Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha

Question

Of 7,000 concert tickets, 80 tickets were not sold and of the ones that were sold, 50 percent were sold at 10 percent higher than the average price. If the average price of the sold tickets is $10 what is the total revenue?

A. 70,000
B. 69,200
C. 70,800
D. 69,120
E. 69,080

A. 70,000
B. 69,200
C. 70,800
D. 69,120
E. 69,080

DavidTutorexamPAL · Answer

As the calculation seems relatively straightforward, we'll just do it.
This is a Precise approach.

The total revenue is the average price of sold tickets * # of tickets sold.
This is $10 * (7000 - 80) = 69,200

(B) is our answer.

Mo2men · Answer

Hi David,

How is the highlighted above reflected in your calculation?

DavidTutorexamPAL · Answer

Hi Mo2men,

It isn't.
I'm pretty sure this is a trick question... let's wait for the OA.

Breaking it down into 3 groups would be
1) 80 tickets at $0
2) 3460 tickets at average of all tickets +10%
3) 3460 tickets at who knows need to calculate
But since the average of 2) and 3) is $10, there is no need to calculate.

Note the word games between 'average price of sold tickets' and 'average price'.
TBH, took me a while to notice this. I assume this is what makes the question hard.

Mo2men · Answer

Can you elaborate more please your idea?

DavidTutorexamPAL · Answer

I'll try. Tell me if there is something specific you don't understand / agree with?

Usually, to calculate the revenue you'd divide the tickets into different price groups and multiply by the price per ticket in each group.
For example, if you had 5 tickets at $1 and 5 tickets at $2 then the revenue would be 1*5 + 2*5 = 15.

In this case, when you first read the question the instinct is to divide the tickets into 3 groups:
1) tickets that weren't sold. There are 80 of these and each generated $0 of revenue
2) 50% of the tickets that were sold. This is (7000 - 80)/2 = 3460 tickets. These were sold at "10% higher than the average price".
3) the other 50% of tickets that were sold - so another 3460 tickets. We have no information on the selling price of these tickets.

Creating an equation with the above 3 groups would give:
revenue = 80*0 + 3460*(average + 10%) + 3460*(unknown number)
Using this: "average price of the sold tickets is $10"
we can solve the above equation but it isn't fun.

Alternatively, we can divide all the tickets in the question into two groups:
1) this is the same as above - tickets that weren't sold. Each gives $0 of revenue.
2) all the tickets that were sold - a total of 6920 tickets. Each gives $10 on average of revenue.
So, our total revenue is 80*0 + 6920*10 = 69,200.

This is a trick question because the entire middle part of the prompt - "and of the ones that were sold, 50 percent were sold at 10 percent higher than the average price."
is useless and misleading. If the question were instead:
"Of 7,000 concert tickets, 80 tickets were not sold. If the average price of the sold tickets is $10 what is the total revenue?"
It would be much easier, wouldn't it?

Hope that helps!

Mo2men · Answer

Thanks David, I thought 10 % of the average price = 10% of 10 = 11 If I follow my assumption above it would end up = 10 * 3460 + 11 * 3460 = 72,660 which does not exist in the answer choices.

So I agree with your explanation.

aanjumz92 · Answer

We are told that there are 7000 concert tickets. If 80 are unsold, then there are 6920 sold tickets.
50% of 6920 = 3460 tickets

First 50% were sold at 10% higher than average price.
That means, 3460 tickets were sold at $11 dollars because the average price is $10 and 10% more than $10 is $11.
Therefore, 3460 x 11 = 38, 060

Other 50% of sold tickets i.e. remaining 3460 tickets, were sold at 10% LOWER than average price. THIS IS THE KEY WORD.
If half were sold at 10% more, then the other half obviously is sold at 10% less, so we have
3460 x 9 = 31,140 
Why 9? (because 10% less than average of $10 is $9)

SO TOTAL REVENUE: 38,060 + 31,140 = 69, 200

ANSWER: B

Mo2men · Answer

From where did you get this assumption that other half sold less than 10%? It could possible that half sold at same price and other with 10% higher.

rahul16singh28 · Answer

The highlighted part is a Tricky.   It says that the 50 percent were sold at 10 percent higher than the average price - Here, the average price is not $10. Note that $10 is average price of sold tickets only  . Someone posted above that 80 tickets that weren't sold are of $0 value, this is wrong assumption. It might be that those 80 tickets were very expensive. So, its just a simple calculation of the total tickets sold i.e. 6920*10 = 69,200

asfandabid · Answer

Bunuel

Can you please provide the O.E

KanishkM · Answer

We dint need to calculate here anything the fact that average price of the sold tickets = 10

How many tickets were sold = 7000 - 80 = 6920

Average = Revenue / Number of tickets sold

Revenue = 69200

TheNightKing · Answer

I took 2 minutes and got the right answer. But after reading this solution I feel so dumb :-P Thanks David

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Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha

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