CAT Model Paper 1 Questions and Answers with Detailed Explanations (Official Sample Questions-Most Important for 2022-2023) Part 3

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13. There are 170 people each one of them likes at least one of the fruits, 60 like grapes, 40 like papaya , 50 like watermelon and 70 like pomegranate. If there are exactly 10 people who like all four fruits. Then, Find maximum number of people who like only like only watermelon: .

(A) 40

(B) 30

(C) 35

(D) 38

Answer: (A)

If we want to maximize I, then we need to minimize to others.

In equation (1)

Now, we can draw diagram.

Draw Diagram Papaya, Watermelon, Pomegranate

14. For what values of x will the following inequality hold true





Answer: B


Let a = 3 the inequality holds goods as

Option C & data elinated.

Let the inequality holds good as

Option a is eliminated

15. Arnab need to pay ₹ 210 for his dinner. He has au unlimited supply of ₹ 2, ₹ 5 and ₹ 10 notes; in how many ways can he pay?

(A) 210

(B) 253

(C) 231

(D) None of these

Answer: (B)


Equation become like where

X should be a multiple of 5 and Y should be a multiple of 2.

So, We can take X and Y as 5P and 2Q respectively.

Now equation becomes:

Where P, Q and Z are non-negative integers. Number of soluctions of the given equation is

16. A hare conpletes a straight 300-meter downhill run in t seconds and at an average speed of meters per second. The hare then cycles up the mountain (the same distance) at an averege speed of meters per second. If the ride up the mountain took 135 seconds longer than its run down the mountain, what was the hare՚s average speed, in meters per second, during its downhill run?

(A) 10

(B) 15

(C) 20

(D) 25

Answer: C


Approach Revers gear

Since the difference in time is given, and time = distance/speed

Now going from answer options, we can easily substitute and see Which value satisfies this equation

Option (C) is the correct answer choice.

17. Vikrani drives to office from home every day at a steady rate of X kilometers per hour. On a particular day, vikrant had a flat tire exactly halfway to office. He immediately started walking to office at a steady pace of y kilometers per hour. He arrived. He arrived at office exactly t hours after leaving his home. How many kilometers is it from the office to vikrant՚s home?





Answer: C


Note that it is a variable question. It can be solved in no time at all using assumption.

Let the totla distance and

Then t = 2

Look where you are getting 2 in the answer options.

Answer is option (C)

18. If m times term of an AP is equal to n times its tern, find the term of that AP?




(D) 0

Answer: D


This is a property of an AP

eg 1, 0 is one such AP when m = 1 and n = 2.

19. Given that What is the minimum value of

(A) 5

(B) 10

(C) 25

(D) 50

Answer: D


The minimum value of

The minimum value of

20. Disha wants to paint her room a unique brown. For that she uses a certain viole paint which contains blue pigment and red pigment by weight. She mixes that violet paint with a certain green paint which contains blue pigment and 50 % yellow pigment. When these paiints are mixed to produce the brown paint which she uses, it contains 40 % blue pigment. If the brown paint weight?

(A) 2.8 gms

(B) 3.5 gms

(C) 4 gms

(D) 5.3 gms

Answer: (B)


Considering only the blue pigment in all the paints

Draw the Value Mixture Value

Thus, 5 gms of each paints is used Weight of red paint

34. Six reviewers – Anil (A) , Bindu (B) , Chandan (C) , Deepak (D) , Esha (E) , and Farida (F) will review four movies Kahaani, Paan singh tomar, Agent vinod and HOusefull 2-according to the following conditions:

Each reviewer reviews exactly D reviews either kahaani or Housefull 2.

C does not review Housefull 2.


Farida can review any of the following except

(A) Kahaani with Bindu

(B) Kahaani with Esha

(C) Paan Singh tomar with Esha

(D) Agent vinod with Esha

Answer: B


Chandan is not reviewing Housefull 2. So. From given conditione Anil will not review Housefull 2

Housefull 2 Table Name
KahaaniPaaninghtomarAgent vinodHousefull 2

From the given table it is clear, at least one between Esha and Farida will review, we can easily determine Farida cannot review Kahaani with Easha because Bindu is reviewing Kahaani.

It means Chanda will review kahaani From the given condition “F review the same movie as exactly one other review” So, Option (a) is not possible

Option (b) Anil Farida review Housefull2. From the given table, It is clear that A cannot review Housefull 2. Option (b) is not possible. Option (c) Bindu and Deepak review Kahaani From the given conditions:- ″ C ″ review the same movie as A and F reviews the same movie as exactly one other review ″ we cannot fulfill the condition that all 4 movies are reviewed

Option (C) is not Possible.