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# M25-33

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Math Expert
Joined: 02 Sep 2009
Posts: 47946

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16 Sep 2014, 01:24
1
9
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Difficulty:

95% (hard)

Question Stats:

48% (02:15) correct 52% (02:23) wrong based on 313 sessions

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If a 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 were to raise the ticket price by 5% and sell 200 tickets, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. $$\frac{100}{21}$$
D. $$\frac{110}{20}$$
E. $$\frac{9}{4}$$

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Math Expert
Joined: 02 Sep 2009
Posts: 47946

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16 Sep 2014, 01:24
3
6
Official Solution:

If a 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 were to raise the ticket price by 5% and sell 200 tickets, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. $$\frac{100}{21}$$
D. $$\frac{110}{20}$$
E. $$\frac{9}{4}$$

For a percentage questions like this one, it's almost always better to plug in some smart numbers than trying to build an equation.

Let the usual price of a ticket be $20 (choose$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: $$\text{percent}=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}%$$. Answer: C _________________ Manager Joined: 11 Sep 2013 Posts: 156 Concentration: Finance, Finance Re: M25-33 [#permalink] ### Show Tags 09 Nov 2014, 10:54 6 Last Year Let. Price for last year = 1 Revenue= 220 which is 110% So 100% =$200 Revenue

This Year.
Price =1.05
Revenue= 200*1.05 = 210

Therefore, Revenue increases = 210-200 = 10

Percentage = (10/210)*100 =100/21
Ans-c
Intern
Joined: 11 Sep 2015
Posts: 8
Location: India
GMAT 1: 710 Q48 V40
GPA: 3.5

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14 Jul 2016, 22:33
3
Algebraic Method:
Last Month
Say, tickets sold = q
price of each ticket = p
Revenue last month (R1) = price per ticket * number of tickets = p * q

This month:
tickets sold = 220
price of each ticket = p
Revenue this month (R2) price per ticket * number of tickets = 220 * q

From the question stem:
R2 = 10% greater than R1 = R1 + 10% (R1)
Therefore, R2 = 1.1 (R1)
Simplify the above equation.
220 * q = 1.1 (p*q)
=> p = 200
Therefore, R1 = 200q

Hypothetical case: (Raise ticket price by 5% and sell 200 tickets)
New Price = 1.05 p
Tickets sold = 200
New Revenue (R3) = 1.05p * 200

Find percentage change:
Given : what percent less would last month's revenue be compared to this month's revenue?
So, Initial Value (IV) = R3
Final Value(FV) = R1
% change formula = $$\frac{IV - FV}{IV}$$ * 100
= $$\frac{200*1.05*p - 200 * p}{200*1.05*p}$$
= $$\frac{1}{21}$$*100
= choice C
Intern
Joined: 26 Dec 2016
Posts: 20

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16 Feb 2017, 00:47
Hi Bunuel,

how do I figure out whether to plug-in numbers or set up an equation ?

Thanks and regards,
Manager
Joined: 22 Apr 2017
Posts: 112
Location: India
GMAT 1: 620 Q46 V30
GMAT 2: 620 Q47 V29
GMAT 3: 630 Q49 V26
GMAT 4: 690 Q48 V35
GPA: 3.7

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11 Jul 2017, 03:19
Hi Bunuel,
Can you pls tell me where is the gap in my understanding?

Let's suppose Last Month's revenue to be R.
This Month revenue: 1.1R (10% inc)
Let the ticket price be P.
So, 220*P=1.1R, =>R=200*P --(1)
Revenue obtained with hypothetical case
R2= 200*1.05P (200 tickets with 5% increase in rate), ==>R2 = 1.05R
Hence, difference in % (R2-R)/R...(.05)*100%=5 Hence B.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 47946

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11 Jul 2017, 03:31
1
ManishKM1 wrote:
Hi Bunuel,
Can you pls tell me where is the gap in my understanding?

Let's suppose Last Month's revenue to be R.
This Month revenue: 1.1R (10% inc)
Let the ticket price be P.
So, 220*P=1.1R, =>R=200*P --(1)
Revenue obtained with hypothetical case
R2= 200*1.05P (200 tickets with 5% increase in rate), ==>R2 = 1.05R
Hence, difference in % (R2-R)/R...(.05)*100%=5 Hence B.

Thanks

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

Should be (R2 - R)/R2
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Manager
Joined: 25 Jul 2017
Posts: 96

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12 Jul 2018, 21:25
1
Bunuel wrote:
If a 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 were to raise the ticket price by 5% and sell 200 tickets, what percent less would last month's revenue be compared to this month's revenue?

A. 2
B. 5
C. $$\frac{100}{21}$$
D. $$\frac{110}{20}$$
E. $$\frac{9}{4}$$

This question is majorly a Word-Problem. We have to be very attentive to solve this one.
Let's go one by one:

Had circus sold all the 220 tickets at it's usual price (say 10), it would have 220*10= 2200 Revenue, which is in turn 10% higher to the last month.
=> Last month Revenue = 2200/1.1= 2000.... (1)
Now, Tickets' price are raised by 5% i.e. new ticket's price is 10.5 & Total Tickets are 200
=> This month's revenue = 200*10.5= 2100

Now this is 2100-2000= 100 more than last month's revenue
=> (100/2100)*100 = 100/21 % less would be last month's revenue from this month.

Re: M25-33 &nbs [#permalink] 12 Jul 2018, 21:25
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# M25-33

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