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If the circus were to sell all of its 220 tickets for this

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If the circus were to sell all of its 220 tickets for this [#permalink] New post 23 Jan 2012, 13:33
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A
B
C
D
E

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51% (03:02) correct 49% (01:59) wrong based on 67 sessions
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4
[Reveal] Spoiler: OA

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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 23 Jan 2012, 16:38
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manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4


For a percentage questions like this one, it's almost always better to plug some smart numbers.

Let the usual price of a ticket be $20 (I chose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was $4,400/1.1=$4,000;

Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was 200*$21=$4,200;

What percent less would last month's revenue be compared to this month's revenue: percent=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%. General formula for percent increase or decrease, (percent change): percent=\frac{Change}{Original}*100, so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.

Answer: C.
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circus [#permalink] New post 07 Feb 2012, 22:56
I'm not sure what the question is asking:

"what percent less would last month's revenue be compared to this month's revenue?"

The way I interpreted the question was "last month's revenue is less than this month's revenue by how many percent?"

I got 5%,
(this month)-(last month)] / (last month)

but the OA is C. Please explain. Thanks.
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Re: M08#03 [#permalink] New post 08 Feb 2012, 00:18
I think the answer is B.
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Re: circus [#permalink] New post 08 Feb 2012, 01:04
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Samwong wrote:
I'm not sure what the question is asking:

"what percent less would last month's revenue be compared to this month's revenue?"

The way I interpreted the question was "last month's revenue is less than this month's revenue by how many percent?"

I got 5%,
(this month)-(last month)] / (last month)

but the OA is C. Please explain. Thanks.


I merged similar topics. Please refer to the solutions above. Hope it helps. Please let me know if you have any questions.
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Re: M08#03 [#permalink] New post 08 Feb 2012, 01:08
It's B for sure, human error in inputing OA.

1.1 Y = 220*X
Y = 200X

This month ticket price went up by 5% total number of people is 200. You need to find out how much LESS last month's revenue is compare to this month.

(last month-this month)/this month.

(200X-(200*1.05*X))/(200*1.05*X)

(-200*.05)/(200*1.5*X) ==> (-10/210X) ==> 1/21 (ignored negative since they only want the percent).

1/21 is a real number n not a percent, so in order to get a percent you need to times it by 100 (.03 = 3%, 1= 100%) ==. 100/21.

Answer = B

The wording is pretty crappy... Took me a while to get what it meant
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 08 Feb 2012, 09:55
Bunuel wrote:
manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4


For a percentage questions like this one, it's almost always better to plug some smart numbers.

Let the usual price of a ticket be $20 (I chose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was $4,400/1.1=$4,000;

Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was 200*$21=$4,200;

What percent less would last month's revenue be compared to this month's revenue: percent=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%. General formula for percent increase or decrease, (percent change): percent=\frac{Change}{Original}*100, so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.

Answer: C.


Let's suppose that if question is "what percent increase would this month's revenue be compare to last month's revenue?"

Would the answer then be 5%?
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 08 Feb 2012, 11:13
Yup. The denominator will be 20 instead of 21. 1/20 = 5%.
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 09 Feb 2012, 08:12
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manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4


This is what comes to mind when I read this question:

"If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month."

220 tickets at usual price make 10% extra revenue. In case last month the tickets were sold at usual price, they would have sold 200 tickets (10% extra revenue would be due to 10% extra tickets sold if the price is the same)

"If the circus raised the ticket price by 5% and sold only 200 tickets as a result"

If the circus sold the same number of tickets as sold last month but increased the price by 5%, the revenue would also increase by 5%. (Revenue increases by either increasing the number of tickets or increasing the price or both)

"what percent less would last month's revenue be compared to this month's revenue"
The question isn't the % by which this month's revenue is greater (which we know is 5%). The question is by what percent is last month's revenue less?
If last month's revenue = 100, this month's revenue = 105
Last revenue is less by 5/105 * 100 = 100/21%
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 09 Feb 2012, 20:36
Let p be the original price so this month revenue is 220p
if p is increased by 5% so the new price is 1.05p
now revenue from sale of 200 tickets is 210p
so 220p-210p/210*100 = 100/21
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Re: circus [#permalink] New post 01 Apr 2012, 00:27
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johndoey725 wrote:
say the usual price is x.

total revenue - 220x (now)

last month revenue - here is the trick - say last month`s revenue is y. Then 1.1y = 220x which means y is 200x.

but if price is increased by 5% i.e. 1.05x then we sell only 200 tickets

total revenue - 200 * 1.05x = 210x

so increase compared to last month`s revenue - 210x - 200x = 10x

so 200x is greater than the new revenue by 10x or (10/200)*100 = 5% which is B.

the key is not to get tricked in the second step and say that the last months revenue is 90% of 220x.


Answer to this question is C, not B. Please refer to the posts above and ask if anything remains unclear.
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 29 Jun 2013, 04:11
Bunuel wrote:
manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4


For a percentage questions like this one, it's almost always better to plug some smart numbers.

Let the usual price of a ticket be $20 (I chose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was $4,400/1.1=$4,000;

Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was 200*$21=$4,200;

What percent less would last month's revenue be compared to this month's revenue: percent=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%. General formula for percent increase or decrease, (percent change): percent=\frac{Change}{Original}*100, so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.

Answer: C.

Thank you for your comment.
I don't quite agree with the % change formula.
Common formula for % change is
Change % = (Current month less Last Month)/Last Month *100% (this approach is consistent with 13th OE, please refer to question 177 problem solving).
But even if you would like to use current month as a reference value then the formula should be
Change % = (Last month less Current Month)/Current Month *100
You always deduct and divide by the same amount (i.e. reference value)
Common approach is to use prior month as a reference value.
Thus the correct answer should be either negative (if current month is used as a reference value) or recalculated using last month as a reference value
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Re: If the circus were to sell all of its 220 tickets for this [#permalink] New post 29 Jun 2013, 04:17
Expert's post
NikRu wrote:
Bunuel wrote:
manalq8 wrote:
If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. 100/21
D. 110/20
E. 9/4


For a percentage questions like this one, it's almost always better to plug some smart numbers.

Let the usual price of a ticket be $20 (I chose $20 because $20+5%=$21=integer, which will make calculations easier). This month's revenue for this price would be 220*$20=$4,400 and we are told that it's 10% greater than the revenue collected last month, hence the last month's revenue was $4,400/1.1=$4,000;

Circus raised the ticket price by 5%, so the new price was $21 and the actual revenue from 200 tickets was 200*$21=$4,200;

What percent less would last month's revenue be compared to this month's revenue: percent=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%. General formula for percent increase or decrease, (percent change): percent=\frac{Change}{Original}*100, so as we are comparing the difference to this month's revenue we should put this value ($4,200) in the denominator.

Answer: C.

Thank you for your comment.
I don't quite agree with the % change formula.
Common formula for % change is
Change % = (Current month less Last Month)/Last Month *100% (this approach is consistent with 13th OE, please refer to question 177 problem solving).
But even if you would like to use current month as a reference value then the formula should be
Change % = (Last month less Current Month)/Current Month *100
You always deduct and divide by the same amount (i.e. reference value)
Common approach is to use prior month as a reference value.
Thus the correct answer should be either negative (if current month is used as a reference value) or recalculated using last month as a reference value


Not quite understand what you mean here.

Anyway, check here: if-the-circus-were-to-sell-all-of-its-220-tickets-for-this-126466.html#p1041966 Might help.

Revenue this month = $4,200.
Revenue last month = $4,000.

4,000 is ~4.8% (100/21%) less than 4,200.
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Re: If the circus were to sell all of its 220 tickets for this   [#permalink] 29 Jun 2013, 04:17
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