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

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For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 27 Sep 2015, 11:21
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C
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Difficulty:

  55% (hard)

Question Stats:

62% (02:16) correct 38% (01:56) wrong based on 222 sessions

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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.

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Re: For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 27 Sep 2015, 12:23
Bunuel wrote:
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.


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
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Re: For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 27 Sep 2015, 18:56
Bunuel wrote:
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.


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
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Re: For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 27 Sep 2015, 23:13
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
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Re: For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 27 Sep 2015, 23:33
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
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For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 25 Apr 2018, 03:23
niks18 amanvermagmat Bunuel gmatbusters VeritasPrepKarishma chetan2u

Quote:
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


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
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Re: For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 25 Apr 2018, 03:46
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.


adkikani wrote:
niks18

Quote:
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


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

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Re: For a certain concert, the price of balcony tickets was exactly half  [#permalink]

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New post 18 Aug 2018, 08:52
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.
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Re: For a certain concert, the price of balcony tickets was exactly half &nbs [#permalink] 18 Aug 2018, 08:52
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