Great Lakes - PGDM & PGPM Admissions 2026
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024
CAT Application Date:01 Aug' 25 - 13 Sep' 25
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.
This Story also Contains
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.
For instance, given the number 234432, how would you determine the unit digit and the last two digits of the number?
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.
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
Ans: (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.
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
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 = 04
Odd20k = 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 = 75
Even20k= 76(last two digits) where k is a positive integer.
Eg: 48200 = 76 (last two digits)
Practice Mock Tests and CAT Question Paper
Learn the concept of class 9 Mathematics NCERT (for theory)
Arun Sharma: A Quantitative Approach for CAT (6th Edition)
YouTube Channel of 2iim
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
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.
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%.
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.
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.
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
1. CAT previous year's papers
2. Question bank from CAT-Holic
3. How to Prepare for Data Interpretation for CAT by Arun Sharma
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. |
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.
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)
Advanced English Grammar by Martin Hewings
2iim YouTube Channel
CAT's previous year's papers
Objective General English (Arihant)
On Question asked by student community
Yes, you can fill the CAT form even if you currently have a backlog. CAT eligibility requires you to be in your final year of graduation or already graduated backlogs don’t stop you from applying.
While filling the form:
Enter the aggregate percentage/CGPA of marks you have obtained up to the latest semester for which results are declared (in your case till 4th semester).
There will be an option to mention that you have a backlog.
If you clear the backlog later, you’ll just need to show the updated marks during admission.
Hello Aspirant,
Yes, you can apply for the CAT exam as a final-year student. You must declare your backlog on the online application form. You do not write about it on the final-year student certificate; that document is to certify your enrollment status. You must clear all backlogs before the final admission process to any MBA college.
Hello,
Thank you for your question!
KL- MAT syllabus: Quantitative Aptitude, Reasoning, English/Verbal Ability, and General Awareness (similar to MAT/CMAT pattern).
CAT scores are valid in many private universities including KL University, but always check the year’s admission notification.
CAT vs other exams: CAT is toughest (IIMs + top B-schools), while MAT/CMAT/ATMA are relatively easier and accepted by many mid-level private universities.
Hello it will clear your doubt!
Hello Aspirant,
I saw a cat. The cat found an old map inside a drawer of the king's palace.
Here's why:
"a cat": It's the first time we mention the cat, so it's indefinite.
"The cat": Now we're talking about that specific cat we just mentioned, so it's definite.
"an old map": It's the first time we mention a map, and "old" starts with a vowel sound, so "an."
"a drawer": It's one of possibly many drawers, not a specific one known to us yet.
"the king's palace": This is a specific, unique place, so "the."
Hello Kapish
You can find the last 5 year questions of DILR for CAT at Careers360 website. Moreover, you can find the previous year papers of all the subjects i.e. DILR, Quants and VARC. I am attaching the link through which you would be able to access the same.
Here's the link:
CAT Previous Year Papers by CAREERS360
Sample paper of DILR:
CAT Sample Paper (DILR) by CAREERS360
Thank You!!!
Admissions Open | Globally Recognized by AACSB (US) & AMBA (UK) | 17.3 LPA Avg. CTC for PGPM 2024
IBSAT 2025-Your gateway to MBA/PGPM @ IBS Hyderabad and 8 other IBS campuses | Scholarships worth 10 CR
Amongst top 3% universities globally (QS Rankings) | Ranked among top 10 B-Schools in India by multiple publications
75+ years of legacy | #1 Entrance Exam | Score accepted by 250+ BSchools | Apply now
NAAC A+ Grade | Among top 100 universities of India (NIRF 2024) | 40 crore+ scholarships distributed
1 Exam accepted by 17 Top Symbiosis Institutes for 29 MBA programmes.