M25-33

Question

If a circus sells all of its 220 tickets for this month's performance at the regular price, the revenue from these sales would exceed the revenue from the previous month by 10%. If the circus were to increase the ticket price by 5% and only sell 200 tickets, by what percentage would the revenue of the previous month be less compared to this month's revenue?

A. $2$

B. $4$

C. $\frac{100}{21}$

D. $5$

E. $\frac{11}{2}$

Show Answer

Official Answer

C

A.  2

B.  4

C.  \frac{100}{21}

D.  5

E.  \frac{11}{2}

Bunuel · Accepted Answer

Official Solution:

If a circus sells all of its 220 tickets for this month's performance at the regular price, the revenue from these sales would exceed the revenue from the previous month by 10%. If the circus were to increase the ticket price by 5% and only sell 200 tickets, by what percentage would the revenue of the previous month be less compared to this month's revenue?

A. $2$

B. $4$

C. $\frac{100}{21}$

D. $5$

E. $\frac{11}{2}$

Show Answer

Official Answer

C

A.  2

B.  4

C.  \frac{100}{21}

D.  5

E.  \frac{11}{2}

For percentage questions like this one, it's almost always better to plug in some smart numbers rather than trying to build an equation.
 
Assume the usual ticket price is $20 (we choose $20 because $20 plus 5% equals $21, an integer, which makes calculations easier). With this price, this month's revenue for 220 tickets would be  220*$20 = $4,400 , which we are told is 10% greater than the revenue collected previous month. Hence,  previous month's revenue was  \frac{$4,400}{1.1} = $4,000  .
 
If the circus were to raise the ticket price by 5%, the new price would be $21. Therefore,  the actual revenue from selling 200 tickets would be  200 * $21 = $4,200  .
 
To find out what percent less previous month's revenue would be compared to this month's revenue, we calculate the following:  	ext{percent}=\frac{4,200-4,000}{4,200}*100=\frac{100}{21}\% .

Answer: C

Raihanuddin · Answer

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

phaneendrasristi · Answer

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

anuj04 · Answer

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.

patto · Answer

I think this is a  high-quality  question and I agree with explanation.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

renzosm93 · Answer

I got 5% = (4200-4000)/4000. Can you please explain why this is not the formula?

Bunuel · Answer

The general formula for calculating percent increase or decrease (percent change) is:  \frac{	ext{Difference in values}}{	ext{Reference value}}*100 .  The reference value is the value you are comparing to.

(When we are talking about percentage change from old value to new value, it would be  \frac{	ext{New Value - Old Value }}{	ext{Old Value}}*100 .)

In this question, we are comparing to this month's revenue (if we sell 200 tickets at a 5% higher price), so the reference value is this month's revenue of $4,200.

Hope it's clear.

finkele · Answer

I think this is a  poor-quality  question and I don't agree with the explanation. Why is the denominator of the last fraction the bigger number? Surely you can interpret it the other way. I know by the wording the question wants you to do that but again it is not entirely clear

bb · Answer

Hi  finkele  . Thanks for the feedback - I am not sure I followed you. 😬
Denominator of 11/2 is 2... what do you mean it is the bigger number? Are you saying the fraction is improper or?

Bunuel · Answer

No, there is only one correct interpretation. It's explained here: https://gmatclub.com/forum/m25-184435.html#p3431576

finkele · Answer

I meant the last fraction of the official solution has its reference value equal to 4200, when 4000 could also be inferred by the way the question is phrased. I can see I’m not the first one to think it that way.

Bunuel · Answer

It's explained here: https://gmatclub.com/forum/m25-184435.html#p3431576

bb · Answer

It is discussed above - the link is not opening for some reason as it is on this same page above. Scroll up.

Yes, you are not the first one to think that way and you are not the first one to make that mistake and you should feel better that you are not the only one who made a mistake, but it is still a mistake.

vestenhaus · Answer

Hi Bunuel,

I mix this (denominator) sometimes could you share some sample statements to understand when to use which one?
Many thanks.

Bunuel · Answer

When calculating percentage change, the reference value is the value you are comparing  to . This means the reference value always goes in the  denominator  of the formula.

In this problem, the question asks:  By what percentage would the previous month's revenue be less compared  to  this month's revenue?  Since we are comparing the previous month's revenue to this month's revenue, the reference value is this month's revenue. This is why 4200 is used in the BOTTOM of the fraction.

Rohan271 · Answer

I like the solution - it’s helpful.

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