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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]

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23 Jan 2012, 14:33
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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]

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23 Jan 2012, 17:38
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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.

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07 Feb 2012, 23:56
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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08 Feb 2012, 01:18
I think the answer is B.
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08 Feb 2012, 02:04
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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08 Feb 2012, 02:08
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.

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]

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08 Feb 2012, 10:55
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.

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]

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08 Feb 2012, 12:13
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]

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09 Feb 2012, 09:12
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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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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 Kudos [?]: 7 [0], given: 2 Math Expert Joined: 02 Sep 2009 Posts: 41913 Kudos [?]: 129537 [0], given: 12201 Re: If the circus were to sell all of its 220 tickets for this [#permalink] ### Show Tags 29 Jun 2013, 05:17 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]

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]

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07 Sep 2015, 09:18
say last month the revenue was x
this month it increased by 10 % =1.1x
now as per the question 1.1x=220
x=200, thus the revenue last month was 200
As per the question :1.05x=200
therefore x=210
and hence increase from last month =(210-200/210)*100
which gives 100/21

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]

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05 Oct 2015, 22:41
y - last month price
x - last month revenue

Price x Number = Revenue
--y---------220--------1.1x
--1.05y----200---------?

220y=1.1x
210y=?x

220y/210y=1.1x/?x => 210y=1.05x

(105-100)/105=(5/105)*100=500/105=100/21

C

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]

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05 Jun 2016, 20:59
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

Let price be 10/ticket
then 220 tickets for this month's performance at its usual price=2200
which is 10%greater than last month(let X)---->x(1+10/100)=2200----->x=2000
now new revenue this month=200*10.5=2100
(Note:- if question asked for what % greater is this month revenue of last month,then =2000((1+A/100)=2100,will make ans choice B i.e 5% as correct answer)
Ans C

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If the circus were to sell all of its 220 tickets for this [#permalink]

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05 Jun 2016, 21:36
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

Price remains unchanged and still revenue is increasing. This means that ticket sales were increased. This increase would be 10 % of the tickets sold last month
Now increased ticket sales were 220.

So last month if tickets sold were x, then
1.1 x = 220; x = 200.

So last month 200 tickets were sold.

Now suppose the usual ticket price was p.

So last month revenue = 200p

This month ticket price has been increased by 5 %. New price = 1.05p
Revenue of this month = 1.05p*200 = 210p

How much % is last month revenue less than this month's revenue.

Reduction: 210p - 200p = 10 p

Key point: Reduction is with respect to this month

so reduction % = $$\frac{10p}{210p}$$ * 100

= $$\frac{100}{21}$$

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Re: If the circus were to sell all of its 220 tickets for this [#permalink]

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06 Feb 2017, 11:04
my equations: 220P=11/10R R=revenue last month
105/100P * 200 = x/100R

200P=R 105P/100*200=x/100*200P

x=105

so: answer B 5% change. I know something is wrong, but this thing makes sense.

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Re: If the circus were to sell all of its 220 tickets for this   [#permalink] 06 Feb 2017, 11:04

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