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The CAT Exam Roadmap: Navigating Success through Practice Set Questions- Day 20

The CAT Exam Roadmap: Navigating Success through Practice Set Questions- Day 20

Edited By Irshad Anwar | Updated on Sep 18, 2023 06:56 PM IST | #CAT

We have developed a study plan to ace the CAT Exam based on the CAT syllabus 2023. From Day 1 through Day 19, we discussed a plan for each day.

A CAT sample paper on Day 20 of our CAT preparation for CAT 2023 is now available. We invite you to take the CAT sample paper on this day based on the CAT syllabus 2023 that we covered in the first 19 days. Take the test having CAT practice papers and track your progress with self-analysis. You can identify your strengths and weaknesses and adjust your study plan. Students can also download the CAT sample paper with solutions pdf.

The CAT Exam Roadmap: Navigating Success through Practice Set Questions- Day 20
The CAT Exam Roadmap: Navigating Success through Practice Set Questions- Day 20

The following CAT practice paper has been made in sync with the format of the CAT exam. Students can take reference and practise more papers in the coming days through our articles.

To get a flow, plan, and schedule for your preparation, use the 60-day CAT exam preparation strategy we created for you and practise daily with these CAT practice papers.

CAT Sample Paper with solutions pdf

This CAT Sample paper consists of three Sections:

  • Part- A consists of 9 questions.
  • Part- B consists of 7 questions.
  • Part- C consists of 9 questions.

Part-A: Quantitative aptitude

Q1. For the given pair (x, y) of positive integers, such that (-x + 3y/2) =7 and x< 210. How many integer values of y satisfy the given conditions? (CAT previous year questions)

  1. 340
  2. 341
  3. 342
  4. 1024

Q2. A quadratic function f(x) attains a maximum of 12 at x = 1. The value of the function at x = 0 is 7. What is the value of f (x) at x = -11? (CAT previous year questions)

  1. -805
  2. -719
  3. -859
  4. -883
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Q3. If the roots of the equation in y i.e. y3 – ay2 + by – c =0 are three consecutive integers, then the smallest possible value of b (nearest to its integer value) is ______________ [TITA]

Q4. The sum of the integers in the solution set of |x2-7x| > 5 is: (CAT exam model paper)

  1. 10
  2. 15
  3. 20
  4. 0
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Q5. The equation x2 + ax + (3-b) = 0 has real roots. What is the minimum value of a2 + b2? (CAT previous year questions)

  1. 0
  2. 2
  3. 4
  4. 8

Q6. X is p% less than Y and Z is p% more than Y. If X is 2.5p% more than Z, then find p. (Note: p≠0) - (CAT previous year questions)

  1. 20
  2. 40
  3. 60
  4. 50

Q7. The value of the base of a triangle for which area is minimum if the relation between the perpendicular distance from the vertex and the base is p = 7b2 - 84 is _______________ (where b represents base and p represents perpendicular distance) [TITA]

Q8. Let f (x) = max (2x + 1, 3 − 4x), where x is any real number. Value of f(x) at x = 7.5 is: (CAT exam model paper)

  1. -11
  2. - 27
  3. 16
  4. 43

Q9. Let g (x) be a function such that g (x + 1) g (x) = 12 for every real x. Then what is the value of g (11) g (0)? (CAT exam model paper)

  1. 1
  2. 12
  3. 1/12
  4. 6

CAT Exam: Sample Paper

Part-B: Logical Reasoning

Direction (Q1-Q3):

Four friends Arun, Bittu, Cirag and Dheeraj went for an excursion with their wives Priya, Renu, Sharita and Varti, not necessarily in the same order. Each couple hails from a different city amongst Madurai, Cutnee, Kurnool and Hapur, not necessarily in that order. They went to Delhi to visit the Pinkfort, where they sat in a row. Each wife always sat to the immediate right of her husband. (CAT practice questions)

(i) Bittu sat to the immediate right of Priya.

(ii) Dheeraj is from Hapur and Priya is not from Madurai.

(iii) Renu and her husband were sitting to the immediate right of the couple that hailed from Cutnee.

(iv) Chirag and his wife were sitting to the immediate left of the couple from Kurnool and Chirag was sitting to the immediate right of Sharita.

(v) Arun sat to the immediate right of Renu, who is not from Madurai.


Q1. Who is Dheeraj’s wife?

(A) Sharita (B) Priya (C) Varti (D) Renu

Q2. Which couple is from Cutnee?

(A) Varti and Bittu (B) Dheeraj and Renu

(C) Chirag and Priya (D) Arun and Sharita

Q3. Who is the husband in the couple, which is seated second in the row from left to right?

(A) Arun (B) Bittu (C) Cirag (D) Dheeraj

Direction (Q4- Q7) (CAT practice questions)

A cube is formed by joining 216 smaller and identical cubes. The bigger cube is painted black colour on all its faces. From the bigger cube, 64 smaller cubes from a corner were taken out and the cube formed by joining these 64 smaller cubes is painted pink in all its faces. Again, this cube is fitted back into its usual position in the large cube.

Q4. How many smaller cubes have no faces painted?

Q5. How many smaller cubes have three faces painted?

Q6. How many smaller cubes have only two faces painted?

Q7. How many smaller cubes have only one face painted?

CAT Exam: Sample Paper

Part-C: VARC (CAT solved papers)


In the questions below, find the phrase with an error.

Q1: If I had known, I would lend you my car.

  1. I will lend you my car
  2. I would lent you my car
  3. I would have lent you my car
  4. No improvement needed
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Q2. You have no trouble at school, if you had done your homework.

  1. You would have had no trouble at school.
  2. You will have no trouble at school.
  3. You would had no trouble at school
  4. No improvement needed

Q3. If you had done better at your interview, you get that job.

  1. You will get that job.
  2. You would get that job.
  3. You would have got that job.
  4. No improvement needed

Q4. While the guests danced, the thieves broke into the house.

  1. While the guests have danced
  2. While the guests were dancing
  3. While the guests had danced
  4. No improvement needed

Error detection - (CAT exam paper sample)

Q5. Take a shower (a)/ you will (b)/ feel better. (c) / No error (d)

  1. (a)
  2. (b)
  3. (c)
  4. (d)

Q6. Whenever I look (a)/ at the moon my heart (b)/ fills with the pleasure. (c)/ No error(d)

  1. (a)
  2. (b)
  3. (c)
  4. (d)

Q7. The whole block of flats (a)/ including two shops were (b)/ destroyed in fire. (c)/ No error (d)

  1. (a)
  2. (b)
  3. (c)
  4. (d)

Q8. The man who cannot (a)/ believe his senses and the man who cannot (b)/ believe anything else are insane. (c)/ No error(d)

  1. (a)
  2. (b)
  3. (c)
  4. (d)

Fill the blank with the correct Article:

Q9. If you go by __ train you can have quite__ comfortable journey, but make sure you get ___ express, not __ train that stops at all the stations.

  1. a, an, a, the
  2. an, a, the, a
  3. No article, an, a, the
  4. No article, a, an, a

CAT Exam: Sample Papers: Answers And Solutions

Part-A: Quantitative aptitude

Ans 1: (2)

3y/2 = 7 + x

Or, y = (14 + 2x)/3; for y to be integer (14 + 2x) should be divisible by 3

x= 2; y = 6x= 5; y = 8

x = 8; y = 10

x = 11; y = 12 and so on…

So, clearly, there is an AP in x with the first term being 2 and common difference 3.

nth term in x must be less than or equal to 210 i.e. 1024.

Therefore, 2 + (n-1)3 ≤ 1024

⇒ n ≤ (1022/3) +1

Therefore, n must be 341.

Hence there can be 341 solutions.

Ans 2: (4)

If the function gets the maximum of 12 at x = 1

f(x) = a(x – 1)2 + 12

So, f (0) = a + 12 = 7 {It is given as 1}

a = –5

f(x) = –5(x – 1)2 + 12

f(-11) = –5(-12 – 1)2 + 12= –845 + 12 = –833

Solution 3:

In a cubic equation, the coefficient of y divided by the coefficient of y3 represents the sum of the product of roots taken two at a time.

So, b = the sum of the product of roots taken two at a time

This is the minimum when roots are -1, 0 and 1.

So, b = -1 x 1+ -1x 0 + 1 x 0 = -1

Answer is -1.

Ans 4: [4]

|x2-7x| > 5

⇒ x2-7x > 5 or x2-7x < -5

Case 1:

⇒ x2-7x > 5

⇒ x2 -7x – 5 > 0

⇒ x > [(7±√69)/2] which gives two solutions x > 7 or x < 0 (for x to be integer).

Case 2:

⇒ x2-7x < -5

⇒ x2 -7x +5 < 0

⇒ x < [(7±√29)/2] which gives two solutions x < 7 or x > 0 (for x to be integer).

x = [1, 2, 3, 4, 5, 6].

There is no common solution in both cases. So, the answer is 0.

Ans 5: (4)

For real roots; a2 – 4(3 -b) ≥ 0

⇒ a2 + 4b – 12 ≥ 0

⇒ a2 + 4b +b2 – b2 – 12 ≥ 0

⇒ a2 + b2 ≥ b2 - 4b + 12

⇒ a2 + b2 ≥ b2 - 4b + 4 + 8

⇒ a2 + b2 ≥ (b – 2)2 + 8

At b= 2, a2 + b2 has the minimum value i.e. 8.

Ans 6: (A)

X = (100 – p) Y/100

Z = (100 + p) Y/100

X = (100 + 2.5p) Z/100

From 1st and 2nd relation, we get X = Z (100 – p) / (100 + p)

So, Z (100 – p) / (100 + p) = (100 + 2.5p) Z/100

⇒ 100(100 – p) = (100 + p) (100 + 2.5p)

⇒ – 100p = 100p – 250p + 2.5p2

⇒ p = 20.

Solution 7:

Area = ½ (base) (height) = ½ b (7b2 - 84) = 7b3/2 - 84b1/2

For Area to be minimum, find dA/db = 21/2 b2 – 42 = 0

⇒ b2 = 4

⇒ b = 2 or b = -2.

Now find d2A/db2 = 21b

At b = 2; d2A/db2 = 42 which is greater than 0, so at b = 2, we get the minimum value of Area.

Hence the answer is 2.

Ans 8: (3)

f(x) = max (2x7.5 + 1, 3 – 4x7.5) at x = 7.5

f(x) = max (16, -27) at x = 7.5

Answer is 16.

Ans 9: (2)

For x = 0; g(1) = 12/g(0)

Similarly g(2) = 12/g(1), which gives g(2) = g(0)

g(3) = g(1) and so on.

Therefore, g(11) = g(9) = g(7) = ……= g(1) = 12/g(0)

⇒ g (11) g (0) = 12.

CAT Exam: Sample Papers: Answers And Solutions

Part B - Logical Reasoning

Solution 3:

Males: - Arun, Bittu, Cirag and Dheeraj Females: - Priya, Renu, Sharita and Varti Cities: - Madurai, Cutnee, Kurnool and Hapur With reference to the couples, the wife always sits to the immediate right of her husband.

From (i), Bittu is not the husband of Priya.

From (ii), Dheeraj is from Hapur.

From (iii), Renu is not from Cutnee.

From (iv), Cirag is not from Kurnool and he is not the husband of Sharita.

From (v), Arun is not married to Renu and Renu is not from Madurai.

Possibility Table

HUSBAND

WIFE

CITY

Bittu

Priya,

Hapur

Dheeraj

Sharita, Reno, Priya, Varita

Hapur

Chirag

Sharita, Renu, Priya or Varita

Hapur,Kurnool, Mudrai or Cutnee

Arun

Renu

Hapur ,Cutnee,Madurai or Kurnool

So, according to the table there were two possibilities for Chirag's wife either Priya or Varita so we will consider these cases one by one

Case I: If we consider Priya as Chirag’s wife and Priya can’t be from Madurai so they must be from Cutnee.

So, the arrangement could look like this:

------ Sharita Chirag --- Priya Bittu---Renu Arun-------

Now after this arrangement only one man and one woman is left so we can consider the woman as Arun’s wife and the man as Sharita’s Husband

Dheeraj ------ Sharita Chirag --- Priya Bittu---Renu Arun-------Varti

This arrangement is fulfilling all the conditions, so it is not required to consider any other case.

Ans 1: Dheeraj is married to Sharita.Choice (A)

Ans 2: Chirag and Priya are from Cutnee. Choice (C)

Ans 3: Chirag and his wife are seated second in the row. Choice (C)

Solution 4 to 7: (CAT solved papers)

1695034328923

1695034328732

Ans 4: By assuming a 4 × 4 × 4 cube is also not painted with pink colour, the number of cubes with no faces painted is = (6 – 2)3 = 64. Of these 64 smaller cubes now, in the second, third and fourth layer leftmost 9 cubes are painted pink, on the bottom surface four smaller cubes are painted pink and on the fourth layer back most six smaller cubes are painted. Hence, the total number of cubes with no face painted = 64 – 19 = 45.

Ans 5: The number of cubes which are three faces painted before removing 64 smaller cubes = 8 and after painting with pink colour to those 64 smaller cubes seven new cubes will have three faces painted. Hence, the total number of cubes with three faces painted = 8 + 7 = 15.

Ans 6: The number of smaller cubes painted on two faces in the larger cube after removing 4 × 4 × 4 is illustrated as shown below. 9 edges with four smaller cubes with two faces painted = 9 × 4 = 36; 3 edges with one cube with two faces painted = 3 × 1 = 3. In the pink cube there are 24 cubes on 12 edges which are painted on two faces. Hence the number of cubes with two faces painted = 36 + 3 + 24 = 63.

Ans 7: The number cubes with one face painted in the larger cube = 3 × 16 + 3 × 7 = 69. Number of cubes with one face painted in the 4 × 4 cube = 6 × 4 = 24 Hence, the total number of smaller cubes with one face painted = 69 + 24 = 93.

CAT Exam: Sample Papers: Answers And Solutions

Part-C: VARC

Ans 1: (C)

if clause: had known (past perfect), Main clause: would/ could have lent.

Ans 2: (A)

if clause: had done (past perfect), the main clause: would/ could/ might have had.

Ans 3: (C)

if clause: had done (past perfect), the main clause: would/ could/ might have had.

Ans 4: (B)

Previous event is simple past, then the next event must be past continuous for continuous action.

Ans 5: A

take a shower is an idiomatic phrase. Hence No error.

Ans 6: (C)

with pleasure is an idiomatic phrase. With pleasure replaces with pleasure.

Ans 7: (B)

was is used instead of were. The whole block is considered a singular subject and the singular subject takes a singular verb.

Ans 8: (D)

when two nouns get added with the use of ‘and’ and a possessive adjective article is used before both the nouns then we use plural verb but when the possessive adjective article is used with only one noun then it is considered to be one and hence singular verb is used.

Ans 9: (D)

No article is used between By and Means of transport. Quite followed by an adjective and noun uses A

Hope everyone practiced all the questions and learned the concepts well!

SEE YOU ON DAY 21

Thank you! All the Best !

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Questions related to CAT

Have a question related to CAT ?

Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

It seems unlikely that you would be able to get admission in the BTech CS branch at BIT Sindri or Mesra with a CML rank of 2058 and category rank of 433.

Key points:

1. The search results indicate that a CML (Common Merit List) rank of 2058 is quite low for admission to premier engineering colleges like BIT Sindri or NIT Mesra.

2. The cutoff ranks for BTech CS branch at these institutes are usually much higher, often in the range of 1000-2000 for the general category.

3. With a category rank of 433, you may have a better chance of getting admission in the reserved category quota, but the competition is still quite high.

4. The search results do not provide specific cutoff details for BIT Sindri or NIT Mesra, but the general trend suggests your current ranks may not be sufficient for the CS branch in these institutes.

My advice would be to:

1. Check the latest cutoff ranks and admission criteria on the official websites of BIT Sindri and NIT Mesra.

2. Explore other options like state-level engineering colleges or NITs where your current ranks may have a better chance of securing admission.

3. Consider improving your performance in the next attempt of the entrance exam to increase your chances of getting into your desired BTech program.



For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

Hello aspirant,

Every year, IIMs conduct the Common Admission Test (CAT), a national MBA entrance exam, in rotation. For admission to over 1,200 institutions and premier B-schools in India, as well as PGDM, Executive MBA, PhD, and FPM programmes, the IIM CAT exam is regarded as one of the most difficult MBA entrance exams to pass. One of the best MBA schools in India, IIMs offers PGDM and MBA programmes for students who pass the CAT exam with scores in the 82nd to 99th percentiles.

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Hope this information helps you.

Hello!

The educational qualification required for CAT exam is bachelor's degree or its equivalent from a recognized university with minimum of 50% for the open category and 45% for the SC/ST/PwD category. Since you have secured more than the required percentage in your bachelor's degree, you are eligible for CAT exam.

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I hope you will find this information helpful. Best wishes ahead!

View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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