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Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 63% (02:25) correct 37% (03:08) wrong based on 75 sessions

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 _________________ examPAL Representative P Joined: 07 Dec 2017 Posts: 1153 Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags Bunuel wrote: 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

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. _________________ SVP  V Joined: 26 Mar 2013 Posts: 2345 Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags DavidTutorexamPAL wrote: Bunuel wrote: 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

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. Hi David, How is the highlighted above reflected in your calculation? examPAL Representative P Joined: 07 Dec 2017 Posts: 1153 Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags Mo2men wrote: DavidTutorexamPAL wrote: Bunuel wrote: 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

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. Hi David, How is the highlighted above reflected in your calculation? 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. _________________ SVP  V Joined: 26 Mar 2013 Posts: 2345 Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags DavidTutorexamPAL wrote: 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. Can you elaborate more please your idea? examPAL Representative P Joined: 07 Dec 2017 Posts: 1153 Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags 1 Mo2men wrote: DavidTutorexamPAL wrote: 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. Can you elaborate more please your idea? 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!
_________________
SVP  V
Joined: 26 Mar 2013
Posts: 2345
Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha  [#permalink]

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DavidTutorexamPAL wrote:
Mo2men wrote:
DavidTutorexamPAL wrote:
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.

Can you elaborate more please your idea?

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! 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. Manager  B Joined: 06 Oct 2017 Posts: 50 Location: Canada Schools: Schulich "22 (A) GPA: 3.6 Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags Bunuel wrote: 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

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

SVP  V
Joined: 26 Mar 2013
Posts: 2345
Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha  [#permalink]

aanjumz92 wrote:
Bunuel wrote:

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

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 _________________ If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !! Intern  B Joined: 11 Dec 2016 Posts: 47 Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags Bunuel Can you please provide the O.E Director  G Joined: 09 Mar 2018 Posts: 994 Location: India Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha [#permalink] Show Tags Bunuel wrote: 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

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
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Director  G
Joined: 18 Dec 2017
Posts: 516
Location: United States (KS)
Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha  [#permalink]

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DavidTutorexamPAL wrote:
Bunuel wrote:
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 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.

I took 2 minutes and got the right answer. But after reading this solution I feel so dumb :-P
Thanks David _________________
----The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long ----
Software Tester currently in USA ( ) Re: Of 7,000 concert tickets, 80 tickets were not sold and of the ones tha   [#permalink] 16 Sep 2019, 08:16
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