CAT Model Paper 4 Questions and Answers with Explanation Part 3

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Q: 11. , where A, B are integers. What is the product of A and B?

(A)

(B)

(C)

(D)

Ans: B

Solution:

By trial and error,

So, product

Hence,

Q: 12. Find the remainder when is divided by ?

(A)

(B)

(C) 5

(D)

Ans: D

Solution:

When is divided by , remainder is

When is divided by , remainder is

When is divided by 9. Remainder is .

So, we can say when is divided by , remainder is .

Hence 7

Q: 13. A circle circumscribes a regular hexagon and is inscribed inside a regular hexagon . What is the ratio of the areas of and ?

(A)

(B)

(C) 3: 4

(D)

Ans: C

Solution:

Side of a hexagon inscribed in a circle (where ‘r’ is the radius of the circle)

Side of a hexagon that circumscribes a circle (where ‘r’ is the radius of the circles)

Area of a hexagon of side ‘a’

Hence, ratio of the areas

Hence option .

Q: 14. The two sides of a rectangle are cm and 8 cm long. If this rectangle is folded along the side measuring cm what is the volume of the cylinder so formed?

(A)

(B)

(C)

(D) None of these

Ans: D

Solution:

Height

The other side

Circumference of base

Volume of cylinder

Hence option None of these

“Cinematrix” is a popular single-screen cinema theatre in Mumbai that runs four shows of a movie every day. The theatre has a seating capacity of 1000 people divided across three classes namely Elite, Premium and Economy. The number of seats in each class and the ticket price of a movie for each class are listed in the table below.

Q_15_to_17_Table of the Number of Seats in Each Class and the Ticket Price of a Movie
ClassNo. Of SeatsPrice of a Ticket
Elite200₹ 350
Premium300₹ 250
Economy500₹ 175

The movies Ek Tha Giraffe, Mere Dad Ki Ferrari, Four Idiots, The Beautiful Picture, and Gangs of Sholapur were among the highest incoming generating movies for the theatre last year. The total ticket revenue from these five movies is ₹ 7 core. Ticket revenue is defined as the revenue obtained by the sales of tickets. The following pie-chart shows the ticket revenue of each movie as a percentage of the total ticket revenue of the five movies.

Q_15_to_17_Pie-Chart of Ticket Revenue

For a movie, average occupancy is defined as the ratio of the average number of tickets sold in a particular class for one show to that of the number of seats available in the class for that show. For a movie, Revenue factor is defined as the ratio of average ticket revenue per show to that of the maximum possible ticket revenue per show.

Q: 15. For the movie Four Idiots, the average occupancies for the Elite class, Premium class and the Economy class were 0.5,0.6 and 0.8 respectively. For how many days did Four Idiots run in Cinematrix?

(A) 35 days

(B) 50 days

(C) 100 days

(D) 60 days

Ans: A

Solution:

The total ticket revenue for the five movies is . Based on the information given in the pie-chart, the ticket revenue of each movie is listed in the table below:

Q_15_1_Table of Ticket Revenue of Movie
MovieTicket Revenue
Ek Tha Giraffe₹ 14000000
Mere das Ki Ferrari₹ 7000000
Four Idiots₹ 21000000
The Beautiful Picture₹ 16800000
Gangs of Sholapur₹ 11200000
  • For each class, Average occupancy
  • Average occupancy
  • Average number of tickets sold per show
  • For Premium Class: Average occupancy 0.5
  • Average number of tickets sold per show = 180
  • For Economy Class: Average occupancy 0.8
  • Average number of tickets sold per show = 400

Hence, the total tickets revenue of Cinematrix per show can be obtained from the table given below:

Q_15_2_The Ticket Revenue of Each Movie
CassAverage No. of tickets sold per showPrice of a ticketTicket revenue per show
Elite₹ 350₹ 35000
Premium₹ 250₹ 45000
Economy₹ 175₹ 70000

Hence total ticket revenue per show = ₹ 35000 + ₹ 45000 + ₹ 70000 = ₹ 1,50, 000

Every day four shows of a movie are run.

Hence, tickets revenue per day = ₹ 1,50, 000 4 = ₹ 6,00, 000

Total tickets revenue for the movie ‘Four Idiots’

Hence, the number of days for which, “Four Idiots” was run in Cinematrix days.

Q: 16. What is the minimum possible number of days for which The Beautiful Picture could have run at Cinematrix?

(A) days

(B) days

(C) days

(D) days

Ans: C

Solution:

  • For a movie to generate a certain amount of ticket revenue in the minimum possible time, it should run to packed houses (i.e.. , all the tickets should have sold) .
  • Hence, for the movie ‘The Beautiful Picture’ to make revenue of ₹ 1, 68,00, 000 at Cinematrix in the minimum possible number of days, every ticket should have been sold.
  • In other words, the average occupancy for the movie should be ‘1’ . If the average occupancy is ‘1’ , then the revenue made by the movie in each class is listed below.
Q_16_Table of the Revenue Made by the Movie in Each Class
CassPrice of a ticketTicket revenue per show
Elite100₹ 350₹ 35000
Premium180₹ 250₹ 45000
Economy400₹ 175₹ 70000

Hence, total ticket revenue per show = ₹ 70000 + ₹ 75000 + ₹ 87500

  • Every day, for shows are being run. Hence, total ticket revenue per day = ₹ 2,32, 500
  • ‘The Beautiful Picture’ makes total ticket revenue of ₹ 1, 68,00, 000 during its run at
  • Cinematrix.
  • Hence, minimum number of days for which it was run in Cinematrix
  • The movie has to definitely run for at least more than 18 days to generate the given ticket revenue. The question set clearly states that, everyday four shows of a movie are run.
  • Hence, a particular movie cannot be telecast in the morning and a different movie cannot be telecast in the afternoon of the same day.
  • Therefore, “The Beautiful Picture” has to run for at least 19 days.

Q: 17. The movies Mere Dad Ki Ferrari and The Gangs of Sholapur had average occupancies of and respectively in the Elite class. Mere Dad Ki Ferrari ran for 30 days in Cinematrix while The Gangs of Sholapur ran for days in Cinematrix. What is the difference between the Elite class Ticket revenue earned from Mere Dad Ki Ferrari and The Gangs of Sholapur?

(A)

(B)

(C)

(D)

Ans: C

Solution:

Average occupancy

In the ‘Elite class’ :

  • Average occupancy for ‘Mere Dad Ki Ferrari’
    • Hence, average number of elite class tickets sold per show
    • ‘Mere Dad Ki Ferrari’ ran for 30 days.
    • Hence the total number of shows
    • Hence total number of elite class tickets sold for ‘Mere Dad Ki Ferrari’
    • Tickets Revenue obtained for ‘Mere Dad Ki Ferrari’ from ‘Elite classes’
  • Average occupancy for ‘Gangs of Sholapur’ =
    • Hence, average number of elite class tickets sold per show
    • ‘Mere Dad Ki Ferrari’ ran for 40 days. Hence the total number of shows
    • Hence total number of elite class tickets sold for ‘Mere Dad Ki Ferrari’
    • Tickets Revenue obtained for ‘Meri Dad Ki Ferrari’ from ‘Elite class’
    • Therefore, difference in Ticket revenue between the two movies ₹ 2,80, 000

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