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

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

Edited By Irshad Anwar | Updated on Sep 14, 2023 09:59 AM IST | #CAT

As the CAT 2023 exam date is approaching, you will get to know what strategy to use, which sources are the best for theory and practice, how to study for CAT in 2 months, or about the CAT exam preparation time required, how many months preparation is required for CAT, Can I crack CAT in 2 months, how to prepare for CAT in 2 months, or is there any CAT study plan for 2 months and many more. You might be looking for a CAT 2 months crash course. In this article, you'll be able to find topics on CAT inequality questions, CAT logical reasoning questions and vocabulary for CAT.

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

CAT Exam: We have developed a study plan to ace the CAT Exam based on the CAT syllabus 2023. From Day 1 through Day 16, we discussed a plan for each day.

On the basis of the CAT syllabus 2023 we covered in the first 15 days, we hope all aspirants have attempted the CAT sample paper (CAT Practice Set 4) we provided in the previous article - the day 16 of CAT preparation. After completing each CAT exam practice paper, conduct a self-analysis. This will enable you to monitor your progress, recognize your strengths and weaknesses, and tailor your study strategy.

We're back with a strategy for the Day 17 of our preparation for the CAT 2023. In this article, we will be discussing strategies for the following topics, including CAT inequalities questions and simple equations CAT questions. Students can download CAT algebra questions pdf.

Crack the CAT 2023 with the 60-day CAT exam preparation schedule we prepared for you to get a flow, plan, and schedule for your preparation.

Part-A: Quantitative Aptitude for CAT 2023

The topic covered for the day is given below:

Topic: Inequalities questions for CAT (Algebra) or Inequalities CAT questions

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, we 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, then a can have values 4, 5, 6, ………. (If integer solutions are required)

Generally, two types of cat inequalities questions are asked:

  • CAT Inequalities questions on Linear Equation
  • CAT Inequalities questions on Quadratic Equation
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CAT 2023: Inequalities questions with Answers

Inequality Questions for CAT

Aspirants can also download the CAT inequalities questions pdf for further references and practice. The CAT 2023 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, total of 12 solutions are possible.


Q2. The smallest integer n for which 4n > 1719 holds, is closest to [CAT Exam 2018]

A. 33 B. 39 C. 37 D. 35

Ans: B

Such questions can be solved by eliminating wrong options.

4n = 16n/2, For n = 38, 1619 can not be greater than 1719. So, n must be greater than 38. Of the given options only option B satisfies.

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

  • Number line.
  • Linear Equation.
  • Quadratic Equation.
  • Polynomials.
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Tips and Tricks for Preparing Inequality for the CAT Exam:

There are some important rules that has to be remembered

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

  • Modulus function gives the magnitude only.

  • Modulus always opened in negative and positive value.

  • 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.

References to Study (Theory):

  • NCERT Class 9-10
  • Handbook-Inequalities-by-Ck.pdf
  • CetKing (YouTube)

References to Study (Practice):

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

Part-B: CAT Logical Reasoning and Data Interpretation:


The topic covered for the day is given below:

Topic: Linear Arrangement questions for CAT (Problem Solving/ Puzzles) and LR di questions for CAT

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

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

Concepts involved and importance of Linear Arrangement questions CAT:

Questions of Linear Arrangements involve the concept of ranking, Blood Relation, Direction Sense etc.

It carries 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 respective positions of persons.
  • Relations among the persons/ objects.

Previous Years Questions on Linear Arrangement (LRDI questions for CAT)

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 of MT and the last one in ET. Dave prepared the last question of MT and the first one in ET.

Q1. The second question in ET was prepared by:

  1. Chetan
  2. Esha
  3. Beti
  4. Dave

Ans: (4)


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

  1. 13
  2. 10
  3. 12
  4. Cannot be determined

Ans: (1)


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

Ans: (1)


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

  1. Tenth question
  2. Ninth question
  3. Fourth question
  4. Seventh question

Ans: (1)

Solution:

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

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

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. But 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.















Q No.

1

2

3

4

5

6

7

8

9

10

11

12

13

Marks (ET)

5

5

5

5

5

5

5

5

10

10

10

15

15

Faculty Name (ET)

D

D

C

C

A

A

A

E

E

B

B

F

F

Marks (MT)

5

5

5

5

5

10

10

10

15

15

15

NA

NA

Faculty Name (MT)

F

F

C

C

A

B

B

E

E

D

D



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.

Therefore, B must prepare Q10 and 11 in ET.

Prerequisite for CAT questions on Linear Arrangement:

  • Sometimes arrangements are done on the basis of 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:

There are some points that can help you to solve the problems on 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 persons sitting in the row. (This is the most important, most of the mistakes are done 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

Part-C: CAT Exam VARC

Topic: How to learn new words (vocabulary for CAT)

Vocabulary and its importance:

Vocabulary is the collection of words and their meanings. It is an important part of our life and day-to-day communication.

With the help of good vocabulary, you will be able to:

  • Communicate in an effective way.
  • you can express what you actually want to say.
  • Your reading and writing skills will be improved.
  • You can understand the others properly.
  • In CAT Exam, long passages are given. Without 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 to score well in the CAT Exam.

Tips to Learn new words:

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

  1. Keep an organized notebook with you always.
  2. Read the newspaper articles and write the new words along with their meanings.
  3. Revise the written words on regular basis.
  4. Try to use these new words in your communication.
  5. Solve puzzles and cross-words.
  6. Read novels.
  7. Use dictionary
  8. Make a target of learning at least 10 new words every day.
  9. Try to form sentences with the new words learnt.

Practice Questions on Vocabulary [Based on cat previous year vocabulary]

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)

Ans: 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 $100 bottle than from a $10 bottle.

  1. AABA

  2. BAAB

  3. BAAA

  4. ABAB

Ans: A.

We have to choose correct word in all sentences.

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.

We will be back with CAT Preparation Day 18 tomorrow. Do practice and be focused.

Thank You

All the best.

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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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