CAT Mock Test Series 6- Sample Paper, Quant, LR, VARC | Day 24

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The CAT 2024 Exam is scheduled for November 24, 2024, To help you in preparing, we have produced a 60-day program complete with sample assessments and practice papers. This article features previous CAT question papers with answers to clear up any of your doubts, This will help in increasing your preparation, and boost your confidence.

CAT Mock Test Series: Sample Questions and Solutions

This CAT question paper with solution based on the CAT syllabus 2024 has been covered in 23 days, and consists of three Sections:

Part- A consists of 8 questions.

Part- B consists of 6 questions.

Part- C consists of 10 questions.

CAT Test Series 2024 (Quantitative Aptitude) CAT Exam Sample Paper:

Q1. log₄₉ (7log₂ (2 + log₃ (1 + 2log₂x))) = 1/2. Find the value of x.

1. 4

2. 1

3. 2

4. ½

Q2. The value of x satisfying log₁₀(x² + 3x + 21) = (2 − log₁₀4) is:

1. 5

2. 0

3. 1

4. 3

Q3. If log₅₄, log₅ (3x – 1), log₅ (3x +7) are in arithmetic progression, then the value of x is equal to:

1. 5

2. 0

3. 2

4. 3

Q4. A family consists of a mother, a father, and some children. The average age of the members of the family is 30, the father’s age is 50 years, and the average age of the mother and children is 20. Children in the family are ______________ [TITA]

1. 2

2. 3

3. 1

4. 5

Q5. Consider a group of 30 persons whose average weight is 30 kg. If n new persons join this group whose average weight is m kgs. If it is known that m > 30 and m + n = 37, what is the maximum possible average weight of the group now?

1. 30.363 kgs

2. 30.193 kgs

3. 30.352 kgs

4. 30.166 kgs

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)

1. 20

2. 40

3. 60

4. 50

Q7. Find the average increase rate of increase in the price of an article in the first year is 40% and that in the second year is 30%.

1. 41

2. 56

3. 40

4. 38

Q8. A can type a sheet in 4 minutes, B in 5 minutes and C in 6 minutes. The average number of sheets typed per hour per person for all three persons is

1. 25/3

2. 30/3

3. 65/3

4. 37/3

CAT Mock test series 2024: CAT DILR sample Questions (Logical Reasoning and Data Interpretation)

Direction (Q1-Q3):

Annie, Ben, Cain, Dan and Engel are five friends who purchased a book each that was related to one of the following fields: Architecture, Biotechnology, Criminology, Demography and Economics. Further, the following information is known.

1. No friend's first letter of the name matches with the field to which the book purchased is related.

2. Annie and Dan love to read books related to Criminology apart from the books they purchased.

3. Engel hates Criminology and Biotechnology and hence did not purchase them

4. The first letter of the field to which the book that Ben purchased pertains, matches with the first letter of the name of the friend who purchased a book about Biotechnology.

Q1. After a month of reading, Annie exchanges her book with Dan and then Dan exchanges this book with Engel. The exchanges resulted in the first letter of the friends matching with the field to which the book belonged without violating conditions (b) to (d).

Which of the following is true?

1. Engel bought a book related to Demographics.

2. Annie bought a book related to Demographics.

3. Dan bought a book related to Economics.

4. Engel bought a book related to Architecture.

Q2. Which of the following is not necessarily true?

1. Either Annie or Ben bought a book related to Criminology.

2. Dan bought a book related to either Architecture or Economics.

3. Either Dan or Engel bought the book related to Architecture.

4. Either Engel or Cain bought the book related to Demographics.

Q3. While delivering the books, the salesman interchanged the books of two friends in such a manner that the field to which the book belonged and the starting letter of only one of the friends matched. However, conditions (b) to (d) were not violated.

Which of the following conditions lets you completely determine the fields of the books possessed by the five friends?

1. Annie’s and Engel’s books were interchanged.

2. Neither Annie nor Engel possesses a book related to Economics after the salesman interchanged their books.

3. Neither Dan nor Engel had books related to Biotechnology after the interchange

4. Interchange happened between the books of Annie and Dan.

Q4. Ajay, Bablu, Chinti, Dev, Elish and Faijal are six persons in six chairs around a table with only six chairs. Ajay is opposite Dev. Chinti is to the immediate right of Ajay and is next to Elish.

Which of the following is definitely FALSE?

1. Ajay and Elish are not opposite each other.

2. Elish is between Chinti and Dev.

3. Chinti is between Ajay and Elish.

4. Bablu and Faijal are opposite each other.

Q5. A, B, C, D and E are five apartments on a floor. Each pair of apartments has a path connecting them. How many paths are there in all?

1. 12

2. 10

3. 5

4. 2

Q6. A doctor, a lawyer and an engineer meet at a place. The doctor has not come from the hotel or the club. Each of them has come from only one of the following places, the club, the hotel and the theatre. Also, no two people have come from the same place. If the engineer has come from the hotel, then the lawyer has not come from

1. the theatre or the hotel.

2. the theatre or the club.

3. the club or the hotel.

4. the club or the theatre or the hotel.

CAT Exam sample paper 2024: CAT sample questions for VARC (Verbal Ability & Reading Comprehension) Previous year question paper of CAT Exam

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

Q1: If he was to decide to go to college, I for one, would recommend that he go to Yale University.

1. If he were to decide to go to college

2. Had he decided to go to college

3. In the event that he decides to go to college

4. No correction required

5. Error Detection

Q2. Our mathematics teacher often emphasizes (a)/ on the need (b)/ for a lot of practice (c)/ No error (d)

1. (a)

2. (b)

3. (c)

4. (d)

Q3. I do not mind (a)/ to be disturbed (b)/ while watching T.V. (c)/ No error (d)

1. (a)

2. (b)

3. (c)

4. (d)

Q4. Reforms can elevate (a)/ poverty and usher (b)/ in economic prosperity (c)/ No error (d)

1. (a)

2. (b)

3. (c)

4. (d)

Fill in the appropriate word/Phrase

Q5. _____, doesn’t she?

1. Anna doesn’t visit her friends daily

2. Anna has a red pen

3. Anna doesn’t play volleyball

4. Anna does not do a quick revision before the exam

Reading Comprehension

IT’S LIKE READING Dostoevsky on a bad summer day. There are so many tormented souls out there caught in a morality play. Its emotional intensity is only matched by the inevitability of the x xx it raises about country, religion, power, and retribution. It’s big, shapeless, chaotic, and in the end, a rewarding experience of the imagination. But then, you’re not reading Great Russian. You’re living in, dare I say, a creative phase of politics. Rich in ideas and arguments, intense in its interplay of passions, nuanced in its undertones of morality and ethics, and ambitious in its pursuit of freedom, politics today, as a genre in creativity, is as good as the original works in other realms of the human mind, be it fiction or philosophy.

A sign of the times could be the profusion of political titles in publishing. They are mostly built on the themes of populism, outsiderhood, globalisation and resentment. Hardly a week passes without a full-length review in the book pages on yet another tome on a world gone astray, a world that’s being led to an incendiary denouement by revolutionaries and revisionists. The moment deserves such interventions because, by common intellectual consensus, in the evolution of post-World War II politics, we are at the next history-shifting stage after 1989, Europe’s annus mirabilis.

Then, the stage was an extension of literature: what was imagined in a controlled society sought freedom as the Lie unravelled. In Russia once imagined by Gogol, and lately reclaimed by Solzhenitsyn, the sight of the last general secretary of the Soviet Union letting the empire crack and go away needed another prophet, another novelist. Elsewhere, in a vassal state, revolution earned an adjective as romantic as ‘velvet’, and in the vanguard of its freedom struggle were writers and singers. In the end, the philosopher would be king. It was a time when an idea that promised man an alternative more liberating than religion proved to be history’s biggest ghost story.

Today, it’s the idea of freedom, as it has always been, that propels politics. It’s a different cast. No figures larger than their historical size. No one is pretending to be the last arbiter of our destiny. And no one is talking in a language that would be taught generation after generation. The disappearance of grandeur from the arena even prompted some pundits a while ago to wail over the death of politics. This moment in politics has an overwhelming sense of ordinariness about it. The new salvation theologians are all ordinary guys, tapping into the fears of people who have lost their balance in a world moving at a pace they cannot cope with. They can easily be categorised into types.

Q6. What does the author mean by the phrase “a creative phase of politics”?

(I) Politics today, as a genre in creativity, is as good as the original works in other realms of the human mind, be it fiction or philosophy.

(II) Politics today, on moral and creative grounds, is big, shapeless, chaotic, and in the end, a rewarding experience of the imagination.

(III) Politics today is rich in ideas and arguments, fervent in its interplay of passions and nuanced in its undertones of morality and ethics.

1. Only (I) is correct

2. Only (II) is correct

3. Both (I) and (II) are correct

4. Both (I) and (III) are correct

5. All are correct

Q7. Which of the following statements summarizes Paragraph 04 in the best possible manner?

1. Modern politics has evolved after the death of primeval politics and it finds no relevance in its classical glory as the idea of freedom and the sense of ordinariness have substituted the core ideologies.

2. In an unequal world, the old bipolarity of politics has ceased to work, for the Left and the Right have not only lost the social space, they have lost the argument to a new set of liberators for whom it is not ideology that matters but ideas that feed on resentment.

3. The importance and culture of politics have diminished since the arrival of ordinary people in the arena that witnessed the death of ancient political ideologies.

4. As history choreographs a heady piece of politics, a certain amount of pessimism has taken over the fears of people who have lost their balance in a world moving at a pace they cannot cope with.

5. None of the above.

Directions: Choose the word/group of words which is most similar in meaning to the word/group of words printed in bold as used in the passage.

Q8. Vanguard

1. Pattern

2. Avant-garde

3. Criterion

4. Inspiration

5. Standard

Directions: Choose the word/group of words which is most opposite in meaning to the word/group of words printed in bold as used in the passage.

Q9. Denouement

1. Misfortune

2. Adjournment

3. Genesis

4. Epilogue

5. Transpiration

Q10. Grandeur

1. Inclusiveness

2. Sophistication

3. Magnification

4. Indifference

5. Classicalism

CAT Question Paper with solutions Part-1: CAT Test Series 2024 (Quantitative Aptitude)

Answer 1: (B)

log₄₉ (7log₂ (2 + log₃ (1 + 2log₂x))) = ½

⇒ 7log₂ (2 + log₃(1 + 2log₂x)) = 49^1/2= 7

⇒ log₂(2 + log₃ (1 + 2log₂x)) = 1

⇒ 2 + log₃ (1 + 2log₂x) = 2

⇒ log₃ (1 + 2log₂x) = 0

⇒ (1 + 2log₂x) = 3⁰ = 1

⇒ 2log₂x = 0

⇒ log₂x = 0

⇒ x = 1

Answer 2: (C)

log₁₀(x² + 3x + 21) = (2 − log₁₀4)

⇒ log10(x² + 3x + 21) = (log¹⁰ 10² − log₁₀ 4)

⇒ log10(x² + 3x + 21) = (log₁₀ 100 − log₁₀4)

⇒ log10(x² + 3x + 21) = (log₁₀ 100/4)

⇒ log10(x² + 3x + 21) = (log₁₀25)

⇒ x² + 3x + 21 = 25

⇒ x² + 3x - 4 = 0

⇒ (x + 4) (x - 1) = 0

⇒ x = - 4 or 1.

Hence, the correct answer is 1.

Answer 3: (C)

log₅ 4, log₅ (3x – 1), log₅ (3^x +7) are in Arithmetic progression(AP).

⇒ log₅(3^x – 1) - log₅ 4 = log₅(3^x + 7) - log₅ (3^x – 1)

⇒ log₅[(3^x – 1)/4] = log₅ [(3^x +7)/(3^x – 1)]

⇒ (3^x – 1)/4 = (3^x +7)/(3^x – 1)

Let 3^x = y

⇒ (y – 1)/4 = (y +7)/(y – 1)

⇒ (y – 1)² = 4 (y +7)

⇒ y² + 1 – 2y = 4y + 28

⇒ y² – 6y – 27 = 0

⇒ y² – 9y + 3y – 27 = 0

⇒ (y – 9) (y + 3) = 0

⇒ y = 9 or –3

3x cannot be negative.

So, 3^x = 9
⇒ x = 2

Hence, the correct answer is 2.

Answer 4: (C)

Let the average age of children be x and there are n children in the family.

Let the age of the mother be y.

So, nx + y = (n + 1) 20 - - - - - - -(1)

Also, nx + y + 50 = (n + 2) 30 - - - - - - (2)

Subtracting 1st equation from the 2nd, we get,

50 = 30n + 60 – 20n – 20

⇒ 50 = 10n + 40

⇒ n = 1

Hence, there is only 1 child in the family.

Answer 5: [A]

Total weight of 30 + n persons = 30x 30 + m x n = 900 + mn

Average = (900 + mn)/ (30+ n)

Use hit and trial

m = 31; n = 6; Average = 1086/36 = 30.166

m = 32; n = 5; Average = 1060/35 = 30.285

m = 33; n = 4; Average = 1086/34 = 30.352

m = 34; n = 3; Average = 1002/33 = 30.363

m = 35; n = 2; Average = 970/32 = 30.312

m = 36; n = 1; Average = 936/31 = 30.193

So, the maximum possible average weight can be 30.363 kgs.

Answer 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

⇒ 50p = 2.5p²

⇒ p = 20

Hence, the correct answer is 20.

Answer 7: (A)

Let the initial Price = 100

Price after 1st year after 40% increase = 140

Price after 2nd year after 30% increase = 140 × (130/100) = 182

∴ Net increase in Price = 182 - 100 = 82

Average change per year = 82 / 2 = 41

Hence, the correct answer is 41.

Answer 8: (D)

A can type 60/4 = 15 sheets in 1 hour

B can type 60/5 = 12 sheets in 1 hour

C can type 60/6 = 10 sheets in 1 hour

Total sheets typed in 1 hour = 15 + 12 + 10 = 37

So, Average sheets per person = 37/3

Hence, the correct answer is 37/3.

CAT Question Paper with solutions Part-2: CAT Mock test series 2024: CAT DILR Sample Questions

Answer 1: (A)

Let us represent the person’s name with A, B, C, D and E and also the fields to which each book belongs to A, B, C, D and E.

Annie exchanges with Dan and Dan exchanges with Engel so the book possessed by Annie goes to Engel. Hence, Annie purchased a book related to Economics. Don Purchased a book related to Architecture and Engel purchased a book related to Demographic.

Answer 2: (D)

See Solution of Q1.

Statement (A) is true.

Statement (B) is true.

Statement (C) is true.

Statement (D) is not necessarily true.

Answer 3: (B)

Condition (A) Annie and Engel's books were interchanged. There can be two possibilities with this condition with Annie taking books related to Demography or Architecture.

Condition (B) states that neither Annie nor Engel possess books related to economics.

Since Annie and Engel did not get a book related to economics that means Dan possessed a book related to economics, Annie possessed a book related to Architecture and Engel possessed a book related to demographics.

Answer 4: (D)

Ajay is opposite Dev. Chinti is to the immediate right of Ajay and next to Elish. So, the arrangement is as follows:

Answer 5: (B)

A, B, C, D and E are five apartments. Each pair has a path between them. The pairs may be AB, AC, AD, AE, BC, BD, BE, CD, CE, or DE. So, there are altogether 10 paths. i.e. ⁵C₂ = 10.

Answer 6: (A)

It is clear that the doctor is not from the Hotel or Club, the Engineer is from the Hotel.

So, the Lawyer must be from the club. So, the combination is as follows.

(Engineer − Hotel) (Doctor − Theatre) (Lawyer − Club)

So, the Lawyer has not come from the Theatre or Hotel.

CAT Question Paper with solutions Part-3: CAT Exam sample paper 2024: CAT sample questions for VARC

Answer 1: (A)

According to the imaginary condition we use ‘were’ (past simple) in place of was. We use past simple with the modal with its past form as the main clause.

Answer 2: (B)

Start/emphasis/deny/order etc. these verbs generally do not take prepositions.

Answer 3: (B)

Use “being disturbed” instead of “to be disturbed”.

Mind verb uses gerund.

Answer 4: (A)

Replace elevate with alleviate

Explanation: Elevate- to give sb/sth a higher position or rank.

Alleviate- to make sth less severe.

Answer 5: (B)

“has” is used to show possession. It is Present Indefinite’s Affirmative sentence hence doesn’t she is used.

Answer 6: (D)

Explanation: Refer to 1st paragraph of the passage, You’re living in, dare I say, a creative phase of politics. Rich in ideas and arguments, intense in its interplay of passions, nuanced in its undertones of morality and ethics, and ambitious in its pursuit of freedom, politics today, as a genre in creativity, is as good as the original works in other realms of the human mind, be it fiction or philosophy. So only statements (i) and (iii) explain what the author meant to convey. Hence option (d) is correct.

Answer 7: (A)

Explanation: Read the 4th paragraph carefully, it mentions how politics has evolved over time, and modern politics has no significance in comparison to the old and historical ones. Today politics has its own ideologies which are marked as ordinary by the author.

Hence, only option (a) summarizes the paragraph appropriately and explains its context briefly and precisely.

Answer 8: (B)

Explanation: Vanguard means a position at the forefront of new developments or ideas. Avant-garde means a group of artists, musicians, or writers working with new and experimental ideas and methods. Hence both are similar in meaning.

Answer 9: (C)

Explanation: Denouement means the outcome of a situation when something is decided or made clear. Genesis means the origin or mode of formation of something.

Hence, both have opposite meanings.

Answer 10: (D)

Explanation: Grandeur means splendour and impressiveness, especially of appearance or style. Indifference means unimportance.

Hence, both have opposite meanings.

Study material for CAT 2024