Globsyn Business School PGDM Admissions 2025
Highest CTC: Rs 18.33 LPA | Average CTC: Rs 7.39 LPA | Experiential Learning | Classes by Industry Professionals | Alumni Mentorship Program
Unlocking CAT Exam Essentials: Exploring Unit Digits, Pie Charts, and Pronouns - Day 2
Edited By Team Careers360 | Updated on Sep 19, 2024 02:25 PM IST | #CAT
In our previous article, we covered the CAT Preparation Strategy for Quantitative Ability on Day 1, focusing on the number system and its components, such as classification, converting decimals to fractions, and base systems, along with relevant CAT quant questions.
In this article, we will study deep into the unit digit and the last two digits of a number as outlined in the CAT Quant syllabus for 2024. We'll also review previous year's CAT questions related to the number system. Typically, there are about 3-4 questions on this topic in the exam, based on past CAT quant papers.
This Story also Contains
- Part 1: Quantitative Aptitude For CAT 2024
- Part 2: Data Interpretation And Logical Reasoning For CAT 2024
- Part-3: VARC for CAT 2024 Exam
- Free PDFs for CAT 2024 preparation
For instance, given the number 234432, how would you determine the unit digit and the last two digits of the number?
Part 1: Quantitative Aptitude For CAT 2024
Topic: What is “Cyclicity”?
Cyclicity is used to determine the unit digit. Cyclicity is the power of a number after a multiple in which a unit digit is repeated.
For example, 21 = 2; 22 = 4; 23 = 8; 24 = 16; 2 5= 32 and so on.
As it is shown in the above example, after every fourth power of 2, the unit digit is repeated. So, 4 is cyclicity of 2.
So, you have to learn the cyclicity of every digit.
Digit | Cyclicity (Power Cycle) | Digit | Cyclicity (Power Cycle) |
0 | 1 (Gives always 0 at unit place) | 5 | 1 (Gives always 5 at unit place) |
1 | 1 (Gives always 1 at unit place) | 6 | 1 (Gives always 6 at unit place) |
2 | 4 (2, 4, 6, 8) | 7 | 4 (7, 9, 3, 1) |
3 | 4 (3, 9, 7, 1) | 8 | 4 (8, 4, 2, 6) |
4 | 2 (4, 6) | 9 | 2 (9, 1) |
CAT quant questions based on the last two digits of a number are asked frequently in the CAT Exam.
Eg: Find the last two digits of 3737.
It is practically not so easy to solve this power. So, you need to learn the tricks to find the last two digits without actually solving this problem. Some of the tricks will be discussed later in this article, like dividing a number by 100 so that the remainder is the last two digits.
CAT Quant Questions From CAT Previous Year Papers
Question 1: The product of the last two digits of (1! + 2! + 3!….. 50!) is?
3
4
5
6
Ans: (A)
Divide the given number by 100 to find the last two digits.
Number 10! And greater than 10! are divisible by 100.
So, find (1! + 2! + 3!….. +9!) and divide the result by 100 to get the remainder and hence the last two digits of the number.
So, 1! + 2! + 3!….. +9! = 1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40230 + 362880
So, the sum of the remainder is (1+ 2 + 6 + 24 + 20 + 20 + 40 + 30 + 80). On dividing this result by 100, we get 13 as the remainder.
Product of digits of 13 = 1 × 3 = 3.
Question 2: What are the last two digits of 72008? [CAT Question Paper 2008]
21
61
01
41
CAT 2025: VARC, DILR, and Quant MCQs & Weightages
Comprehensive CAT prep guide with focused practice on Verbal Ability, Data Interpretation & Logical Reasoning, and Quantitative Aptitude.
Download NowAns: (C)
(1,3,7,9)20k = 01 (Last two digits) where k is a positive integer.
So, 72008 = 72000 x 74 x 74 = 01 x 01 x 01 (Taken last two digits only) = 01
So, the answer is 01.
Prerequisite:
While preparing for the number system, a student must learn:
Squares of the first 25 natural numbers
Cubes of natural numbers till 15
Knowledge of Prime and Composite
Knowledge of powers
Knowledge of factorial
Knowledge of Even and Odd Numbers
Basic Knowledge of Multiples and Factors
Tips On CAT Preparation For the Number System (Unit Digit And Last Two Digits):
Learn Cyclicity to find the unit digits as discussed in this article.
Use the Concept of cyclicity in Practice Problems.
To find the last two digits, the following tips may help you
The last two digits of x2, (50+ x)2, (50- x)2, (100+ x)2, (100- x)2 are the same.
Eg: 022 = 04
522 = 04
482 = 04
1022 = 04
982 = 04Odd20k = 01(last two digits) except for 5. Where k is a positive integer.
Eg. 2342 = 01(a5)even = 25 (last two digits)
(a5)odd = 75 (last two digits); where can be any digit.
Eg: 13572 = 25, 13523 = 75Even20k= 76(last two digits) where k is a positive integer.
Eg: 48200 = 76 (last two digits)
Practice Mock Tests and CAT Question Paper
References for Study (Theory):
Learn the concept of class 9 Mathematics NCERT (for theory)
Arun Sharma: A Quantitative Approach for CAT (6th Edition)
YouTube Channel of 2iim
References for Practice(Number System Questions And Answers):
Master Number System for CAT and GMAT by Nishit K Sinha.
CAT previous year papers: practice previous year CAT questions on number system
Question bank from CAT-Holic
Part 2: Data Interpretation And Logical Reasoning For CAT 2024
Topic: Data Interpretation (Pie Graphs)
As discussed in the previous article, Data interpretation is the most important topic for the CAT exam and other management entrance Exams.
Skills of observation, doing calculations quickly, analyzing things, and comparison of values will help you in solving questions based on Data interpretation (Pie Charts).
In this topic, we are going to discuss strategies to prepare Data Interpretation based on Pie Charts. We will discuss some Pie chart questions on CAT below as well.
What is a Pie Chart (Pie chart basic concept for CAT Exam)?
Sample pie charts of distribution of 6 parameters.
In the pie chart, data is distributed in a circle, which forms 360 degrees at its centre and comprises 100% of its area. Students must know how to derive the relation between angle and Percentage to calculate the parameter’s value.
Pie chart questions and concepts for CAT preparation from CAT Previous Year Papers:
Direction: The break-up of the students in a university by subject major is given in the polar pie chart. The bar chart shows the number of students who major in physics by geographic location. [XAT 2019, based on CAT PYQ]
Question 1. How many students major in chemistry?
200
175
170
190
180
Solution: (B)
Students major in physics = 18 + 36 + 80 + 40 + 23 + 28 = 225 which is 18% of total students.
So, 18% = 225
Major in Chemistry
14% = (225/18) x 14 = 175
Question 2. If the proportion of physics majors who are from Delhi is the same as the proportion of engineering majors who are from Delhi, how many engineering majors are from Delhi?
22
26
18
20
24
Solution: (D)
Students major in physics = 18 + 36 + 80 + 40 + 23 + 28 = 225 which is 18% of total students.
So, 18% = 225
So, Total students in Engineering major = 225×20/18 = 250
According to question
18/225 = x/250 (where x are students from Delhi with Engineering major)
⇒ x = 20
Question 3. 12% of all students are from Chennai. What is the largest possible percentage of economics students that can be from Chennai, rounded off to the nearest integer?
73%
77%
75%
71%
69%
Solution: (A)
Total number of Physics majors = 225
Total number of students = 225 x 100/18 = 1250
Students from Chennai = 12% x1250 = 150
Number of Physics majors from Chennai (from graph) = 40
Maximum possible number of Economics majors from Chennai = 150 - 40 = 110
Maximum Percentage of Economics Major from Chennai = 110 x 100/150 = 73.33%.
Prerequisite:
To prepare Data Interpretation (Pie Chart), a student must learn
The Basics of Trigonometry
Percentage (Basic)
Squares and Cubes of 20-30 first natural numbers.
Knowledge of fractions and Ratio
Must know to find Average
Knowledge of mean, Mode , and median.
Tips On CAT Preparation For DI (Pie Chart):
Practice questions on simplification and approximation.
Practice questions on the basics of percentages.
Try to solve addition, subtraction, and multiplications mentally.
Understand the conversion of angles into percentages.
Practice the questions on the basics of average.
References To Study (Theory):
LRDI for CAT and GMAT by Nishit K Sinha.
To learn the basics of bar graphs read statistics of class 9 and Class 10 Mathematics from NCERT (For Theory)
2iim YouTube Channel
References To Study (Practice):
1. CAT previous year's papers
2. Question bank from CAT-Holic
3. How to Prepare for Data Interpretation for CAT by Arun Sharma
Part-3: VARC for CAT 2024 Exam
Topic: Pronoun and Its Type
Pronouns are used in place of nouns to avoid repetition of the nouns to which they refer. Pronouns have different forms and are used in different ways.
Eg: I, me, he, she, they, each, few, many, etc
To understand them in a better way, they are categorized into different categories as shown:
Type | Example | Uses |
Personal Pronoun (Used in place of the name of a person) | I, Me, He, She, You, They, Her, Us etc | He is going to meet her. |
Possessive Pronoun (Shows possession of something) | My, Mine, ours, your, its, hers, etc | This T-shirt is mine. |
Relative Pronoun (used before describing the features or properties of the subject) | That, who, whom, whose, which etc | The thief who stole the money has been successfully punished. |
Reflexive Pronoun (Used when the subject and the object of a sentence are the same) | herself, myself, yourself, yourselves, himself, oneself, etc | He used to believe in himself. |
Intensive Pronoun (Similar to Reflexive pronoun but emphasise more intensely on Subject) | herself, myself, yourself, yourselves, himself, oneself, etc | I myself cook my food. |
Indefinite Pronoun (Used when the subject is not certain) | nobody. anybody everybody, somebody Anyone, no one, everyone, someone etc. | No one is perfect in this world. |
Demonstrative Pronoun (Used to show the closeness of the subject or its position) | This, that, these, such, those, etc. | I had the privilege to visit the Prime Minister’s office, that was worth remembering. |
Interrogative Pronouns (used to ask questions) | What, which, whose, whom, who, etc. | Who is confident enough to clear the CAT this year? |
Reciprocal Pronoun (Used when the sentence has the two actions are performed by two parties) | Each other, one other | The kids threw stones at one another. |
Distributive Pronoun (refers to individuals in a group) | none, each, either, neither, any, everyone, no one etc. | None of our friends was involved in the fighting. |
Questions on Pronouns From CAT Previous Year Papers (CAT VARC pronoun)
Direction- Find the correct alternative for the underlined sentence:
Question 1. My mother bought ice creams for my brother and me, but she didn’t buy one herself.
for my brother and me, but she didn’t buy one for herself.
for my brother and myself, but she didn’t buy herself one.
for my brother and I, but she didn’t buy one for her.
for my brother and I, but she didn’t buy one for herself.
Ans. (A)
Option C and D are wrong because the use of ‘I’ does not make any sense, In place of I, ‘me’ should come (pronoun in place of a noun)
Option B is wrong since ‘myself’ (reflexive pronoun) refers to when I purchased the ice-cream but her mother purchased it.
Therefore, option A is correct because correct pronouns were used.
Question 2. He ____ saw the running Dog.
(a) himself (b) him (c) them (d) themselves
Ans: (a)
The correct pronoun for "he" is himself.
Question 3. Shreeti and ____ went to a movie.
(a) I (b) themselves (c) myself (d) ourself
Ans: (a)
Personal pronouns should be used here. So, the correct answer is option A.
Question 4. When a girl asked how I got _____ address, I told her that it was with the help of a relative of _____.
(a) my/ me (b) mine/ his (c) her/hers (d) she/ she
Ans: (c)
The address here is related to a girl, so "her" should come
Relative to mine or a relative of hers; both can be correct. However according to the options given, option (C) will be correct.
Tips On CAT Preparation for Verbal Ability (Pronoun):
Learn the pronouns by categorizing them and their uses in different situations.
Learn the basics of Grammar
Practice different pronouns in different situations.
Practice CAT Question Papers and Mock tests.
Develop the habit of reading (Newspapers, Novels, Articles etc)
References To Study (Theory):
Advanced English Grammar by Martin Hewings
2iim YouTube Channel
References To Study (Practice):
CAT's previous year's papers
Objective General English (Arihant)
Free PDFs for CAT 2024 preparation
Articles
Certifications By Top Providers
Accounting with Tally ERP9
Via NIIT Digital Banking Business Model
Via State Bank of India Digital Skills Artificial Intelligence
Via Accenture Thinking Critically
Via Harappa Banking 101 A Guide for Beginners in the Banking Sector
Via EduBridge Business Analytics Foundations
Via PW Skills Explore Top Universities Across Globe
University of Essex, Colchester
Wivenhoe Park Colchester CO4 3SQOxford Brookes University, Oxford
Headington Campus Oxford OX3 0BP UKNorthumbria University, Newcastle City Campus
Sutherland Building, Northumberland Road, Newcastle-upon-Tyne, NE1 8STCardiff Metropolitan University, Cardiff
Llandaff Campus, Western Avenue, Cardiff, CF5 2YBUniversity of Reading, Reading
Whiteknights PO Box 217 Reading Berkshire RG6 6AHBristol Baptist College, Bristol
The Promenade, Clifton Down, Bristol BS8 3NJSAT 2025 Exam: Dates, Registration, Fees, Syllabus, Eligibility
20 min ⋆ Jun 23, 2025 12:06 PM ISTSAT Exam Dates in India 2025, Month Wise Test Date - Check Here
9 min ⋆ Jun 23, 2025 07:06 AM ISTPTE Describe Image Practice Test: Sample Questions and Answers
10 min ⋆ Jun 23, 2025 11:06 AM ISTIELTS Full Form - Types, Pattern, Eligibility and Fees
9 min ⋆ Jun 09, 2025 09:06 AM ISTACT Exam 2025: Dates, Registration, Fees, Eligibility, Syllabus, Sample Paper and Results
15 min ⋆ Jun 23, 2025 10:06 AM ISTPTE Summarize Spoken Text Tips and Tricks To Score High
9 min ⋆ Jun 23, 2025 10:06 AM ISTPopular Courses and Specializations
List of colleges accepting CAT
Browse Bschool Colleges by State
Questions related to CAT
Have a question related to CAT ?
Hello aspirant,
The question papers for CAT MGU University can be found on their official website, or you can also visit careers360 website for the same.
The link of which, I am attaching here,
https://university.careers360.com/articles/mgu-cat-2025
Regards
Mansi Satwani 07 July,2025
Hello Anshuman!!!
You have gotten 86% in 10th, which is a good score. 70% in graduation is not the best but decent. But the main problem is your 12th score which is 62%.
You would be already aware that the Top IIMs (BLACKI) give a big emphasis on your academic score. Let me tell you one example of IIM Ahmedabad,
According to a research i read a few days ago, in IIM Ahmedabad,
70.8%
of students has 90+ percent in 12th,
25.8%
has 80-90 percent and around
3.8%
has less than 80% with the bracket of 60-69 having only
0.26%
students of the total batch. Nearly same is the case of the other top IIMs like IIM Bangalore, IIM Calcutta, IIM Lucknow, IIM Kozhikode and IIM Indore.
Statistically, getting into these TOP IIMs is possible with 62% in 12th is possible (0.26% has done it) but practically you cannot get into these TOP IIMs unless you top the CAT exam.
See, I don't wish to dishearten or demotivate you but I wish to tell you the truth. Although the probability of you getting into these TOP IIMs is very less, but trying is better than doing nothing. You have a good score in 10th which will certainly help you. The least you could do is try your best.
My advice would be that you should not focus on these things like "Will I get top IIM" or negative talk like " I got low marks I won't qualify" etc.
The main focus should be on your preparation.
Give 100% in your preparation because that's the only thing in your hand. You can't change your 10th/12th/Graduation scores but you can put some more effort in your preparation which would certainly help to get better percentile.
Keep working hard and give your best. You might surprise yourself!!! And if not BLACKI, there are many other good colleges like FMS, MDI, newer IIMs etc.
Yash Teotia 06 July,2025
Hello,
Yes, with a 622 rank in IPU CET for MBA and being a Delhi candidate, you have a good chance of getting admission in MAIT (Maharaja Agrasen Institute of Technology).
You don’t need to worry about not giving the CAT exam. IPU CET rank is enough for admission in MAIT under the CET quota.
Just make sure to keep MAIT high in your preference list during counselling.
Hope it helps !
Prachi Kumari 04 July,2025
Hello,
A NEET 2025 score of 333 marks, an All India Rank (AIR) near 3,56,000, and belonging to the SC category from Andhra Pradesh suggest a fair possibility of obtaining an MBBS seat within the state quota, especially in private medical colleges under Category A (government quota seats in private institutions).
In Andhra Pradesh, SC category cut-offs for Category A seats in private institutions generally vary from 320 to 370, influenced by the college and the counselling round. Government medical colleges tend to be more competitive, with the SC cut-off for MBBS frequently rising, often exceeding 400 marks.
Although obtaining a government MBBS seat is improbable, you stand a feasible opportunity in private medical colleges within A category (which offer lower tuition than B and C categories). In Round 2 or the Mop-Up round, you can anticipate improved opportunities, since cut-offs generally decrease when other students move to superior colleges or vacate seats.
Colleges such as NRI Medical College (Guntur), Katuri Medical College (Guntur), Great Eastern Medical School (Srikakulam), Alluri Sitarama Raju Academy of Medical Sciences (Eluru), and Fathima Institute of Medical Sciences (Kadapa) are among those where seats could become available for SC students in subsequent rounds under Category A.
Hope this helps. All the best!
Samriddha Pal 08 July,2025
Yes, candidates who qualify in CUSAT CAT can gain admission to various participating institutes based on their rank. These include engineering colleges associated with CUSAT, such as its own School of Engineering in Kochi, Model Engineering College, and over 20 government and private engineering colleges across Kerala like College of Engineering Thrikkaripur, Co-operative Institute of Technology Vadakara, and MG College of Engineering Thiruvallam. The final seat allotment is based on your rank and your choice of program during the counselling process.
Pradeepa P 02 July,2025
Popular CAT Questions
Directions for question :
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Option: 1
September 2020
Option: 2
May 2021
Option: 3
January 2021
Option: 4
January 2022
Directions for question:
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
Option: 1 None
Option: 2 None
Option: 3 None
Option: 4 None
Explore Career Options (By Industry)
Marketing Director
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.
4 Jobs Available
Business Development Executive
A Business Development Executive identifies and pursues new business opportunities to drive company growth. They generate leads, build client relationships, develop sales strategies, and analyse market trends. Collaborating with internal teams, they aim to meet sales targets. With experience, they can advance to managerial roles, playing a key role in expanding the company’s market presence and revenue.
3 Jobs Available
Content Marketing Specialist
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.
3 Jobs Available
Sales Manager
A Sales Manager leads a sales team to meet targets, formulates strategies, analyses performance, and monitors market trends. They typically hold a degree in management or related fields, with an MBA offering added value. The role often demands over 40 hours a week. Strong leadership, planning, and analytical skills are essential for success in this career.
2 Jobs Available
Marketing Manager
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.
2 Jobs Available
SEO Analyst
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.
2 Jobs Available
Digital Marketing Executive
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.
2 Jobs Available
Business Analyst
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.
2 Jobs Available
MBA/PGDM Admissions OPEN
Amity University Noida MBA Admissions 2025
ApplyAmongst top 3% universities globally (QS Rankings)
Graphic Era (Deemed to be University) Admissions 2025
ApplyNAAC A+ Grade | Among top 100 universities of India (NIRF 2024) | 40 crore+ scholarships distributed
UPES MBA Admissions 2025
ApplyRanked #41 amongst institutions in Management by NIRF | 100% Placement | Last Date to Apply: 15th July
Galgotias University | Admissions 2025
Apply25+ years of legacy | NAAC A+ Grade | 800+ Recruiters | 1.5 CR-Highest Package
Shoolini University Admissions 2025
ApplyNAAC A+ Grade | Ranked No.1 Private University in India (QS World University Rankings 2025)
GNA University MBA Admissions 2025
Apply100% Placement Assistance | Avail Merit Scholarships
News and Notifications
February 07, 2025 - 05:12 PM IST
January 27, 2025 - 05:47 PM IST
January 23, 2025 - 07:45 AM IST
January 19, 2025 - 02:21 PM IST
January 16, 2025 - 02:32 PM IST
January 13, 2025 - 10:45 AM IST
January 10, 2025 - 04:28 PM IST
Stay up-to date with CAT News
Back to top