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Math Expert V
Joined: 02 Sep 2009
Posts: 58320

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Difficulty:   95% (hard)

Question Stats: 48% (02:38) correct 52% (03:00) wrong based on 230 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 V
Joined: 02 Sep 2009
Posts: 58320

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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  S Joined: 11 Sep 2013 Posts: 132 Concentration: Finance, Finance Re: M25-33 [#permalink] Show Tags 7 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  B
Joined: 11 Sep 2015
Posts: 8
Location: India
GMAT 1: 710 Q48 V40 GPA: 3.5

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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  B
Joined: 26 Dec 2016
Posts: 18

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Hi Bunuel,

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

Thanks and regards,
Current Student S
Joined: 22 Apr 2017
Posts: 106
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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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 V
Joined: 02 Sep 2009
Posts: 58320

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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  S
Joined: 25 Jul 2017
Posts: 93

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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.

C is the answer.
Manager  G
Joined: 22 Jun 2017
Posts: 168
Location: Argentina
Schools: HBS, Stanford, Wharton
GMAT 1: 630 Q43 V34 Show Tags

I think this is a high-quality question and I agree with explanation.
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Intern  B
Joined: 29 Jun 2017
Posts: 37

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Bunuel wrote:
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

Bunuel,
We divide by the old price normally, right? Then why divide by R2 in this case?

I get confused at times as to what should be used in the denominator. Can you please shed some light?

Thanks,
Megha.

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 58320

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Megha1119 wrote:
Bunuel wrote:
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

Bunuel,
We divide by the old price normally, right? Then why divide by R2 in this case?

I get confused at times as to what should be used in the denominator. Can you please shed some light?

Thanks,
Megha.

Posted from my mobile device

Not quite. Put in the denominator the value you are comparing to. For example: what percent is 10 greater than 8? (10 - 8)/8*100 = 0.25
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Intern  B
Joined: 17 Feb 2019
Posts: 3

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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. $$\frac{9}{4}$$

Hi Bunnel ,

I solved it in a different manner :

220 * S = 1.1 R

S = price of the ticket , R = Revenue last month.

Now 220 has become 200 which would be 220*10/11
and S became 1.05 S

so 1.1R *10/11 *1.05 to balance both sides gives = 1.05 R which suggests an increase if 5% from last month . Where did I got wrong in here ?

Thankyou ! Re: M25-33   [#permalink] 16 Jun 2019, 07:08
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