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Cracking CAT 2024: Your Guide to Understanding Factors, Tables, Conjunctions, and Interjections - Day 5
Edited By Team Careers360 | Updated on Jan 08, 2025 07:11 AM IST | #CAT
The CAT exam for MBA admissions 2026-2028 is expected to be scheduled for November 2025. In this 60-day CAT 2025 preparation guide series by Careers360, we’ll discuss strategies for tackling Permutation and Combination problems on Day 37, helping you prepare effectively and succeed in the CAT entrance test.
This Story also Contains
- Part-1: Quantitative Aptitude for CAT 2025
- Previous Year CAT questions on number system
- Part-2: Data Interpretation And Logical Reasoning For CAT 2025
- Part-3: VARC for CAT 2025
- Free PDFs for CAT Preparation 2025
This article covers Permutation and Combination problems, Syllogism questions with answers, and tips for understanding comparison in VARC. Permutation and combination problems are often considered challenging, and many aspirants struggle with them. To aid your preparation, we've included permutation and combination examples with answers, as well as previous years' questions (PYQs) for practice.
Part-1: Quantitative Aptitude for CAT 2025
Topic: CAT Number System-4 (Factors and Trailing Zeroes)
CAT number system questions based on factors are regularly asked in the CAT exam and other MBA entrance examinations.
Questions about factors are of the form of
To find the number of all factors
To find the number of even factors
To find the number of odd factors
To find the number of factors of multiple of some value (Value will be given)
To find the number of factors which are perfect squares/perfect cubes etc
To find the number of Co-prime factors
To find the sum of factors
To find products of all factors etc.
Number of ways of writing a number N as a product of two numbers?
Important Formula for CAT number system questions
Number of factors:
Do Prime factorization first
N = pa × pb × rc × … where p, q, r are prime numbers; a, b, c are positive integers
The number of factors of N= (a+1)(b+1)(c+1)…
Sum of factors
Do prime factorisation first.
N = pa × qb × rc × … where p, q, r are prime numbers; a, b, c are positive integers
Sum of factors = (pa+1-1/p-1) (qb+1-1/q-1) (rc+1-1/r-1)
Trailing Zeroes and Exponent of a prime number:
Trailing zeroes give the number of zeroes at the end of the number.
For example, 54600 has two trailing zeroes.
In a product, a pair of 2 and 5 forms one trailing zero. This concept is used to find the number of trailing zeroes.
From this topic following types of questions were asked:
- Find the trailing zeroes in 54! etc
- Find the trailing zeroes in x3b x5c etc
- Find the highest power of 7 in 200! etc
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Use NowPrevious Year CAT questions on number system
The two previous year CAT questions as per the number system CAT Syllabus are given below:
Q1. How many factors of 24 × 35 × 104 are perfect squares which are greater than 1? [TITA- CAT Question Paper 2019]
Solution:
N = 24 × 35 × 104 = 24 × 35 × 24 x 54 = 28 × 35 × 54
Perfect square factors will be formed only for even (including 0) powers of prime factors.
Powers of 2 for which perfect square factors will be found for = 0, 2, 4, 6, 8 (5 ways)
Powers of 3 for which perfect square factors will be found for = 0, 2, 4 (3 ways)
Powers of 5 for which perfect square factors will be found for = 0, 2, 4 (3 ways)
Total number of perfect square factors will be = 5 x 3 x 3 = 45
Total number of perfect square factors greater than 1 will be = 45 – 1= 44
So, the answer is 44.
Q2. What is the highest power of 12 that divides 54!
[Based On CAT Question Paper ]
25
26
30
4
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Solution: A
12 = 22 x3, so we need to count the highest power of 2 and highest power of 3 that will divide 54!
The highest power of 2 divides 54! = [54/2] + [54/4] + [54/8] + [ 54/16] + [54/32]
= 27 + 13 + 6 + 3 + 1 = 50, where [x] ? greatest integer function.
Highest powers of 4 that divides 54! = 50/2 = 25
Highest power of 3 that divides 54! = [54/3] + [54/9] + [54/27] = 18 + 6 + 2 = 26, where [x] ? greatest integer function.
So, the highest power of 12 that divides 54! = min (25, 26) = 25.
Prerequisite:
To prepare for the number system for CAT exam according to the number system CAT syllabus, a student must have knowledge of
- Prime, Composite and Co-primes
- Even and Odd numbers
- Sum of Geometric Progression
- Exponents
- Factorials
Tips On CAT Preparation For Number System (Factors and Trailing Zeroes)
- Find the number of 5s to find the trailing zeroes is n! as the number of 2s is always greater than the number of 5s.
Eg: number of trailing zeros in 100! = [100/5] + [100/25] = 20 + 4 =24 where, [x] is the greatest integer function.
So, we can write the number of trailing zeroes in n! = [n/5] + [n/25] + [n/125] + ………. - Product of all factors of N = N (no of factors/2)
- To find the even factors, divide the given number by 2 and find the number of total factors of the quotient.
- Apply the concepts to practice Number System questions.
- Practice previous year CAT questions on number system
References to Study (Theory):
- 1. Learn the concept of factors and Multiples from class 9 Mathematics NCERT (For Theory)
- Arun Sharma: A Quantitative Approach for CAT (6th Edition)
- Kailasha Online Learning Classroom
References to Study (Practice):
- MASTER Number System for CAT and GMAT by Nishit K Sinha.
- Sample Papers
- CAT previous year papers
Part-2: Data Interpretation And Logical Reasoning For CAT 2025
Topic: Data Interpretation (Table)
In previous articles, we have covered DI based on Bar graphs, Pie charts and Line graphs. In this article, we will deal with data represented in the form of a table for the CAT exam. Data interpretation is a must-come topic in the CAT Exam and other management entrance exams.
DI on Table Chart
In this section, we will discuss the basics of a table chart. The boxes of the table consist of different types of information such as the population of a town, marks of a student, expenses of a company, production data of any industry etc. Table Chart questions are extremely important and have a good weightage as well. Many students sometimes find it difficult to solve these types of questions. Therefore, its recommended for students to practice these questions rigorously.
Sample:
Average marks of students of class 10 of different schools of a city are represented subject wise as shown in table:
Maths | Science | English | Social Science | Hindi | |
St. Marry | 81 | 81 | 81 | 81 | 81 |
Elite | 78 | 78 | 78 | 78 | 78 |
Romex | 64 | 64 | 64 | 64 | 64 |
DPS | 91 | 91 | 91 | 91 | 91 |
Questions On the Line Graph From CAT Previous Year Papers
Answer the questions on the basis of the information given below. A study was conducted to ascertain the relative importance that employees in five different countries being assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country. [ CAT Question Paper 2015]
Q1. Which of the following pairs of countries are most dissimilar?
China and Japan
India and China
Malaysia and Japan
Thailand and Japan
Ans: (4)
Difference in ranks skills-wise is shown as below:
C | N | D | V | P | |
China and Japan | 3-2 =1 | 2-1 =1 | 4-1 =3 | 5-4 =1 | 5-3= 2 |
India and China | 2-1= 1 | 3-1 =2 | 5-4 = 1 | 5-4 = 1 | 3-2 =1 |
Malaysia and Japan | 4-3 =1 | 5-2 =3 | 2-1= 1 | 4-1 = 3 | 5- 3 =2 |
Thailand and Japan | 3-2 =1 | 3-2 =1 | 5-1 =4 | 4-1 =3 | 5-4=1 |
Thailand and Japan should be the answer since these countries show the maximum difference in ranks (i.e., 4) on the basis of decisiveness.
No other countries show a difference of 4.
Q2. Which of the following countries is least dissimilar to India?
- China
- Japan
- Malaysia
- Thailand
Ans: (1)
Difference between the ranks on the basis of given traits of other countries with India is calculated.
Traits | China | Japan | Malaysia | Thailand |
C | 2-1=1 | 5-1=4 | 4-1=3 | 2-1=1 |
P | 3-2=1 | 4-2=2 | ||
N | 3-1=2 | 3-3=0 | ||
V | 5-4=1 | 4-2=2 | ||
D | 5-4=1 | 5-5=0 |
India and China show a maximum difference of 2 for 1 time.
India and Japan show a difference of greater than 2 (Compassion), so it cannot be least dissimilar and we need not to calculate differences for other traits.
Similar is the case with Malaysia.
With Thailand, the difference of 2 appeared twice. Therefore it can not be least dissimilar. The answer is China.
Q3. Which amongst the following countries is most dissimilar to India?
- China
- Japan
- Malaysia
- Thailand
Solution: (2)
since China is the least dissimilar, as discussed in the previous question. So, China cannot be the answer, and we will not find the differences for China in this case.
Traits | Japan | Malaysia | Thailand |
C | 5-1=4 | 4-1=3 | 2-1=1 |
P | 5-2 =3 | 3-2=1 | 4-2=2 |
N | 3-2=1 | 5-3=2 | 3-3=0 |
V | 4-4=0 | 4-1=3 | 4-2=2 |
D | 3-1=2 | 5-2=3 | 5-5=0 |
Clearly, Japan shows the maximum difference in ranks, So Japan is most dissimilar in ranks with India
Prerequisite:
To prepare Data Interpretation (Line Graph) for the CAT exam, a student must learn
- Percentage (Basic)
- Averages
- Calculations based on ratios
- Approximation
Tips On CAT Preparation For DI (Table Chart):
- Use Approximation.
- Observe the data carefully.
- Solve small calculations mentally.
References to Study (Theory):
- LRDI for CAT and GMAT by Nishit K Sinha.
- To learn the basics of bar graph read statistics of class 9 and Class 10 Mathematics from NCERT (For Theory)
- Kailasha Online Learning Classroom YouTube Channel
References to Study (Practice):
1. Sample Papers
2. Question bank from CAT-Holic
3. How to Prepare for Data Interpretation for CAT by Arun Sharma
4. CAT previous year papers
Part-3: VARC for CAT 2025
Topic: Conjunction and Interjection and its uses:
Conjunctions are used to connect more than two words or phrases. It defines the connection between the joined sentences.
Examples:
He likes to eat both Noodles and Pizza.
The tulips and orchids are flowers.
Until next month, I can’t afford to travel.
Conjunctions are useful as well as convenient. Conjunctions are extremely common.
There are three types of English conjunctions:
Coordinating: for, not, yet, so etc
Subordinating: Although, though, while, if, until etc.
Correlative: Neither/ Nor, Whether/ Or, Either/ Or etc.
Interjections are used to express emotions in a sentence. Also, interjections are grammatically independent of the words around them.
Examples:
Greeting: Hey! After such a long time, I am seeing you.
Joy: Oh my gosh! What is happening there?
Surprise: Ah! Finally you clear your CAT Exam!
Approval: Yes! you are hired!
Attention: Listen, you are fired.
Sorrow: Oh dear, I really wanted to marry you.
Questions On Conjunction and Interjection from CAT Previous Year Papers/ CAT practice questions on conjunctions
Direction: Choose the part which requires correction. [Based on Previous Years Questions]
Q.1 As soon as (1) / he got the (2) / courier, at once (3) / he started. (4) / No Error (5)
(1)
(2)
(3)
(4)
Ans: C
The conjunction 'as soon as is used to show two simultaneous actions. So, in the third part, the use of ‘at once’ is incorrect
Q2. I will either (1) / go for an interview (2) / else play (3) / Cricket. (4) / No Error (5)
1
2
3
4
5
Ans: C
With “Either’, ‘Or’ comes.
So, (3) contains error. ‘else’ should be replace by ‘or’.
Q3. Be kind (1)/ not only in words (2) / and also (3) / in behavior. (4) / No Error (5)
1
2
3
4
5
Ans: C
The correct conjunction to be used is ‘but’ in place of ‘and’.
Prerequisite:
- Knowledge of sentence formation
- Basic Knowledge of Sentence Formation
- Use of Nouns, Pronouns and Verbs.
CAT Preparation Tips for Verbal Ability (Conjunction and Interjection)
Use of the comma when a coordinating conjunction is joining two independent clauses.
When a conjunction joins two words in a sentence, then the sentence cannot be separated in two independent sentences.
Learn all the conjunctions and their uses separately with the help of examples.
References to Study (Theory):
Advanced English grammar by Wren and Martin
2iim YouTube Channel
References to Study (Practice):
Question Bank from iquanta.com
CAT previous year papers
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
We will be back with Day-6 strategy. Do practice and be focused.
Thank You
All the best.
Free PDFs for CAT Preparation 2025
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 ?
Hello
If you are aiming for the CAT exam this year and considering joining the fourth year, it might be a good idea if you are confident in managing both your academic workload and CAT preparation .
However, the CAT exam is competitive and balancing your BCom studies and preparation might be challenging.
If you think you can handle the extra year and need more time for focused preparation , joining the fourth year could provide that but you should also evaluate your current academic commitments and your ability to stay consistent with CAT preparation .
Hope this gives you the clarity you need.
Mitali Sharma 17 February,2025
Hello,
Securing a seat in a National Institute of Technology (NIT) with a JEE Main score of 67 as an SC category candidate is challenging. Consider the following points:
-
Qualifying Cutoff : The expected qualifying cutoff for SC candidates in JEE Main 2025 is around 65 marks.
-
Admission Prospects : While you may qualify for JEE Advanced, admission to NITs typically requires higher scores. For instance, in previous years, SC candidates needed higher marks to secure seats in NITs.
-
Improvement Opportunity : Consider preparing for the next JEE Main attempt to achieve a higher score, thereby enhancing admission prospects in subsequent counseling rounds.
You can also use the JEE Mains College Predictor Tool to predict which college you can get based on your score.
Hope you find it useful!
Prachi Kumari 13 February,2025
Hello,
With an 88 percentile in the JEE Main exam and belonging to the SC category from Karnataka, your chances of securing a Computer Science Engineering (CSE) seat in NITs, IIITs, or GFTIs are as follows:
-
NITs :
- Top NITs like NIT Trichy or NIT Surathkal have higher cutoffs for CSE. For instance, in 2024, the closing rank for SC category in CSE at NIT Trichy was around 1,171.
- With an 88 percentile, your rank might be higher than these cutoffs, making it challenging to secure a CSE seat in top NITs.
-
IIITs :
- IIITs also have competitive cutoffs for CSE. For example, IIITM Gwalior had a closing rank of 11,494 in 2024, making it highly competitive.
- Your current percentile may not meet the typical cutoffs for CSE in top IIITs.
-
GFTIs :
- GFTIs generally have higher closing ranks compared to NITs and IIITs, providing a more accessible option.
- You may have a better chance of securing a CSE seat in GFTIs with your current percentile.
Hope you find it useful !
Prachi Kumari 13 February,2025
Hello,
According to the NIFT 2025 exam schedule , the General Ability Test (GAT) is from 9:00 AM to 11:00 AM, and the Creative Ability Test (CAT) is from 2:30 PM to 5:30 PM. This indicates a gap of 3.5 hours between the two tests.
The official guidelines do not specify whether candidates are allowed to leave the exam center during this interval. Therefore, it's advisable to:
-
Check the Admit Card : Specific instructions regarding breaks may be mentioned.
-
Contact the Exam Center : Reach out directly to confirm their policy on leaving during the interval.
By taking these steps, you can ensure compliance with the exam center's policies and plan your day effectively.
Hope you find it useful !
Prachi Kumari 09 February,2025
The CDAC C-CAT exam dates for the August 2025 batch haven't been announced yet. However, I can provide you with some information on the exam schedule for the February 2025 batch, which might give us an idea of what to expect for the August batch.
The CDAC C-CAT exam for the February 2025 batch was held on January 11 and 12, 2025.The application form for the February batch was available from November 2024 to December 30, 2024.
Typically, the CDAC C-CAT exam is conducted twice a year, in June and December, for admissions to the August and February batches, respectively. However, the exact dates for the August 2025 batch will be announced separately.
To stay updated on the CDAC C-CAT exam dates and other important events, I recommend checking the official CDAC website regularly.
BEST OF LUCK!!
sadafreen356 04 February,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
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