Is the syllabus of MAT IBT, PBT and CBT mode exams common?

Yes, the syllabus MAT IBT, PBT and CBT mode exams is common. In fact the exam pattern and marking are also same for all three modes. MAT syllabus for all modes includes topics from Language Comprehension, Intelligence and Critical Reasoning, Data Analysis and Sufficiency, Mathematical Skills and Indian and Global Environment. The candidate needs to prepare all the topics mentioned above on this page to crack MAT exam. The total time required for completion of MAT syllabus is about 3 months. If a candidate has appeared for MAT before or any other MBA entrance exam then they can complete the syllabus in lesser time. The only difference between the three MAT modes is that, in IBT, candidates have to take the test from home on a computer. In PBT, candidates have to appear for the test at an exam centres and fill the OMR sheet as part of the test. In CBT, candidates have to take the test on a computer at an exam centre.

Is DILR a theory-based section or practice-based?

The DILR section is mostly practice-based. There is not much theory-based or conceptual parts involved in the question unlike Quantitative Ability or Verbal Ability sections. Here, rather than focusing on the definitions of the topics, students get more accustomed to the question types and excel in the areas through practice. As it takes practice to improve the analytical and critical thinking ability rather than rote learning the concepts. The Data Interpretation is all about reading and comprehending tables and charts. The questions are calculation based, so you need to a strong base in Maths and practice. Logical Reasoning too is all about deciphering puzzles and patterns so even for that no theoretical knowledge is required. Practice questions are the key.

What are the best ways to prepare for the DILR section?

The best way to prepare for DILR section is through practice. Before starting the preparation, aspirants should check previous years’ question papers. Since there is not much conceptual understanding required in this section, practice is important. Some of the most popular books on DILR section that you can refer are How to Prepare for Data Interpretation and Logical Reasoning for CAT by Arun Sharma, Logical Reasoning and Data Interpretation for the CAT by Nishit Sinha, Data Interpretation and Logical Reasoning for CAT by Pearson, to name a few.

Is it necessary to have Maths background to perform well in DILR?

While candidates belonging to Science and Engineering background do have an edge over Data Interpretation and Logical Reasoning (DILR), it is not impossible for students from non-Science background to crack this section of an MBA entrance exam. They do need to prepare harder which includes going back to study fundamentals of Mathematics such as Arithmetic, Algebra, Geometry and Mensuration. With regular practice and understanding of the question types and topics, candidates, irrespective of the educational background, can crack this section. Aspirants must note that it is important to identify the weak areas and improve on them to get a stronghold on this section. For Logical Reasoning, a good amount of practice of sample questions will be enough.

How can I master Logical Reasoning and Data Interpretation topics of CMAT?

Cracking Logical Reasoning section of CMAT is all about how well and how quickly you understand the puzzles and patterns. To master this section of CMAT exam, sample questions for practice and sectional mock tests for CMAT are the best resource. You should start practicing Logical Reasoning questions early on in the preparation cycle. Pay attention to the topics from which Logical Reasoning questions are asked in CMAT. Prepare for those type of questions only. For Data Interpretation section of CMAT. You should be well versed with reading tables, graphs and charts correctly. For quick calculation, you should strengthen basic mathematical calculations like multiplication, division, square, square roots, cube, cube roots, etc. This section is all about observation and ability to break down information into pieces, so you need to practice a wide range of data interpretation questions.

What does Data Interpretation and Logical Reasoning (DILR) mean?

Data Interpretation and Logical Reasoning or DILR is one of the main sections of the MBA entrance exams and competitive exams. This section carries questions on a particular situation or graphs/charts/diagrams, etc. which test-takers have to study and examine properly to answer the multiple-choice questions that are related to the caselets or figures and diagrams. DILR section tests candidates’ analytical bent of mind and critical thinking ability. In DILR, the questions are based on Tables, Graphs (Line and Bar), Charts (Pie, Area, Line), Data Analytic Caselets, Data Structure, Calendar, Clocks, Data Sufficiency, Venn Diagram, Blood Relations, Arrangement (Seating, Linear and Matrix), Coding-Decoding, Logical Sequence, Assumption, Binary Logic and Critical Reasoning

What are the best ways to prepare for the DILR section?

The best way to prepare for DILR section is through practice. Before starting the preparation, aspirants should check previous years’ question papers. Since there is not much conceptual understanding required in this section, practice is important. Some of the most popular books on DILR section that you can refer are How to Prepare for Data Interpretation and Logical Reasoning for CAT by Arun Sharma, Logical Reasoning and Data Interpretation for the CAT by Nishit Sinha, Data Interpretation and Logical Reasoning for CAT by Pearson, to name a few.

Is DILR section part of all MBA entrance exams?

Yes, DILR section is a major section of all the MBA entrance exams. It covers almost 1/3rd of a test paper. In some exams, Data Interpretation is clubbed with Quantitative Aptitude and Logical Reasoning is an individual section. Irrespective of what the composition is, the both DI and LR are a part of MBA entrance exams. The section includes graphs, charts, diagrams, caselets, clocks & calendars, blood relation, family tree, number system, coding-decoding, arrangements and other such topics. There are a few state-level exams like TANCET, which does not have a separate section on DILR area, but the topics from this area are included in Data Sufficiency.

Is DILR one section in all MBA entrance exams?

No, DILR is not a combined section in all the MBA entrance exams. In some exams, the LR section is combined with DI, whereas in some exams DI is clubbed with Quantitative Analysis. For example, in CAT, DILR is a combined section, in XAT, the DI area is combined with Quantitative Ability and LR is combined with Verbal Ability. The DILR section is also known as Decision Making, Data Analysis, Critical Reasoning, Logical Ability, Analytical Ability, etc. This section is named differently but comprises common topics such as Bar Graph, Line Chart, Tabular Form, Caselet Form, Pie Chart, Missing Data, etc.

How many questions should I solve to get a good score in CMAT 2027?

Since every section of CMAT has 20 questions in total, solving 15 to 18 questions in each section with 80 percent accuracy is considered a good attempt in CMAT, and it can ensure a good percentile in the exam. In the GK section, about 10 to 12 correct attempts will be enough. Out of 100 questions, candidates must try to solve about 70 to 75 questions to achieve a 99 percentile. However, candidates must aim to solve a higher number of questions with maximum accuracy and minimize negative marking. To be able to achieve this target, candidates have to prepare for the CMAT in a disciplined manner. Candidates must set aside about three months to complete the CMAT syllabus, as they have to study five subjects and their numerous topics. If they have appeared for CAT, XAT, and IIFT exams, then they can complete the CMAT syllabus in one month as well. However, it is advised that candidates spend at least three months on CMAT syllabus for complete preparation.

What are the important topics of MAT exam?

Questions in MAT are asked from verbal ability, reading comprehension, arithmetic, algebra, geometry, arrangement, coding decoding, graphs and tables, family tree, blood relation, clocks and calendars, time, speed and distance, statements, etc.

What is the weightage of the DILR section in CAT?

In CAT exam, there are 20 questions in the Data Interpretation & Logical Reasoning section and the total sectional marks is 60 out of 198. In CAT 2020, there were 24 question on DILR and the sectional marks were 72. In CAT 2021 and CAT 2022, there were 20 questions and the sectional marks were 60. The 20 questions are equally divided into both Data Interpretation and Logical Reasoning. That means, Both Data Interpretation and Logical Reasoning have 10 questions each. The questions are mostly in sets. There’s rarely any standalone question in DILR. Some of the top MBA entrance exams carrying a high weightage of Data Interpretation and Logical Reasoning questions are MAH CET, ATMA, CAT, CMAT, XAT IIFT, to name a few.

What is the SNAP syllabus for Analytical and Logical Reasoning?

The syllabus for Analytical and Logical Reasoning section of SNAP exam includes topics such as Family Tree/Blood Relations, Coding/Decoding, Analogy & Series, Seating Arrangement, Direction Sense, Mathematical Reasoning, Clocks & Calendars, Syllogisms, Meaningful Word/Matrix, Critical Reasoning, Visual Reasoning, Verbal & Miscellaneous Reasoning. The Analytical and Logical Reasoning section of SNAP carries maximum number of questions i.e. 25. Candidates have to choose the questions they can answer correctly, otherwise they will be given negative marks. So, SNAP aspirants must practice ample number of sample questions from these topics. The more they will practice, the better they will get at solving reasoning questions as it is all about knowing the patterns and unravelling the puzzles. Since, this section carries maximum marks, you cannot be ill prepared for it.

What is the MAT syllabus for Intelligence and Critical Reasoning?

The important topics included in the MAT syllabus for Intelligence and Critical Reasoning include Family Tree, Strong Arguments and Weak Arguments, Multi-Dimensional Arrangements, Course of Action, Puzzles, Visual Reasoning, Arrangement, Series, Numeric Grid, Pie Chart, Blood Relations, Critical Reasoning, Calendars, Coding & Decoding, Syllogisms, Statement Conclusions, Column Graphs, Graphs Representing Area. Candidates must note that covering MAT syllabus for Intelligence and Critical Reasoning is tough because it is not Mathematics. There is no concept to be understood, there is no formula to be memorized. It is also not like General Knowledge, where facts are to be memorized. This section of MAT requires developing intelligence and reasoning skills. Most of the questions in this section are based on puzzles and patterns so one needs to develop the skill of identifying key details. Practice of several types of questions from all the topics is one of the best ways to cover the syllabus of this section of MAT.

What is the syllabus of MAH MBA CET Logical Reasoning and Abstract Reasoning?

The syllabus of MAH MBA CET Logical and Abstract Reasoning section includes Arrangements, Family tree, Coding-Decoding, Direction, Clock and Calendars, Groups and Conditionality, Number Series, Venn Diagrams, Syllogisms, Odd Word Out, Analogies, Blood Relations, Proposition, Direction Sense, Assumptions, Puzzles, Binary Logic, Clock and Calendars, Sets and Caselets, etc. This section is divided into two parts. The Logical Reasoning section has 75 questions and Abstract Reasoning Section has 25 questions. Each question has five option to choose the correct option from. Each correct option fetches 1 mark and incorrect option fetches 0 marks. The candidates need to focus more on this section of MAH MBA CET as it carries the maximum weightage. Prepare for this section by practicing a large number of practice questions.

What are the important topics for DILR in IIFT syllabus?

The important topics of DILR syllabus for IIFT include Decision Making, Series, Data Structures, Blood Relations, Coding-Decoding, Alphabetical Series, Syllogisms, Verbal Logic, Visual & Critical Reasoning, Linear & Matrix Arrangements, Puzzles, Family Tree Problem, Statement & Conclusion, Cause & Effect, Input & Output, Partnership, Line Graph, Tables, Bar Graph and Pie Graphs. The IIFT DILR section has 30 questions in total. To prepare for these topics, candidates need to first learn the types of questions and their key elements. LR questions are mostly like a puzzle where you have to uncover a pattern and to complete the series. This requires a bit of analytical and a bit of logical deduction. Practice a good number of IIFT DILR questions of previous years as well as sample papers to master this section.

Where can I find study material for Decision Making syllabus for XAT?

Since Decision Making section is unique to XAT, study material for the same in not readily available. Thus the best source of preparation material for Decision Making section is XAT previous years’ question papers. This section has passages related to business situations. Candidates have to select the closest solution to the given situation from the list of four options. You have to make an informed decision regarding the decision which has be in favour of the larger good. This section essentially tests your ability to take objective decisions regarding various business situations and activities. Candidates can practice Decision Making questions from XAT question papers of previous years to know the types and difficulty level. In a way, this section is similar to Reading Comprehension and requires same skills as that.

What is the difficulty level of SNAP question paper?

The SNAP exam is short and simple to pass compared to other MBA tests. The exam takes only 60 minutes for 60 questions and covers English, Reasoning and Math. It leaves out hard topics like long reading stories and tricky data puzzles and you can try the test three times to get your best score.

What are the important topics that usually dominate the SNAP question paper?

Candidates preparing for SNAP exam must study all the topics included in the SNAP syllabus i.e. General English and Quantitative Ability, Data Interpretation & Data Sufficiency and Analytical and Logical Reasoning.

What makes CAT tougher than other MBA entrance exams?

India's premiere b-schools accept CAT for MBA admissions. More than 2.5 lakh candidates fighting for limited seats at these institutes make the exam tough to crack.

How can I prepare for XAT by self study?

If you are planning to prepare for XAT exam by self study, you need to start early. At least six months before. XAT exam is conducted on the first Sunday of January every year. So, if you start preparing for the XAT in June or July, you will have good six months to prepare. Make a preparation plan that includes XAT syllabus coverage, problem solving sessions, mock tests and revision. Get hold of best books for XAT. Consult mentors or previous year toppers for selecting the best books for preparation. Join online study groups where you can get the help of mentors and peers for problem solving and clearing of doubts in topics. Work in tough topics first and then move to easier topics. Solve a large number and variety of XAT mock tests to master the syllabus. You will need to do a rigorous work on XAT mock tests as for candidates who opt for self study, have to rely on practice.

How should I prepare for Data Analysis and Sufficiency section of MAT?

For Data Analysis and Sufficiency of MAT test takers should constantly revise the topics and practice sample questions as this section can be cracked only by enough practice of all types of questions. It is also important to strengthen basic calculations of Maths. Candidates must memorise Tables up 20, Cubes, Cube roots, square, square roots, percentage, pie value, etc. For quick multiplication and division, Practicing adequate number of MAT mock tests and sample papers will prepare you for the main exam, so you should practice 30-35 mock tests. To improve percentile score, focus on maximizing accuracy of every question that you solve in mock tests and sample papers. Candidates must attempt questions of all types and all difficulty levels to master this section of MAT exam. They should also practice every MAT sample question 2-3 times, to gain speed and accuracy.

Number Systems Questions with Answers for MBA Preparation: Download PDFs

Updated on Mar 12, 2026 17:41 IST

By Vipra Shrivastava, Senior Manager - Content

Number System is an integral part of MBA entrance exam syllabus and of other competitive exams too. One needs to master it to be able to not only solve specific questions but also related Mathematical problems. Having complete understanding of decimal number system, binary number system, octal number system and hexadecimal number system is very essential for quick calculations. Number System requires practice as well. Read below all about Number System for MBA entrance exams.

Types of Number Systems:

Decimal (Base-10): Using ten digits (0-9).
Binary (Base-2): Using only two digits (0 and 1).
Octal (Base-8): Uses eight digits (0-7).
Hexadecimal (Base-16): Uses sixteen digits (0-9 and A-F).

Table of contents

What is Number Systems?
Terminating and Non-Terminating Decimal Expansion
Questions on Number Systems with Solutions
DILR Practice Questions with Solutions PDFs
FAQs Regarding Number Systems

What is Number Systems?

Number System can be understood as the method by which we formulate numbers. There are several forms of number systems including binary, decimal, etc. It is a system wherein numbers are expressed. It is the mathematical notation for describing numbers with a consistent sequence of digits or symbols. It proceeds to represent any number and the arrangement of the figures.

Number System Concepts

Here are the definitions of several Number Systems used in calculation.

Numeral System: It is defined as the way in which numbers are written and represented using digits or symbols.
Natural Numbers: It refers to positive whole numbers used for counting (example: 1, 2, 3, ...).
Whole Numbers: It refers tonatural numbers and zero (example: 0, 1, 2, 3, ...).
Integers: It refers to hole numbers and their negative counterparts (example: -4 -3 -2, -1, 0, 1, 2, 3, 4...).
Rational Numbers: When numbers are expressed as a fraction p/q, where p and q are integers and q is not zero, then it is called Rational Numbers.
Real Numbers: It refers to all rational and irrational numbers.
Complex Numbers: It refers to those numbers that are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit (√-1).

Number System was an important chapter in Class 9 and 10 Mathematics, and we all are well aware of it. However, to prepare for competitive exams, one needs to study advance level concepts of this chapter.

Terminating and Non-Terminating Decimal Expansion

A rational number either has a finite expansion into rational numbers, or it continues forever.

The decimal expansion of an irrational number is not terminating or recurring.

1. Demonstrate that 0.3333 … = 0.3, may be represented in rational form; i.e, p/q.

Let x = 0.33333.

10 x = 10 × (0.333….) = 3.333....

3.3333... = 3 + x.

10x = 3 + x.

9/x = 3.

x = ⅓.

2. Write the following in decimal form and name expansions.

36/100.
1/11.

Solution:

36/100 = 0.36.

It is terminating.

1/11 = 0.09090909…

The solution is non-terminating and repeating.

Illustrated Examples:

1. Multiply 5√3 by 4√3.

Solution: 5√3 x 4√3

5 x 4 x √3 x √3

= 20 x 3

= 60

2. Rationalise the denominator of √3/(√2-√7).

Solution: Multiply both numerator and denominator by √2+√7

[√3/(√2-√7)] x [(√2+√7)/(√2+√7)]

Numerator = √3(√2+√7)

Denominator = (√2-√7)(√2+√7) = (√2)^2-(√7)^2 = 2-7 = -5

Therefore,

[√3(√2+√7)]/-5

= -√3/5(√2+√7)

3. Rationalise the denominator of 1/√5.

Solution: To rationalise the denominator of 1/√5, we need to multiply the numerator and denominator by √5

1/√5 x (√5/√5)

= √5/5

Also Read: MBA Preparation 2025: Tips to Prepare for MBA Entrance Exams

Questions on Number Systems with Solutions

1. What are the five numbers between one and two?

There are 5 rational numbers between one and two.

Solution: We need to find 5 rational numbers between 1 and 2

Divide and multiple both the numbers by (5+1)

Hence,

6/6 and 12/6 are rational numbers now.

Therefore, 6/6, 7/6, 8/6, 9/6, 10/6, 11/6, 12/6.

Irrational numbers cannot be represented as either a fraction or a decimal.

2. Is there a number √3 on the number line?

Solution:

To locate √3 on the number line, we need to:

Build BD that passes via point OB perpendicular to it.

Using Pythagora's theorem, we notice that OD = √((√2)^2+1^2) = √3.

Draw an arc with centre O and radius OD to cut the number line at Q.

DILR Practice Questions with Solutions PDFs

Get here free PDFs of DILR practice questions with solutions. Practice these DILR questions to improve your performance in CAT and other MBA entrance exams:

DI Easy Questions Set 1	DI_Easy_Set 1 Solutions
DI Medium Questions Set 1	DI_Medium_Set 1Soutions
DI Difficult Questions Set 1	DI Difficult Set 1 Solutions
DI Easy Questions Set 2	DI Easy Set 2 Solutions
DI Medium Questions Set 2	DI Medium Set 2 Soutions
DI Difficult Questions Set 2	DI Difficult Set 2 Solutions
LR Easy Questions Set 1	LR Easy Set 1 Solutions
LR Medium Questions Set 1	LR Medium Set 1 Solutions
LR Difficult Questions Set 1	LR Difficult Set 1 Solutions
LR Easy Questions Set 2	LR Easy Set 2 Solutions
LR Medium Questions Set 2	LR Medium Set 2 Solutions
LR Difficult Questions Set 2	LR Difficult Set 2 Solutions
LR Easy Questions Set 3	LR Easy Set 3 Solutions
LR Medium Questions Set 3	LR Medium Set 3 Solutions
LR Difficult Test Set 3	LR Difficult Set 3 Solutions

FAQs Regarding Number Systems

Q: What is the significance of number systems?

A: In mathematics, a number system is characterised as a framework that allows all numbers to be represented. The number method offers a distinct means of communicating numbers and the logical basis for a math equation.

Q: Describe the various groups of numbers.

A: The various kinds of numbers are:

Natural numbers
Whole numbers
Real numbers
Rational numbers
Irrational numbers
Complex numbers

Q: Why are the numbers used?

A: The numbers define the spectrum of everything. Numbers are used to measuring anything from income to time. Without statistics, we cannot realise how useful items are.

Q: What are the four different types of number systems?

A: The four major types of number system are:

Binary number system (base 2 number system)
Octal number system (base 8 number system)
Decimal number system (base 10 number system)
Hexadecimal number system (base 16 number system)

Q: What are the uses of number systems?

A: The most popular usage of the number system is in computers. The binary number system is used. Binary numbers are used in the encoding process of digital.