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📌 Section 1 is Logical reasoning specially designed for CAT

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SET 1 — 🔍 CAT Level

Four multiplex chains – PVRX, CineHub, Moviemax, and SilverScreen – screened four categories of movies: Action, Comedy, Drama, and Thriller during a festive week. The total number of movie screenings conducted by each multiplex chain is shown in the bar graph below.

The additional information is also known:

(i) The multiplex with the highest number of Action movie screenings conducted exactly 2/3 as many Action screenings as the number of Drama screenings conducted by SilverScreen. CineHub was not the multiplex with the highest Action screenings.

(ii) In PVRX, the number of screenings across the four movie categories forms an arithmetic progression. Thriller screenings were the lowest with 3 screenings, while Action screenings were the highest.

(iii) The total number of Action screenings across all multiplexes and the total number of Drama screenings across all multiplexes are distinct perfect squares greater than 10.

(iv) Across all multiplexes combined, the total number of Comedy and Thriller screenings equals the total number of Drama screenings.

(v) Comedy had the lowest overall number of screenings, with exactly 15 screenings across all multiplexes. Each multiplex conducted at least 3 Comedy screenings.

(vi) In Moviemax:

  • The number of Thriller screenings was 40% more than the number of Action screenings.

  • The number of Comedy screenings was 25% of the number of Drama screenings.

(vii) All screening values are natural numbers.

❝

Question 1

Which of the following could represent the ratio of the number of Comedy screenings in Moviemax to the number of Thriller screenings in CineHub?

  1. 1 : 5

  2. 2 : 5

  3. 1 : 3

  4. 4 : 9

Question 2

What is the combined number of Drama and Thriller screenings in CineHub, Moviemax, and SilverScreen?

Question 3

Suppose 3/5th of all Action and Comedy screenings were housefull, while 2/3rd of all Drama and Thriller screenings were housefull. How many screenings across all the multiplex chains were not housefull?

Question 4

Each multiplex chain introduces a premium pricing surcharge for any movie category that accounts for more than one-third of its total screenings. How many such surcharge cases would arise in total?

  1. 1

  2. 4

  3. 3

  4. 2

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✅ Answers & Explanations

Case 1

Multiplex

Action

Comedy

Drama

Thriller

Total

PVRX

9

5

7

3

24

CineHub

1

3

2

10

16

Moviemax

5

3

12

7

27

SilverScreen

10

4

15

1

30

Case 2

Multiplex

Action

Comedy

Drama

Thriller

Total

PVRX

9

5

7

3

24

CineHub

1

4

2

9

16

Moviemax

5

3

12

7

27

SilverScreen

10

3

15

2

30

❝

Set 1

Total screenings:
PVRX = 24
CineHub = 16
Moviemax = 27
SilverScreen = 30
Total = 97

Step 1: Overall category totals

Comedy total = 15

Comedy + Thriller = Drama
So, Drama = 15 + Thriller

Also, Action + Comedy + Drama + Thriller = 97
Since Comedy + Thriller = Drama:

Action + Drama + Drama = 97
Action + 2Drama = 97

Action and Drama totals are distinct perfect squares greater than 10.

Possible pair:

Action = 25, Drama = 36

So:

Comedy = 15
Thriller = Drama - Comedy = 36 - 15 = 21

Step 2: PVRX

PVRX total = 24
Values form an AP. Thriller is lowest = 3, Action is highest.

So AP values are:

3, 5, 7, 9

Hence:

PVRX Action = 9
PVRX Thriller = 3

Comedy and Drama are 5 and 7.

But Comedy total is only 15. Moviemax Comedy will be 3, so PVRX Comedy must be 5.

Therefore:

PVRX = Action 9, Comedy 5, Drama 7, Thriller 3

Step 3: Moviemax

Let Moviemax Action = A.

Thriller = 40% more than Action = 1.4A
Comedy = 25% of Drama = D/4

Total = 27

Only possible natural number solution:

Action = 5
Thriller = 7
Drama = 12
Comedy = 3

So:

Moviemax = Action 5, Comedy 3, Drama 12, Thriller 7

Step 4: Remaining for CineHub + SilverScreen

After PVRX and Moviemax:

Action remaining = 25 - 9 - 5 = 11
Comedy remaining = 15 - 5 - 3 = 7
Drama remaining = 36 - 7 - 12 = 17
Thriller remaining = 21 - 3 - 7 = 11

SilverScreen Drama must make highest Action = 2/3 of SilverScreen Drama.

Q1 Answer

Moviemax Comedy = 3

CineHub Thriller can be 10 or 9.

So possible ratios:

3 : 10 or 3 : 9 = 1 : 3

✅ Answer: 3) 1 : 3

Q2 Answer

Drama + Thriller in CineHub, Moviemax, and SilverScreen:

Case 1:
CineHub = 2 + 10 = 12
Moviemax = 12 + 7 = 19
SilverScreen = 15 + 1 = 16
Total = 47

Case 2:
CineHub = 2 + 9 = 11
Moviemax = 19
SilverScreen = 15 + 2 = 17
Total = 47

✅ Answer: 47

Q3 Answer

Action + Comedy = 25 + 15 = 40
Housefull = 3/5 of 40 = 24
Not housefull = 16

Drama + Thriller = 36 + 21 = 57
Housefull = 2/3 of 57 = 38
Not housefull = 19

Total not housefull = 16 + 19 = 35

✅ Answer: 35

Q4 Answer

More than one-third of total screenings:

PVRX total 24 → more than 8 → Action 9 only
CineHub total 16 → more than 5.33 → Thriller only
Moviemax total 27 → more than 9 → Drama 12 only
SilverScreen total 30 → more than 10 → Drama 15 only

Total surcharge cases = 4

✅ Answer: 2) 4

⚡ Brain teasers are not just about getting the right answer — they train you to think differently under pressure.

Stay consistent with your daily practice, challenge your assumptions, and keep sharpening your reasoning skills.

See you in tomorrow’s challenge!