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CAT 2025 Preparation Strategy on Quant (QA), DI, VA and LR - Day 1
CAT 2025 Preparation Strategy-Day 1: A strong foundation in Quantitative Aptitude (QA), Data Interpretation (DI), Verbal Ability and Logical Reasoning (LR) is crucial for success in the CAT 2025 exam. As part of our structured 60-day CAT 2025 preparation plan, this article provides strategies to help aspirants build conceptual clarity, improve accuracy, and strengthen problem-solving skills across these sections. On Day 1, we begin with one of the core topics of Quantitative Aptitude, Number System. This fundamental concept is frequently tested in the exam. A clear understanding of number properties, divisibility rules, and factors will establish a solid mathematical base, preparing you to tackle more advanced topics in the days to come.
This Story also Contains
- What are Numbers?
- Previous Year CAT Questions on the Number System
- How to prepare for Number Systems (Basics)?
- Easy tips and formulae for Number Systems:
- References to practice number systems questions for the CAT 2025 exam
- Data Interpretation(DI) for CAT 2025
- What is a Bar graph?
- CAT 2025 preparation Tips - DI (Bar Graph):
- References for CAT DI 2025
- CAT 2025 Preparation for VARC: Noun Questions for CAT Exam
- What are Nouns?
- Tips On CAT 2025 Preparation for Verbal Ability (Noun):
- References for CAT 2025 (Nouns)
- Free PDFs for CAT Preparation 2025
What are Numbers?
A number is referred to as a mathematical value which represents a certain quantity. In the international number system, the place values are called “Ones(1), tens(10), hundreds(100), thousands(1000), ten thousands(10,000), hundred thousands(1,00,000), millions(10,00,000), ten millions(107), hundred millions(108), billions(109) and so on.
The classification of the Number system is as follows:
Real numbers: All numbers in the number line, including positive, negative and zero.
Imaginary numbers: Numbers when squared, give a negative number.
Rational Numbers: Numbers that can be expressed in the p/q form, q ≠ 0
Irrational numbers: Numbers that cannot be expressed in the p/q form
Integers: Numbers that can be positive, negative and zero, excluding fractions.
Whole numbers: Positive numbers, including zero
Natural numbers: Positive numbers excluding zero, start from 1.
The number system is one of the important topics that come up in QA questions for the CAT exam. To prepare for number system questions for the CAT exam, the topic has been segregated into five parts as given below in the CAT questions on number system:
Classification of Numbers, Base System, Decimal to Fraction Converter
Divisibility Rules and Remainder Theorem
CAT 2025 College Predictor
Use CAT 2025 College Predictor to check your chances for IIM and top MBA calls based on CAT percentile, profile, work experience and cut-off trends.
Use NowCareers360 has prepared a 60-day series for CAT 2025 preparation for students for the above-mentioned topics to discuss various examples and practice problems. This article includes the discussion of topics of Classification of Numbers, fractions to decimals examples, the Indian number system, binary number system, number system in computer, Decimal to fraction CAT questions, and base systems concepts and questions for the CAT exam, as well as CAT practice questions on number systems.
Previous Year CAT Questions on the Number System
Question 1: Let m and n be natural numbers such that n is even and 0.2 < m/20, n/m, n/11< 0.5.
Then m–2n equals:
[CAT Question Paper 2020]
4
2
1 - Correct answer
3
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Solution:
0.2 < m/20, n/m, n/11 < 0.5
⇒ 1/5 < m/20, n/m, n/11 < ½
Taking one at a time, we get
1/5 < m/20 and m/20 < ½
So, m > 4 and m < 10
Therefore, possible values of m = 5, 6, 7, 8, 9
Now, 1/5 < n/11 and n/11 < ½ and n is even.
So, n > 11/5 and n < 11/2
Therefore, a possible value of n is 4 (since 4 is the only even natural number between 11/5 and 11/2)
Since 0.2 < n/m < 0.5
⇒ 20 > m > 8 [Putting the value of n = 4]
So, the only possible value of m is 9.
Now, m – 2n = 9 – 2 × 4 = 1
Hence, the correct answer is 1.
Question 2: Convert the number 1982 from base 10 to base 12. The result is?
(CAT Question Paper 2000)
1182
1912
1192 - Correct answer
1292
Answer:
For that, divide 1974 by 12 as shown:
Divisor | Quotient | Remainders |
12 | 1982 | |
12 | 165 | 2 |
12 | 13 | 9 |
12 | 1 | 1 |
0 | 1 |
Write the remainder from bottom to top.
So, in base 12, 1982 is 1192.
Hence, the correct answer is 1192.
Question 3: If n is an integer and n(n + 1)(n + 2) is divisible by 8, which of the following is necessarily true?
n is even - Correct answer
n is odd
n is divisible by 8
n is not divisible by 8
Answer:
For n(n+1)(n+2) to be divisible by 8, at least one of the factors n, (n + 1), (n + 2) must be divisible by 2, and at least one must be divisible by 4.
The product of three consecutive integers always contains at least one multiple of 2 and one multiple of 4, ensuring that their product is divisible by 8.
This happens when n is even.
Hence, the correct answer is “n is even”.
Question 4: If the sum of the squares of three consecutive positive integers is 2030, then the middle integer is:
25
26 - Correct answer
27
28
Answer:
Let the three consecutive integers be n, n + 1, and n - 1.
According to the question,
$n^2 + (n + 1)^2 + (n - 1)^2 = 2030$
⇒ $n^2 + n^2 + 2n + 1 + n^2 - 2n + 1 = 2030$
⇒ $3n^2 = 2030 - 2$
⇒ $n^2 = 676$
⇒ $n = 26$, which is the middle number.
Hence, the correct answer is 26.
Prerequisite to CAT preparation for number systems
Here are some must-learn topics for students to do thoroughly while preparing for CAT:
Tables up to 30
Squares up to 30
Cubes up to 20
Prime numbers until 100.
Knowledge of Fractions
How to prepare for Number Systems (Basics)?
Learn the Classification of Numbers (Natural, Whole, Integers, Prime, Composite, Co-prime, etc.). NCERT books (9th and 10th standard) are the best guides for this.
Apply the concepts to number system questions.
Learn Base systems and conversions from numbers in one base system to another. For example, fractions to decimals questions, how to remove decimal points in fractions, how to convert numbers to fractions, and number system questions, and answers.
Practice the previous year's CAT questions on the number system.
Easy tips and formulae for Number Systems:
Following are some useful tips and CAT formulae on the Number system that can help in your preparation:
The sum of a two-digit number and a number formed by reversing its digits is divisible by 11. E.g., 24 + 42 = 66, which is divisible by 11.
At the same time, the difference between those numbers will be divisible by 9. e.g., 42 – 24 = 18, which is divisible by 9.
∑n = $\frac{n(n + 1)}{2}$, ∑n is the sum of the first n natural numbers.
∑$n^2 = \frac{n(n + 1)(2n + 1)}{6}$, ∑$n^2$ is the sum of the Perfect squares of the first n natural numbers.
∑$n^3 = \frac{n^2(n + 1)2}{4} = (∑n)^2, ∑n^3$ is the sum of the perfect cubes of the first n natural numbers.
Learn Recurring and Non-recurring decimal numbers and their conversion to fractions.
$\text{Number of the form } 0.\overline{a} = \frac{a}{9}$
$\text{Eg. } 0.\overline{7} = \frac{7}{9}$
$\text{Number of the form } 0.\overline{ab} = \frac{ab}{99}$
$\text{Number of the form } 0.\overline{abc} = \frac{abc}{999}$
$\text{Eg. } 0.\overline{73} = \frac{73}{99}$
$0.\overline{343} = \frac{343}{999}$
$\text{Number of the form } 0.0\overline{a} = \frac{a}{90}$
$\text{Eg. } 0.0\overline{7} = \frac{7}{90}$
$\text{Number of the form } 3.\overline{ab} = \frac{3ab - 3}{99}$
$\text{Number of the form } 30.\overline{ab} = \frac{3ab - 30}{99}$
References to practice number systems questions for the CAT 2025 exam
Practicing Number System questions is important because it builds a strong foundation for the entire Quantitative Aptitude section. It helps improve speed, accuracy, and confidence in solving basic to advanced math problems. Regular practice also trains the mind to recognize patterns and apply shortcuts effectively during the CAT 2025 exam.
Resources and Books for number systems (theory) | Books for practice - number systems |
NCERT Class 9 and Class 10 Mathematics | Master Number System for CAT and GMAT by Nishit K. Sinha |
A Quantitative Approach for CAT by Arun Sharma | Question bank from CAT-Holic |
2iim YouTube Channel | CAT's previous years' papers |
Data Interpretation(DI) for CAT 2025
Data interpretation is a must-know topic for the CAT Exam and other MBA entrance exams. Data interpretation tests your analytical and observational skills to deduce useful information and apply it to solve the given questions. DI for CAT can be studied in parts such as Bar graphs, Pie charts, Line graphs, Tables, Caselets, Spider charts, and Miscellaneous.
What is a Bar graph?
The bar graph definition says that a graph where data is represented with rectangular bars, where one parameter is given on the x-axis and the other parameter is given on the y-axis.
These bars can be drawn horizontally or vertically. Every bar represents a different category, and the length of the bar is its value.
We also have to study “bar graph maker”, “bar graph examples”, “difference between histogram and bar graph” and practice bar graph questions to delve deeper into this topic.
Examples of Bar graphs with questions
Question. Examine the graph below carefully and answer the following questions. The graph depicts the results of a school’s students.
Which year has the smallest difference between the number of kids who passed and those who failed?
In the last five years, what was the average number of kids who failed in school?
How many times have the same number of kids failed?
Solution:
(A) The number of pupils who passed versus those who failed for the respective years is given below:
1991-1992 = 150 – 100 = 50
1992-1993 = 200 – 100 = 100
1993-1994 = 300 – 50 = 250
1994-1995 = 250 – 100 = 150
The difference in 1991-1992 is minimal.
Hence, the correct answer is 1991-1992.
(B) From the bar graph, we can observe that.
The total number of students failed = 100 + 100 + 50 + 100 + 100 = 450
So, Average = 450/5 = 90
Hence, the correct answer is 90.
(C) According to visual observation, the number of failed students in 1991-1992, 1992-1993, 1994-1995, and 1995-1996 is the same.
Hence, the correct answer is four.
DI based on the Bar Graph for the CAT exam.
Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data. Every bar represents a different category, and the length of the bar is its value. They are also known as bar charts.
As per previous year's question papers for the CAT, about 3 or 4 questions are expected to be related to Bar Graph questions for the CAT, which come in exams.
Questions On Bar Graph From CAT Previous Year Papers
Revenue Shares of Tech Companies
Question 1: In 2001, the company that grew the quickest grew by 100%. What was the growth rate of the company that had the least growth rate?
50%
25%
20%
33% - Correct answer
Solution:
Let the total revenues of the entire industry be 100x in 2000 and 100y in 2001.
Company | Share in 2000 (approx.) | Share in 2001 (approx.) | Share in 2001: Share in 2000 |
FINY | 22.9x | 21.1y | 21.1y : 22.9x |
PRIWO | 17.1x | 19.3y | 19.3y : 17.1x |
SCT | 25.7x | 21.1y | 21.1y : 25.7x |
GOCN | 14.3x | 14y | 14y : 14.3x |
BIM | 8.6x | 10.5y | 10.5y : 8.6x |
CENTURE | 11.4x | 14y | 14y : 11.4x |
The company that grew the quickest would be the one that had the maximum ratio of 2001 revenue share to 2000 revenue share. Only the shares matter; X's and Y's do not matter.
Clearly, CENTURE saw the highest ratio and hence the highest growth, which is equal to 100%, and for that share in 2001: share in 2000 = 2 : 1 (for CENTURE).
$\frac{14y}{11.4x} = \frac{2}{1}$
$\Rightarrow \frac{y}{x} = \frac{11.4}{7}$
The company that saw the least ratio, and hence the least growth rate, is SCT.
$\text{Share in 2001 : Share in 2000} = \frac{21.1y}{25.7x} = \left(\frac{21.1}{25.7}\right) \times \left(\frac{11.4}{7}\right) = 1.33$
So, the percentage change is $33\%$.
Question 2: In 2002, the growth rate of the overall sector was 39%. What was the growth rate seen by SCT?
50% - Correct answer
75%
30%
40%
Solution:
Let Revenue in 2001 be 100.
Then, Revenue in 2002 was 139.
Share of SCT in 2001 = 21.1% of 100 = 21 (Approx)
Share of SCT in 2002 = 22.8% of 139 = 32 (Approx)
Therefore, Percentage Change = 11 × 100/21 = 52% ≈ 50% (Approx)
Question 3: Total revenue in 2006 was 21.2 billion, and total revenue in 2005 was
18.1 billion. What was the growth rate seen in Centure?
11%
35%
20% - Correct answer
27%
Solution:
Growth rate = (8.5% of 21.2 – 8.3% of 18.1) × 100/18.1 = 20% (approx)
Hence, the correct answer is Option C.
Prerequisite:
Here are some must-learn topics for students to do thoroughly while preparing for CAT:
Tables up to 30
Squares up to 30
Cubes up to 20
Basics of Percentage
Must know to find averages
CAT 2025 preparation Tips - DI (Bar Graph):
Bar Graph-based questions are a common and scoring part of the Data Interpretation (DI) section in the CAT 2025 exam. These questions test your ability to read, compare, and analyse data quickly and accurately. Here are some useful tips to prepare well for Bar Graph-based DI sets:
Learn the basics of simplification and approximation
Practice and learn to solve percentages quickly
Do small calculations mentally
Learn the basics of bar graphs
Understand the components on both axes
Interpret the necessary data requirements
References for CAT DI 2025
To master Data Interpretation for the CAT exam, including bar graphs, tables, pie charts, and caselets, using the right study materials is key. Here are some of the most recommended resources:
Theory | Practice |
RDI for CAT and GMAT by Nishit K Sinha | Data Interpretation for CAT by Arun Sharma |
Class 9 and Class 10 Mathematics NCERT for the basics of bar graphs | CAT's previous year's papers and sample papers |
2iim YouTube Channel | Question bank from CAT-Holic |
CAT 2025 Preparation for VARC: Noun Questions for CAT Exam
In the Verbal Ability and Reading Comprehension section, 24 questions are included of which 19 are non-MCQ questions. The Reading Comprehension questions are the majority ( 80%). CAT English practice questions are important, as sometimes students are very overconfident that they can solve the questions, but they can’t, so thorough practice is a must.
What are Nouns?
Nouns are a part of speech comprising words used to name people, places, animals, objects, and ideas. Nouns can act as the subject, an indirect object, a direct object, a subject complement, and an object complement.
Some of the types of nouns are:
Proper nouns: Names of specific persons, places, or things
Common nouns: Names of general items rather than specific names.
Countable nouns: Nouns that can be counted.
Uncountable nouns: Nouns that can not be counted.
Abstract nouns: Nouns that can not be perceived by 5 human senses.
Concentre nouns: Nouns that can be perceived by 5 human senses.
Compound nouns: Made up of two or more small nouns.
Collective nouns: Nouns referring to groups rather than individuals.
To understand better, we can make a types of nouns chart with types of nouns with examples.
We can also practice on the “countable and uncountable nouns worksheet”, “common and proper nouns worksheet with answers”, and “singular and plural nouns worksheet”
Instructions: Q.1 to 2, In each question, there are four sentences or parts of sentences that form a paragraph. Identify the sentence(s) or part(s) that is/are incorrect in terms of grammar, including spelling, punctuation, and usage. Pick out the most appropriate option out of the options that follow the question.
Question 1:
Either the parents or the child is going to talk.
to the principal on this issue, and I find many reasons
Why can't I help the child? Please excuse me now as the principal,
accompanied by the teachers, has to go to the auditorium.
Answer:
Option A: Either the parents or the child is going to talk – verb will follow the latter noun (subject)
Option C: "W" in “why” cannot be capitalised in the middle of a sentence. And there should not be any semicolon after “child”.
Question 2:
Neither the high-profile Manager nor the staff members were able
to calm the distressed customer. On top of it, the
The working team at this FDI-funded store is always
fighting among themselves.
Answer:
Option A: Manager - Here, "M" should not be in capital.
Option C: “The” is repeated and is not needed here.
Tips On CAT 2025 Preparation for Verbal Ability (Noun):
Understand what nouns are and how they are used, and where they are used.
Know the rules to follow while using nouns.
Practice exercises from Wren and Martin
References for CAT 2025 (Nouns)
Understanding nouns is essential for building a strong foundation in grammar and sentence structure, which directly impacts accuracy in Sentence Correction and Reading Comprehension. A clear grasp of noun types, usage, and agreement improves overall verbal performance in CAT. Some references are given below:
Wren and Martin
2iim YouTube Channel
Advanced English Grammar by Martin Hewings
The Pearson Guide to Verbal Ability and Reading Comprehension for CAT by Nishit Sinha (2020)
Question bank from CAT-Holic
The above tips and tricks can be used by students to kick-start their CAT preparations.
Free PDFs for CAT Preparation 2025
If you're preparing for CAT 2025 on a budget, many free PDF resources are available online to help you study effectively. These include topic-wise notes, previous year papers, mock tests, and strategy guides. Here are some of the best sources for free CAT preparation PDFs:
CAT 2024 Official Question Paper and Answer Key ( Slot 1, Slot 2, Slot 3) | |
CAT 2023 Official Question Paper and Answer Key (Slot 1) | |
CAT 2023 Official Question Paper and Answer Key (Slot 3) |
Frequently Asked Questions (FAQs)
Q: How can I improve my performance in Verbal Ability (VARC) for CAT?
A:
Read extensively, understand grammar rules, and practice noun-related questions. Focus on improving reading comprehension by practicing with various RC passages and solving grammar-based exercises.
Q: What are the best books to prepare for CAT 2025?
A:
For Quantitative Aptitude: "How to Prepare for Quantitative Aptitude for CAT" by Arun Sharma. For Data Interpretation: "Data Interpretation for CAT" by Arun Sharma. For Verbal Ability: "The Pearson Guide to Verbal Ability and Reading Comprehension" by Nishit K. Sinha.
Q: How should I start preparing for CAT 2025?
A:
Start with gaining knowledge of the CAT syllabus and pattern. Concentrate on developing a strong aptitude in Quantitative Aptitude (QA), Data Interpretation & Logical Reasoning (DILR), and Verbal Ability & Reading Comprehension (VARC). Develop a planned study schedule, practice mock tests on a regular basis, and evaluate your performance to strengthen weak points.
Q: How many months are required to prepare for CAT?
A:
Ideally, 6–9 months of regular preparation is advised for CAT. Yet, with concerted study and effective time management, candidates may prepare in 3–6 months by mastering key topics, cracking previous year papers, and appearing for regular mock tests.
Q: How to improve accuracy in CAT Logical Reasoning and Data Interpretation (LRDI)?
A:
Daily solve puzzles, seating plans, and DI caselets to enhance logical reasoning. Enhance speed and pattern identification through regular practice of various types of LRDI sets. Mock tests and last year questions assist in increasing accuracy as well as managing time.
Q: How to score 99+ percentile in CAT?
A:
To achieve 99+ percentile, the candidates need to excel at all three sections, learn time management, and attempt 30–40 full-length mocks with a thorough analysis. Being consistent, working on improving weak areas, and implementing an exam-day strategy for each section are the most important considerations to achieve a high percentile.
Q: How many mock tests should I take before CAT?
A:
Ideally, 30-40 mock tests must be practiced before the exam. Begin with one mock per week in the first phase and increase to 2-3 mocks per week in the final 2 months. Mistakes must be reviewed and performance analyzed after every test to improve.
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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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