4xy=4200
or 7xy=4200
This statement provides no information about the number of seats.
INSUFFICIENT

Statement 2:
The difference between the number of two seats is 40.
or 3y-2y=40
or y=40
This statement provides no information about the price of tickets.
INSUFFICIENT

Combining 1 and 2:
y=40 and 7xy=4200
So,
7x*40=4200
or 280x=4200
or x=15
So,2x=30
SUFFICIENT

Answer:- C

dav90 · Answer

1st Statement:
balcony tickets cost was half of the orchestra tickets, so if the count ratio is 3:2 then the cost ratio is 3:4 
by this we can calculate total earnings from each type,
but not value of a individual ticket
hence not sufficient
2nd statement:
by this statement we can get the exact number of tickets for each type but we dont know the total cost, hence not sufficient

by combining both we can provide exact answer , hence answer is  C

Hemavakade · Answer

Price Of Orchestra tickets - O
Price Of Orchestra tickets - B

B = (1/2)O

Balcony Tickets : orchestra tickets = 3:2

No. of Orchestra tickets = 2x
No. of balcony tickets = 3x

Statement 1 : 
2xO + 3xB = 4200
7xB = 4200
B = 4200/x

we dont know x - Insufficient

Statement 2 : 
3x - 2x = 40

x = 40

But we dont know the price of orchestra or balcony ticket - Insufficient

statements 1 + 2
Sufficient
Answer = C

TheKingInTheNorth · Answer

For a certain concert, the price of balcony tickets was exactly half the price of orchestra tickets. The ratio of balcony to orchestra tickets sold was 3:2. What was the price of one orchestra ticket?

(1) the total revenue taken in from tickets of both kinds was $4200

(2) the difference between the number of balcony tickets sold and the number of orchestra tickets sold was 40

Kudos for a correct solution.
Solution

When we talk about revenue - there has to be fixed number in terms of no of unit and price per unit .
given price of orchestra tickets = x
and price of balcony tickets = x/2
ratio of balcony to orchestra tickets sold was 3:2

Required :the price of one orchestra ticket ??

St 1 : total revenue given =4200
Revenue = (x/2) 3 + (x)2
Note ratio of balcony to orchestra tickets sold was 3:2 ...no specific number given hence it is not possible to cal the the price of one orchestra ticket .

St 2: the difference between the number of balcony tickets sold and the number of orchestra tickets sold was 40
3y-2y=40 
y =40

But not sufficient to cal the the price of one orchestra ticket . As price not given .

Together 1 and 2 
we have both number of ticket and total revenue . Hence we can calculate the price of price of one orchestra ticket .

hence C

adkikani · Answer

niks18   amanvermagmat   Bunuel   gmatbusters   VeritasPrepKarishma   chetan2u

Let:
B : price of each balcony ticket
O : price of each orchestra ticket

total no of Balcony tickets sold: x
total no of orchestra tickets sold: y

What is the correct approach to resolve ambiguity between:
B = 1/2 * O or 2B = O ... (1)
or 
ratio of B:O = 1:2 .... (2)

I ended up messing this solution taking far too many as 4 variables.

Q stem: x:y = 3:2

St1: Bx + Oy = 4200

St 2: x-y = 40

GMATBusters · Answer

Hi
As asked by you, 
"What is the correct approach to resolve ambiguity between:
B = 1/2 * O or 2B = O ... (1)
or 
ratio of B:O = 1:2 .... (2) "

there is no ambiguity both equations are perfectly correct, but it is quite cumbersome to solve equations.

So it is recommended that when ratio is given, like in this question.
Ration of Balcony/Orchestra = 1/2, hence if balcony tickets = x, orchestra is 2x.

Now you can proceed.

Refer the explanation provided above, @hemavakvade has provided a lucid explanation.
If you don't get the explanation, feel free to tag me again.

AliciaSierra · Answer

In the original question in magoosh site, second statement is reverse.

As per Statement 2: the difference between the number of orchestra tickets sold and the number of balcony tickets sold was 4.

That's why i ended up getting this question wrong.

bumpbot · Answer

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For a certain concert, the price of balcony tickets was exactly half

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