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Practicing Number Systems is essential for every MBA aspirant. It’s a broad topic that requires a thorough review alongside other quantitative subjects. In the CAT exam, Number System questions typically make up about 5% of the Quant section, with 1-2 questions appearing each year based on past papers. This article is part of a 60-day preparation plan for CAT. Candidates can use this and other articles in the series to strengthen their understanding of Number System questions for the CAT exam.
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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 as p/q form, q ≠ 0
Irrational numbers: Numbers that cannot be expressed as 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.
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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 CAT questions on number system:
Classification of Numbers , Base System, Decimal to fraction converter
Unit Digit and the Last Two Digit of a number
Careers360 has prepared a 60-day series for CAT 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.
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,
n2 + (n + 1)2 + (n - 1)2 = 2030
⇒ n2 + n2 + 2n + 1 + n2 - 2n + 1 = 2030
⇒ 3n2 = 2030 - 2
⇒ n2 = 676
⇒ n = 26, which is the middle number.
Hence, the correct answer is 26.
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
Learn the Classification of Numbers (Natural, Whole, Integers, Prime, Composite, Co-prime, etc.). NCERT books (9-10th 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.
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, this is divisible by 11.
∑n = n(n + 1)/2, ∑n is the sum of the first n natural numbers.
∑n2 = n(n + 1)(2n + 1)/6, ∑n2 is the sum of the Perfect squares of the first n natural numbers.
∑n3 = n2(n + 1)2/4 = (∑n)2, ∑n3 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.
Number of the form of 0.a = a/9
Eg. 0.77777…. = 7/9
Number in the form of 0.ab = ab/99
Number in the form of 0.abc = abc/99
Eg. 0.73737373….. = 73/99
0.343343343…. = 343/999
Number of the form of 0.0a = a/90
Eg. 0.07777….. = 7/90
Number of the form of 3.ab = (3ab – 3)/99
Number of the form of 30.ab = (3ab – 30)/99
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 year's papers |
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, Caselet, Spider charts, and Miscellaneous.
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.
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.
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 related to Bar Graph questions for the CAT which come in exams.
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 for Question 1:
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).
So, 14y/ 11.4x = 2/1
⇒ y/x = 11.4/7
The company that saw the least ratio, and hence the least growth rate, is SCT.
Share in 2001: Share in 2000 = 21.1y/25.7x = (21.1/25.7) × (11.4/7) = 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 for Question 2:
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 for question 3:
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
Learn the basics of simplification and approximation
Practise 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
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 basics of bar graphs | CAT's previous year's papers and sample papers |
2iim YouTube Channel | Question bank from CAT-Holic |
In the Verbal Ability and Reading Comprehension section, 24 questions are included among which 19 questions 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.
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 are going to talk.
to the principal on this issue, and I find many reasons
Why I can't help the child; please excuse me now as the principal
accompanied by the teachers, has to go to the auditorium.
Answer:
Option A: Either 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 the 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 the capital.
Option C: “The” is repeated and is not needed here.
Understand what nouns are and how they are used, where they are used.
Know the rules to follow while using nouns.
Practice exercises from Wren and Martin
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.
CAT 2023 Official Question Paper and Answer Key (Slot 1) | |
CAT 2023 Official Question Paper and Answer Key (Slot 3) |
The CUSAT CAT previous year question papers are available on the Careers360 website. You can find question papers from 2012 to 2023, which can be downloaded in PDF format HERE
Additionally, the official website of Cochin University of Science and Technology (CUSAT) also provides previous year question papers. To access them, you can follow these steps:
- Visit the CUSAT official website - admissions.cusat.ac.in.
- Click on the resources tab from the homepage.
- Select the previous year's question papers from the drop-down menu.
- Select the Common Admission Test (CAT) question papers link.
- Now click on the B.Tech course.
By practicing with these previous year question papers, you can get familiar with the exam pattern, identify important topics, and improve your time management skills.
Hey Shathvika,
Let's dive deep into MBA Entrance Exams (Other than CAT)
1. XAT (Xavier Aptitude Test)
Conducted by: XLRI, Jamshedpur
Eligibility: Bachelor’s degree in any discipline.
Exam Pattern:
- Sections: Decision Making, Verbal & Logical Ability, Quantitative Ability & Data Interpretation, and General Knowledge.
- Duration: 3 hours.
- Marks: No negative marking for General Knowledge.
Key Highlights:
- The Decision-Making section tests analytical and situational judgment skills.
- General Knowledge is evaluated during interviews, not for percentile calculation.
Official Website: https://xatonline.in
---
2. SNAP (Symbiosis National Aptitude Test)
Conducted by: Symbiosis International (Deemed) University
Eligibility: Bachelor’s degree with 50% marks (45% for reserved categories).
Exam Pattern:
- Sections: General English, Quantitative, Data Interpretation & Data Sufficiency, and Analytical & Logical Reasoning.
- Duration: 1 hour.
- Marks: Total 60 marks (MCQs).
Key Highlights:
- Specifically for admission to Symbiosis institutes like SIBM Pune and SCMHRD.
- Easy-to-moderate difficulty level.
Official Website: https://snaptest.org
---
3. CMAT (Common Management Admission Test)
Conducted by: National Testing Agency (NTA)
Eligibility: Bachelor’s degree in any discipline.
Exam Pattern:
- Sections: Quantitative Techniques & Data Interpretation, Logical Reasoning, Language Comprehension, General Awareness, and Innovation & Entrepreneurship.
- Duration: 3 hours.
- Marks: 400 marks.
Key Highlights:
- Accepted by over 1,000 AICTE-approved institutes.
- Includes an optional Innovation & Entrepreneurship section.
Official Website: https://cmat.nta.nic.in
---
4. MAT (Management Aptitude Test)
Conducted by: All India Management Association (AIMA)
Eligibility: Bachelor’s degree in any discipline.
Exam Pattern:
- Sections: Language Comprehension, Mathematical Skills, Data Analysis & Sufficiency, Intelligence & Critical Reasoning, and Indian & Global Environment.
- Duration: 2.5 hours.
- Marks: 200 marks.
Key Highlights:
- Held multiple times a year in PBT, CBT, and IBT modes.
- Accepted by more than 600 MBA colleges in India.
Official Website: https://mat.aima.in
---
5. NMAT (NMIMS Management Aptitude Test)
Conducted by: Graduate Management Admission Council (GMAC)
Eligibility: Bachelor’s degree with 50% marks.
Exam Pattern:
- Sections: Language Skills, Quantitative Skills, and Logical Reasoning.
- Duration: 2 hours.
- Marks: 360 marks.
Key Highlights:
- Allows three attempts, with the best score considered.
- Accepted by NMIMS and partner universities worldwide.
Official Website: https://www.mba.com/exams/nmat
---
6. IIFT (Indian Institute of Foreign Trade)
Conducted by: National Testing Agency (NTA)
Eligibility: Bachelor’s degree (final-year students can also apply).
Exam Pattern:
- Sections: Quantitative Analysis, Reading Comprehension & Verbal Ability, Logical Reasoning & Data Interpretation, and General Knowledge.
- Duration: 2 hours.
- Marks: 300 marks.
Key Highlights:
- Specifically for IIFT’s flagship MBA in International Business.
- General Knowledge plays a significant role in shortlisting.
Official Website: https://iift.nta.nic.in
---
7. TISSNET (Tata Institute of Social Sciences National Entrance Test)
Conducted by: Tata Institute of Social Sciences
Eligibility: Bachelor’s degree.
Exam Pattern:
- Sections: English Proficiency, Mathematics & Logical Reasoning, and General Awareness.
- Duration: 100 minutes.
- Marks: 100 marks.
Key Highlights:
- Focused on social sciences, HRM, and public policy programs.
- General Awareness is crucial (with emphasis on current affairs).
Official Website: https://admissions.tiss.edu
---
8. MICAT (MICA Aptitude Test)
Conducted by: MICA, Ahmedabad
Eligibility: Bachelor’s degree and a valid CAT/XAT/GMAT score.
Exam Pattern:
- Sections: Psychometric Test, Verbal Ability, Quantitative Ability, General Awareness, Divergent-Convergent Thinking, and Descriptive Test.
- Duration: 2.5 hours.
Key Highlights:
- Psychometric Test is a qualifying section.
- Specifically for MICA’s flagship PGDM-C program in Strategic Marketing and Communications.
Official Website: https://www.mica.ac.in
---
9. GMAT (Graduate Management Admission Test)
Conducted by: Graduate Management Admission Council (GMAC)
Eligibility: No specific eligibility; bachelor’s degree recommended.
Exam Pattern:
- Sections: Analytical Writing, Integrated Reasoning, Quantitative Reasoning, and Verbal Reasoning.
- Duration: 3 hours 7 minutes.
- Marks: 800 (scaled score).
Key Highlights:
- Globally recognized for MBA programs.
- Popular for Indian B-schools like ISB, SPJIMR, and Great Lakes.
Official Website: https://www.mba.com
---
10. MAH-CET (Maharashtra Common Entrance Test)
Conducted by: Maharashtra State CET Cell
Eligibility: Bachelor’s degree with a minimum of 50% marks (45% for reserved categories).
Exam Pattern:
- Sections: Logical Reasoning, Abstract Reasoning, Quantitative Aptitude, and Verbal Ability & Reading Comprehension.
- Duration: 2.5 hours.
- Marks: 200 marks (MCQs).
Key Highlights:
- Accepted by top Maharashtra B-schools like JBIMS, SIMSREE, and PUMBA.
- Known for its speed-intensive nature with 200 questions in 150 minutes.
Official Website: https://cetcell.mahacet.org
Let me know if you have any doubts regarding a specific exam or any other query.
Have a nice day !!
Hello Ayush,
K.R. Mangalam University utilizes a blend of MCQs, descriptive formats, and practical assessments to evaluate student performance. The continuous evaluation system ensures that students are assessed regularly throughout the semester, contributing to a more comprehensive understanding of their academic progress.
Hello,
Here are some simple tips to prepare for the CUSAT CAT exam:
1. Focus on Physics, Chemistry, and Maths (PCM).
2. Give equal time to all subjects.
3. Use NCERT Books as they are best for basics.
You can refer to following study materials for better practice :-
Hope it helps !
Hello there,
Yes, you can apply for CAT examination after completion of Doctor of Pharmacy (Pharm D) .
The Common Admission Test (CAT) has no restrictions regarding your educational background thus allowing you to submit your application following your completion of a Pharm. D degree.
The Common Admission Test permits candidates to take the exam after completing any undergraduate degree without any restrictions to the area of study. The professional doctoral degree of Pharm. D (Doctor of Pharmacy) functions as an equivalent to bachelor's level for CAT eligibility recognition.
Therefore, Candidates who received their Pharm. D degree can pursue the CAT exam application process based on their qualification standards.
Hope this will help!
A career as Marketing Director is also known as a marketing expert who is responsible for the overall marketing aspect of the company. He or she oversees plans and develops the company's budget. The marketing Director collaborates with the business team to plan and develop the marketing and branding strategies for the company's products or services.
A Business Development Executive (BDE) is a professional responsible for identifying growth opportunities and fostering strategic partnerships to enhance a company's market position. Typically, a BDE conducts market research, analyses industry trends, and identifies potential clients or business prospects. He or she plays a crucial role in developing and implementing sales strategies to achieve revenue targets.
A BDE often collaborates with cross-functional teams, including marketing and product development, to align business objectives. Strong communication, negotiation, and relationship-building skills are essential for success in this role. BDE strives to expand the company's customer base, drive sales, and contribute to overall organisational growth in a dynamic and competitive business environment.
Content Marketing Specialists are also known as Content Specialists. They are responsible for crafting content, editing and developing it to meet the requirements of digital marketing campaigns. To ensure that the material created is consistent with the overall aims of a digital marketing campaign, content marketing specialists work closely with SEO and digital marketing professionals.
A sales manager is a revenue-generating source for a company. Any organisation or company which sells a commodity or service requires sales to generate revenue. A Sales manager is a professional responsible for supervising the sales team. An Individual as a sales manager works closely with salespeople, assigns sales territories, sets quotas, mentors the members of the sales, assigns sales training, and builds a sales plan.
The Sales Manager work also includes hiring and laying off sales personnel after evaluating his or her work performance. In bigger entities, sales quotas and plans are usually set at the executive level. He or she is responsible for overseeing the set target or quotas met by salespeople or upholding any policy. He or she guides his or her fellow salespeople and allows them to sell.
Individuals who opt for a career as a business analyst look at how a company operates. He or she conducts research and analyses data to improve his or her knowledge about the company. This is required so that an individual can suggest the company strategies for improving their operations and processes.
In a business analyst job role a lot of analysis is done, things are learned from past mistakes and the successful strategies are enhanced further. A business analyst goes through real-world data in order to provide the most feasible solutions to an organisation. Students can pursue Business Analytics to become Business Analysts.
A marketing manager is a person who oversees a company or product marketing. He or she can be in charge of multiple programmes or goods or can be in charge of one product. He or she is enthusiastic, organised, and very diligent in meeting financial constraints. He or she works with other team members to produce advertising campaigns and decides if a new product or service is marketable.
A Marketing manager plans and executes marketing initiatives to create demand for goods and services and increase consumer awareness of them. A marketing manager prevents unauthorised statements and informs the public that the business is doing everything to investigate and fix the line of products. Students can pursue an MBA in Marketing Management courses to become marketing managers.
An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns.
Digital marketing is growing, diverse, and is covering a wide variety of career paths. Each job function aids in the development of effective digital marketing strategies and techniques. The aims and objectives of the individuals who opt for a career as a digital marketing executive are similar to those of a marketing professional: to build brand awareness, promote company services or products, and increase conversions. Individuals who opt for a career as Digital Marketing Executives, unlike traditional marketing companies, communicate effectively through suitable technology platforms.
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