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CAT 2024 Preparation Strategy on Quant (QA), DI, VA and LR - Day 1
Edited By Team Careers360 | Updated on Sep 18, 2024 05:05 PM IST | #CAT
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.
Free Study Material: VARC | DILR | Quant | Chapter-wise Practice MCQs
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Test: 20 Free Mock Test | 10 Year PYQs | Most Scoring Concepts
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 exam
- Data Interpretation(DI) for CAT 2024
- What is a Bar graph?
- CAT preparation Tips - DI (Bar Graph):
- References for CAT DI
- CAT 2024 Preparation for VARC: Noun Questions for CAT Exam
- What are Nouns?
- Tips On CAT Preparation for Verbal Ability (Noun):
- References for CAT 2024 (Nouns)
- Free PDFs for CAT Preparation 2024
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 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.
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
CAT 2024 Most Scoring Concepts- VARC, DILR & QUANT
Start your CAT journey today and download CAT 2024 most scoring concepts PDF, including study materials based on CAT previous year papers, CAT question papers, and CAT exam sample questions.
Download EBookCareers360 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.
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
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.
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 (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.
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, this is divisible by 11.
- At the same time, the difference between those numbers will be divisible by 9. e.g., 42 – 24 = 18, this is divisible by 9.
∑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…. = 343/999Number of the form of 0.0a = a/90
Eg. 0.07777….. = 7/90Number of the form of 3.ab = (3ab – 3)/99
Number of the form of 30.ab = (3ab – 30)/99
References to practice number systems questions for the CAT 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 year's papers |
Data Interpretation(DI) for CAT 2024
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.
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 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 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
CAT preparation Tips - DI (Bar Graph):
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
References for CAT DI
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 |
CAT 2024 Preparation for VARC: Noun Questions for CAT Exam
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.
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 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.
Tips On CAT Preparation for Verbal Ability (Noun):
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
References for CAT 2024 (Nouns)
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 2024
CAT 2023 Official Question Paper and Answer Key (Slot 1) | |
CAT 2023 Official Question Paper and Answer Key (Slot 3) |
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Questions related to CAT
Have a question related to CAT ?
The student cannot join the postgraduate MA program directly in the second year of the MA after completing the MBA.
Universities generally expect students to begin the first year of a masters' program even though they had qualifications at the level of a bachelor's degree. The university's curriculum along with the courses are planned to give an in-depth knowledge of the subjects.
But you could opt for:
Postgraduate Studies:
Research Career: In case research interests you, then you can pursue a Ph.D. in your specific interest.
Specialized Master's Programs: Find any specific master's course that supports the career goal.
Professional Certifications:
Make a professional certification in CFA, CA, or FRM to enhance the professional skills and better opportunities in the career field.
Job Entry via MBA
After gaining an MBA from a renowned institution, it's possible to get entry into the corporate world where the diversity in the career field is assured.
In the end, it would depend on what you would like and what you are particularly interested in. It will be better if you take a suggestion from your academic advisor or career counselor.
Samprikta Mondal 13 November,2024
Hello Pratik,
If your family income exceeds 8 LPA, it will affect your eligibility for the NC-OBC category under the CAT reservation rules. The NC-OBC category requires that the family income should be below 8 LPA to qualify. If you anticipate that your income will exceed this threshold, you should update your status and notify the CAT authorities .
Here's what you can do:
-
Email the CAT authorities : Inform them about the potential change in your income status and request to be considered under the General category, if applicable. You should do this before the examination or any further processing, as your eligibility for the OBC category depends on the income criteria.
-
Documents and Proof : Make sure you have a valid OBC certificate and any relevant documentation regarding your family income, in case they require verification. Also, be aware that if your income exceeds 8 LPA, you might need to apply under the General category, as the OBC-NC reservation is no longer applicable.
-
General Category Consideration : If your application is accepted as General, you will be evaluated based on the General category criteria, including cutoffs and ranking.
To summarize, notifying the CAT authorities is the correct approach to avoid discrepancies later, and if your income is above the threshold, you will be treated as a General candidate for the admissions process.
For more details about CAT exam you can check out an article by Careers360 whose link is given below:
Link: https://bschool.careers360.com/exams/cat
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
kumardurgesh1802 08 November,2024
Hi Shreya ,
Having a tattoo on your wrist should not create a problem during the CAT exam as long as it does not contain any content that violates exam rules , such as communication-related symbols , unauthorised messages or any text resembling formulas or answers .
For a safe side , it is recommended :
1. Inform the Invigilators : Let them know about your tattoo during the identification check , so there are no misunderstandings .
2. Follow the Guidelines : Ensure you follow all instructions regarding permissible items and dress code on the exam day .
Hope this helps you .
ALL THE BEST .
Mitali Sharma 09 November,2024
To know about this please prefer our college predictor
Sumit Mishra 07 November,2024
Hello,
Yes, you can also join IIMs two years after graduation, depending upon the justification in interviews and your performance in entrance exams. If you are not sure about CAT, try those other management exams less hard:
Common Management Admission Test: Easier than CAT; 4-5 months of continuous preparation will suffice.
MAT : Much easier and takes place thrice a year.
SNAP (Symbiosis National Aptitude Test): A bit easier than CAT, apt for Symbiosis Institutes.
Xavier Aptitude Test or XAT : Hence, easier than CAT but the unique decision-making section.
Use exams like CMAT and MAT as a challenge to be competitively prepared. This can be given about 4-5 months, along with a few rounds of mock tests and smart studying.
Deepti Singh 06 November,2024
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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