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Achieve Success in CAT Exam: Master Inequalities, An Intro to Linear Arrangement, and Elevate Vocabulary Skill
Edited By Team Careers360 | Updated on Sep 19, 2024 03:14 PM IST | #CAT
We're back with a strategy for the Day 17 of our preparation for the CAT 2024. This article will discuss strategies for the following topics, including CAT Inequality questions and simple equations CAT questions. Students can download CAT algebra questions pdf.
Crack the CAT 2024 with the 60-day CAT exam preparation schedule we prepared for you to get a flow, plan, and schedule for your preparation.
Quantitative Aptitude for CAT 2024
The topic covered for the day is given below:
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, 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 Equations
CAT Inequalities questions on Quadratic Equations
This Story also Contains
- Quantitative Aptitude for CAT 2024
- CAT Logical Reasoning and Data Interpretation:
- CAT Exam VARC
- CAT exam books PDF free download
We have to study in detail topics like quadratic inequalities, modulus inequalities, and linear inequalities.
CAT 2024: Inequalities Questions with Answers
Aspirants can also download the CAT inequalities questions pdf for further reference and practice. The CAT 2024 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]
33
39
37
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]
21
19
18
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
0
1
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.
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 2024 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
Students can also refer to our mock tests and practice papers of CAT here: CAT inequalities questions pdf.
CAT Logical Reasoning and Data Interpretation:
The topic covered for the day is given below:
Linear Arrangement questions for CAT (Problem Solving/ Puzzles) and LR di questions for CAT
Placing objects or persons in a line with a specific rule is a called 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 CAT Linear Arrangement questions:
Questions of Linear Arrangement 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.
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowPrevious Year's 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.
Anie prepared the fifth question for both MT and ET. For MT, this question carried 5 marks.
Annie prepared one question for MT. Every other faculty member prepared more than one question for MT.
All questions prepared by a faculty member appeared consecutively in MT as well as ET.
Chetan prepared the third question in both MT and ET; Esha prepared the eighth question in both.
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:
Chetan
Esha
Beti
Dave
Answer: (D)
Q2. How many 5-mark questions were there in MT and ET combined?
13
10
12
Cannot be determined
Answer: (A)
Q3. Who prepared 15-mark questions for MT and ET?
Only Dave, Esha and Fakir
Only Beti, Dave, Esha and Fakir
Only Esha and Fakir
Only Dave and Fakir
Answer: (A)
Q4. Which of the following questions did Beti prepare in ET?
Tenth question
Ninth question
Fourth question
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.
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.
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 ction Sense.
You should have knowledge of Blood Relation .
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:
First, find out the number of persons sitting in the Seating Arrangement .
Determine the rows in the arrangement.
Determine the number of persons in each row.
Determine the direction of facing of persons sitting in the row. (This is the most important rule, most of the mistakes are made here)
Remember the information by short notations.
Use pictorial representations, and tables while solving the problems.
While reading the problem, if you find any line of no importance then skip that line for later.
Do not waste much time on a single line.
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 Exam VARC
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 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 to score well in the CAT Exam.
Tips to Learn new words:
There are some suggestions which can help you to improve your vocabulary.
Keep an organized notebook with you always.
Read the newspaper articles and write the new words along with their meanings.
Revise the written words regularly.
Try to use these new words in your communication.
Solve puzzles and crosswords.
Read novels.
Use a dictionary.
Make a target of learning at least 10 new words every day.
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 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.
Only (I)
Only (II)
Only (III)
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 $100 bottle than from a $10 bottle.
AABA
BAAB
BAAA
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 exam books PDF free download
CAT 2024 preparation tips with 30-day study material by Experts | CAT VARC: 3000+ Most Important English Words |
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Have a question related to CAT ?
Hello Ashish,
Yes, you can get admission to MBA programs at IISWBM without a CAT score, but only for certain courses. Note that IISWBM has MBA programs under the University of Calcutta and flagship courses like MBA (Day) or MBA-HRM typically require a CAT score. Other programs like the PGDM or Executive MBA/Course may have other entrance examinations on which consideration would be made, or considerations may be based on merit, and of course work experience. Always run any eligibility detail checks with the official IISWBM (https://www.iiswbm.edu/) website or The IISWBM prospectus.
gopi 30 June,2025
Hello,
Yes, a state (Delhi) NC-OBC certificate is valid for CAT 2025 , but it must be in the central government format (for appointment to posts under Government of India).
Also, it should be issued after 31st March 2025, as required by IIMs. If your certificate meets these conditions, it will be accepted.
Hope it helps !
Prachi Kumari 28 June,2025
Hello aspirant,
With 375 marks and an AIR of around 2.6 lakh in NEET 2025, getting admission to Ayurvedic & Unani Tibbia College (AUTC), New Delhi under the state quota is quite difficult. The cutoffs for government BAMS seats in AUTC generally stay below AIR 50,000, especially for the General and EWS categories. Your score may not meet the cutoff in the first or second rounds, but you might still have a slim chance in the mop-up or stray vacancy rounds, depending on how many seats remain and how other candidates opt. If you're a Delhi domicile and have all your documents ready, you should definitely apply and fill AUTC as a top choice. It’s also good to keep backup options in other AYUSH colleges open.
OISHEE BANERJEE 01 July,2025
GIBS Business School in Bangalore accepts multiple national and state-level entrance exam scores for admission to its PGDM program. You can apply using scores from exams like CAT, MAT, XAT, CMAT, GMAT, ATMA, or various state-level CETs.
The admission process typically considers your entrance exam score along with your academic record, performance in the group discussion and personal interview, and any work experience you may have. For the BBA program, admissions are generally based on your Class 12 marks and do not require entrance exam scores.
If you're planning to apply, it's a good idea to keep your exam score, academic documents, and personal statement ready for the selection rounds.
OISHEE BANERJEE 24 June,2025
If your son’s first preference is CSE, then Amrita Bangalore clearly leads among the three, simply because CSE opens more doors in terms of placements, internships, and future-proof careers. Amrita is also NAAC A++ and has a strong reputation, especially for CSE. Category 2 is also manageable fee-wise compared to higher categories.
VIT Chennai is a decent campus, and their ECE program is solid, but Category 5 means much higher fees and very low chance of branch upgrade later. CSE at VIT Chennai would have been more competitive here — but ECE at that fee tier is not as strong a deal unless your son has a strong interest in core electronics.
Manipal Bangalore (MIT Bengaluru campus) is a newer campus. ECE there is still developing in terms of placements and faculty compared to the main Manipal campus. Unless your son strongly prefers Bangalore or is getting some advantage here like scholarships or internship access, it doesn't stand out above Amrita.
So, recommendation: Go with Amrita Bangalore CSE (Category 2). It balances a strong branch with a decent campus and better long-term potential in the tech industry. If your son is open to core electronics and you’re okay with the higher cost, VIT Chennai is fine, but still comes second to CSE at Amrita.
All the best!
OISHEE BANERJEE 22 June,2025
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
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