Achieve Success in CAT Exam: Master Inequalities, An Intro to Linear Arrangement, and Elevate Vocabulary Skill

CAT 2025 Quantitative Aptitude

Quantitative Aptitude for CAT 2025 is a critical section that tests your mathematical and analytical skills. Covering topics like Arithmetic, Algebra, Geometry, and Number Systems, mastering this section is key to scoring high. Strengthen your preparation with CAT mock tests, CAT sample papers, and topic-wise practice sets based on the latest CAT Quantitative Aptitude syllabus.

Inequalities Questions for CAT (Algebra)

In Linear Equations and Quadratic Equations, we deal with problems where the Left-hand side is equal to the right-hand side to find the unknown value.

In Inequalities, the LHS and RHS are not equal (but have the possibility of being equal).

Any of the following cases are possible in CAT inequalities questions:

LHS ≥ RHS; LHS > RHS; LHS < RHS; LHS ≤ RHS

For example, if we say a > 3, a can have values 4, 5, 6, ………. (If integer solutions are required)

Generally, two types of cat inequality questions are asked:

• CAT Inequalities questions on Linear Equations

• CAT Inequalities questions on Quadratic Equations

We have to study in detail topics like quadratic inequalities, modulus inequalities, and linear inequalities.

CAT 2025: Inequalities Questions with Answers

Aspirants can also download the CAT inequalities questions pdf for further reference and practice. The CAT 2025 inequalities questions with answers are given below:

Q1. The number of distinct pairs of integers (m, n) satisfying |1 + mn| < |m + n| < 5 is:

[TITA, CAT Exam 2021, Slot-3]

Solution:

|1 + mn| < |m + n| < 5

⇒|1 + mn| < |m + n

On squaring both sides,

(1 + mn)2 < (m + n)2

⇒1 + 2mn + m2n2 < m2 + n2 + 2mn

⇒1 - n2 - m2 + m2n2 < 0

⇒ (1 - m2) (1 - n2) < 0

Case 1:

For integer values of m and n, if n2 > 1,
Then (1 - m2) must be positive which is possible only when m = 0.

|m + n| < 5

⇒ |n| < 5

So, n can be ±2, ±3, ±4 (n cannot be ±1, if taken product becomes 0)

Case 2:

(1 - m2) (1 - n2) < 0

Possible if n = 0 and m2 > 1

Similarly, m can be ±2, ±3, ±4 (m cannot be ±1, if the taken product becomes 0)

In each case, we have six possible solutions.

Therefore, a total of 12 solutions are possible.

Q2. The smallest integer n for which 4n ＞1719 holds, is closest to:

[CAT Exam 2018]

1. 33

2. 39

3. 37

4. 35

Solution:

Given that 4n ＞1719
⇒ (161/2)n ＞1719
⇒ 16n/2＞1719
So, we can say that n/2 > 19
⇒ n > 38
The closest value to 38 from the options is 39.

Hence, the correct answer is 39.

Q3. The number of integers n that satisfy the inequalities |n – 60| < |n – 100| < |n – 20| is:

[CAT 2021 Slot 1]

1. 21

2. 19

3. 18

4. 20

Solution:

Given: |n – 60| < |n – 100| < |n – 20|

The distance between these two points can be represented by |x – y| or |y – x|.

Let's take the first part of the inequality.
|n – 60| < |n – 100|
This inequality holds good for the values of n below 80.
Hence ‘n’ should be less than 80.

Now Let's check for the later part of the inequality.
|n – 100| < |n – 20|
This inequality holds good for the values of n above 60.
Hence ‘n’ should be greater than 60.

∴ Values of ‘n’ range from 61 to 79.
So, the total possible integers that satisfy this inequality are 19.

Hence, the correct answer is 19.

Q4. The largest real value of a for which the equation |x + a|+|x – 1| = 2 has an infinite number of solutions for x is:

[CAT 2022]

1. -1

2. 0

3. 1

4. 2

Solution:

In the question, it is given that the equation |x+a|+|x-1|=2 has an infinite number of solutions for any value of x.

This is possible when x in |x + a| and x in |x - 1| cancel out.
Case 1:
x + a < 0, x ≥ 0
⇒ - a - x + x - 1 = 2
⇒ a = -3
Case 2:
x + a ≥ 0 and x - 1 < 0
⇒ x + a - x + 1 = 2
⇒ a = 1
∴ The largest value of a is 1.
Hence, the correct answer is 1.

Prerequisite to Attempting Tough Questions On Inequalities for the CAT Exam:

• Number line.

• Linear Equations.

• Quadratic Equations.

• Polynomials.

Tips and Tricks for Preparing Inequality for the CAT Exam:

Some important rules have to be remembered.
Those are:

• Arithmetic Mean is always greater than or equal to the Geometric Mean.

• The modulus function gives the magnitude only.

• Modulus always opened in negative and positive values.

• Learn the basic rules of solving inequality.

• If -a > -b, then a < b.

• If -a < -b, then a > b.

• If a > b and c < 0 then ac < bc.

• If a > b and c > d then a + c > b + d.

• If the sides of an inequality are multiplied by the same negative quantity, the sign of inequality must be reversed.

All the rules must be learnt to perform well in the CAT 2025 exam.

References to Study (Theory):

• NCERT Class 9-10

• Handbook-Inequalities-by-Ck.pdf

• CetKing (YouTube)

References to Study (Practice):

• Quantitative Aptitude Quantum CAT by Sarvesh Verma

• https://iim-cat-questions-answers.2iim.com

• CAT Previous Year's Question Papers

Students can also refer to our mock tests and practice papers of CAT here: CAT inequalities questions pdf.

CAT Logical Reasoning and Data Interpretation

CAT Logical Reasoning and Data Interpretation (CAT LRDI) is one of the most challenging yet scoring sections of the CAT exam. It assesses your problem-solving, analytical thinking, and data interpretation abilities. For CAT 2025, focus on mastering puzzles, caselets, graphs, and tables. Regularly practising CAT sample papers and CAT mock tests will enhance accuracy and boost confidence.

Linear Arrangement questions for CAT (Problem Solving/ Puzzles)

Placing objects or persons in a line with a specific rule is called linear arrangement.

According to a given set of rules or instructions, people have to be seated in a single line. Sometimes these arrangements are referred to as “Seating Arrangement.”

Concepts involved and importance of CAT Linear Arrangement questions:

Questions of Linear Arrangement involve the concept of Blood Relation, Ranking, Direction Sense etc.

Also, Ranking questions carry a good weightage in the CAT Exam as seen in last year’s Exams.

Knowledge of solving problems enables you:

• To identify the unique position of a person in an arrangement.

• To identify the respective positions of persons.

• Relations among the persons/ objects.

Previous Year's Questions on Linear Arrangement (LRDI questions for CAT)

Linear Arrangement is a frequently tested topic in the CAT Logical Reasoning and Data Interpretation (LRDI) section. These questions require arranging individuals or objects in a line based on given conditions. CAT previous year papers often feature tricky linear arrangement sets that test your logical sequencing and condition-based deduction skills. Linear Arrangement questions for CAT are given below:

The first-year students in a business school are split into six sections. In 2019 the Business Statistics course was taught in these six sections by Annie, Beti, Chetan, Dave, Esha, and Fakir. All six sections had a common midterm (MT) and a common end term (ET) worth 100 marks each. ET contained more questions than MT. Questions for MT and ET were prepared collectively by the six faculty members. Considering MT and ET together, each faculty member prepared the same number of questions. Each MT and ET had at least four questions that were worth 5 marks, at least three questions that were worth 10 marks, and at least two questions that were worth 15 marks. In both MT and ET, all the 5-mark questions preceded the 10-mark questions, and all the 15-mark questions followed the 10-mark questions.

[CAT Exam 2019]

The following additional facts are known.

1. Anie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.

2. Annie prepared one question for MT. Every other faculty member prepared more than one question for MT.

3. All questions prepared by a faculty member appeared consecutively in MT as well as ET.

4. Chetan prepared the third question in both MT and ET; Esha prepared the eighth question in both.

5. Fakir prepared the first question in MT and the last one in ET. Dave prepared the last question for MT and the first one for ET.

Q1. The second question in ET was prepared by:

1. Chetan

2. Esha

3. Beti

4. Dave

Answer: (D)

Q2. How many 5-mark questions were there in MT and ET combined?

1. 13

2. 10

3. 12

4. Cannot be determined

Answer: (A)

Q3. Who prepared 15-mark questions for MT and ET?

1. Only Dave, Esha and Fakir

2. Only Beti, Dave, Esha and Fakir

3. Only Esha and Fakir

4. Only Dave and Fakir

Answer: (A)

Q4. Which of the following questions did Beti prepare in ET?

1. Tenth question

2. Ninth question

3. Fourth question

4. Seventh question

Answer: (A)

Total Solution:

The number of questions in MT and ET is at least 4 questions for 5 marks, at least 3 ques for 10 marks, and 2 questions for 15 marks

Marks constituted by these questions = 5 × 4 + 10 × 3 + 15 × 2 = 80

The remaining 20 marks can be distributed as (5, 5, 5, 5), (5, 5, 10), (5, 15), (10, 10)

So, the maximum number of questions in a paper can be 4 = 3 + 2 + 4 = 13

It is also given that each faculty (6) prepared an equal number of questions. So, the possibilities of questions (Total of both) are 6, 12, 18, and 24.

So, the total number of questions in both = 24 (as 6, 12, and 18 are less than the required)

Therefore, MT and ET must have 12 questions each. However, this is wrong since the number of questions in ET is greater than the number of questions in MT.

So, ET must have 8 questions of 5 marks, 3 questions of 10 Marks and 2 questions of 15 marks.

MT has 5 questions of 5 marks, 3 questions of 10 Marks and 3 questions of 15 marks. (Since the 5th question is of 5 marks, question case of 10,10 marks is ruled out)

Another only possibility is ET has 13 questions and MT has 11 questions.

A prepared only one question for MT. So, A must be followed by B (only possibility).

Therefore, A must prepare three consecutive questions in ET.

Hence, B must prepare Q10 and 11 in ET.

Prerequisite for CAT questions on Linear Arrangement:

• Sometimes arrangements are made based on Ranking. So, you must have knowledge of Ranking.

• Similarly, you should have knowledge of Direction Sense.

• You should have knowledge of Blood relations.

Tips and Tricks to Solve Linear Arrangement Questions CAT

Mastering Linear Arrangement questions in CAT requires consistent practice and a clear approach. This approach helps candidates create their strategy for the different types of arrangement questions. There are some points that can help you to solve the problems with the linear arrangement:

1. First, find out the number of persons sitting in the Seating Arrangement.

2. Determine the rows in the arrangement.

3. Determine the number of persons in each row.

4. Determine the direction of facing of the persons sitting in the row. (This is the most important rule, most of the mistakes are made here)

5. Remember the information by short notations.

6. Use pictorial representations and tables while solving the problems.

7. While reading the problem, if you find any line of no importance, then skip that line for later.

8. Do not waste much time on a single line.

9. Make all the possibilities. Do not leave any possibility.

References to Study (Theory):

• LRDI by Nishit K Sinha (Basic)

• Cat preparation-iQuanta (YouTube Channel)

• MBAP CAT EBook (Concept Theory)

References to Study (Practice):

• Verbal and Non-Verbal Reasoning by R S Aggarwal. (Basic)

• LRDI for CAT and GMAT by Nishit K Sinha. (Advance)

• MBAP CAT EBook (Practice Questions).

• CAT Previous Years' Question Papers

CAT VARC Vocabulary

CAT 3000+ Vocabulary Ebook has a huge collection of words and their meanings. It is an important part of our life and day-to-day communication. Here are the benefits of having a good vocabulary before the CAT 2025 Exam:

• Communicate effectively.

• You can express what you want to say.

• Your reading and writing skills will be improved.

• You can understand the others properly.

• In the CAT Exam, long passages are given. Without a good vocabulary, understanding them will be difficult for you.

• Direct questions on Synonyms and Antonyms are also asked in CAT. A good vocabulary will help you score well in the CAT Exam.

Tips to Learn new words:

There are some suggestions which can help you improve your vocabulary.

1. Keep an organised notebook with you always.

2. Read the newspaper articles and write the new words along with their meanings.

3. Revise the written words regularly.

4. Try to use these new words in your communication.

5. Solve puzzles and crosswords.

6. Read novels.

7. Use a dictionary.

8. Make a target of learning at least 10 new words every day.

9. Try to form sentences with the new words learnt.

Students can also practice “Vocabulary for CAT exam book”, “5000 CAT vocabulary pdf”, and “CAT vocabulary questions with answers pdf” to grasp more on this topic.

Practice Questions on Vocabulary [Based on CAT Previous year Papers]

Q1. A word has been used in sentences in THREE different ways. Choose the option corresponding to the sentence in which the usage of the word is CORRECT or APPROPRIATE.

[IPMAT 2020 Sample Paper]

CONFLATE

(I) I was able to conflate the two processes into one, blending it down into a solid formula.

(II) The bag is divided into conflate compartments.

(III) The dogs started to snarl at each other so I had to conflate them.

1. Only (I)

2. Only (II)

3. Only (III)

4. Both (I) and (II)

Solution: A

Conflate: Combine two or more sets of information, texts or ideas into one.

Only in (I), sense is off to combine.

Q2. [Based on CAT exam]

The notion that consumers are logical decision-makers with complete insight into the factors determining the choices they make is simplistic (A)/ vapid (B).

A shopper’s mind is not a clean slate. Information and experience are refracted (A)/ retracted (B) through the lens of belief.

Information that’s contrary (A)/ inconsistent (B) with those beliefs is likely to be rejected.

Even experience is malleable (A)/ intractable (B). For many, the same glass of wine tastes better when poured from a

100bottlethanfroma

10 bottle.

1. AABA

2. BAAB

3. BAAA

4. ABAB

Solution: A

Vapid means uninspired or insipid.
"Simplistic" should be used here.

Refracted’ should be used here, as the sentence refers to the “lens of belief.
‘Retracted’ meaning ‘taken back’ does not make sense here.

"Contrary" is normally followed by ‘to’ whereas ‘inconsistent’ is followed by ‘with’.
So "inconsistent" is the right choice here.

‘malleable’ is used in the sense of being moldable or changeable, which is the right choice for this blank. ‘Intractable’ or rigid is the exact opposite of what the author wants to convey.

Prerequisite:

• Commonly used words in daily life.

• Tenses and sentence formation.

References to Study (Theory):

• Word Power Made Easy.

• CAT Edurav (YouTube Channel)

References to Study (Practice):

• Wren and Martin

• Online tool: Burning Vocabulary.

• Practice Sample Question Papers.

CAT 2025 Ebooks by Careers360

CAT 2025 eBooks by Careers360 are expertly curated digital guides designed to support focused and effective exam preparation. Covering all three sections, Quantitative Aptitude, VARC, and DILR, these eBooks include comprehensive theory, shortcut techniques, solved examples, and practice questions.