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Cracking CAT 2025: Your Guide to Understanding Factors, Tables, Conjunctions, and Interjections - Day 5
Edited By Team Careers360 | Updated on Jun 18, 2025 07:14 PM IST | #CAT
With CAT 2025 likely scheduled for 30th November, strategic preparation is crucial. On Day 37 of the Careers360 60-day plan, the spotlight is on mastering Permutation and Combination—an area that often troubles aspirants due to its complexity. This guide not only breaks down tough concepts with solved examples and PYQs related to Permutation and Combination. It also includes insights into Syllogism and VARC comparison questions to strengthen your overall problem-solving and verbal reasoning skills.
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
- Tips and Tricks to Solve Factor and Table Questions
- Free PDFs for CAT Preparation 2025
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
Previous 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
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 NowSolution: 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)
Tips and Tricks to Solve Factor and Table Questions
Mastering factors and multiplication tables is essential for quick and accurate math problem-solving. With the right strategies, identifying factors and solving table-based questions becomes easier. Practice, recognition of patterns, and smart shortcuts significantly improve speed and confidence in exams.
Tip 1: Learn Tables Up to 20 Thoroughly
Example: To solve 14 × 7 quickly, recall the table of 14: 14, 28, 42, 56, 70, 84, 98.
Memorising multiplication tables up to 20 boosts your ability to solve problems swiftly. Knowing answers instantly reduces the time needed for calculations and supports better factor recognition. Use songs, flashcards, or apps to reinforce memory.
Tip 2: Use Factor Pairs
Example: Factors of 36: (1,36), (2,18), (3,12), (4,9), (6,6)
Writing numbers as factor pairs helps in identifying all possible factors efficiently. Start with 1 and go up to the square root of the number. For 36, check from 1 to 6; each valid division gives a complete pair.
Tip 3: Apply Divisibility Rules
Example: 72 is divisible by 3 because 7 + 2 = 9 (which is divisible by 3).
Divisibility rules help identify factors quickly without full division. Learn rules for 2, 3, 5, 6, 9, and 10. These rules simplify spotting common factors and validating whether one number is a factor of another.
Tip 4: Break Numbers into Prime Factors
Example: 60 = 2 × 2 × 3 × 5
Prime factorisation breaks a number down into its simplest building blocks. This is especially helpful in finding LCM, HCF, or solving word problems. Use factor trees or the division method for clarity and systematic calculation.
Tip 5: Use Multiples to Identify Common Factors
Example: Multiples of 6: 6, 12, 18, 24...; Multiples of 8: 8, 16, 24... ⇒ Common multiple: 24
Listing multiples can identify the least common multiple (LCM) or help in comparing tables. It’s useful when solving time-based or event problems where something repeats at different intervals.
Tip 6: Recognise Square and Cube Numbers
Example: 49 is 7²; 27 is 3³
Recognising square and cube numbers helps quickly determine factors and simplify root-based problems. Memorise squares up to 30 and cubes up to 12 to improve speed and pattern recognition in exams and mental math tasks.
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) |
Frequently Asked Questions (FAQs)
1. When will CAT 2025 be conducted?
CAT 2025 is likely to be held in November 2025, tentatively on the last Sunday of the month.
2. Which IIM will conduct CAT 2025?
CAT is organized by one of the IIMs on a rotational basis every year. The organizing IIM for CAT 2025 will be mentioned in the official notification released likely in July 2025. Though the pattern and structure of the exam remain unchanged, the question pattern and difficulty level could be slightly different based on the organizing IIM.
3. Will CAT 2025 be tough?
CAT is a very competitive exam, and the level of difficulty changes every year. Quantitative Aptitude and LRDI are usually moderate to tough, but VARC may be tricky as it involves reading comprehension complexity. But as CAT is a percentile-based test, your ranking depends on how you perform in relation to other candidates.
4. How should I start preparing for CAT 2025?
Begin with the knowledge of exam pattern, going through previous year papers, and making a systematic study plan. Prioritize conceptual clarity and then proceed to mock tests and sectional practice. A constant analysis of mock tests will enable you to realize your weaknesses and enhance your speed and accuracy.
5. Are previous year CAT papers enough for preparation?
Past year papers are needed to grasp the pattern of the exam and the types of frequently asked questions, but they alone are not sufficient. Practice mock tests, sectional tests, and topic-wise questions to enhance speed, accuracy, and problem-solving abilities as well. As CAT questions don't repeat word by word, candidates need to focus on concepts instead of memorization.
6. Why are factors and tables important for CAT 2025 preparation?
Factors and multiplication tables form the foundation of arithmetic problem-solving. CAT Quantitative Aptitude questions often require quick calculations and number sense.
7. What is the best way to memorise multiplication tables efficiently?
Use repetition techniques like writing and chanting tables daily. Break them into patterns (e.g., even numbers for 2’s table) or use apps and flashcards. Learning through rhymes or visual charts can also help retain tables up to 20 quickly and effectively.
8. How do conjunctions and interjections help in CAT’s VARC section?
Conjunctions help understand the logical flow of ideas in reading comprehension and para jumbles. Interjections, though less common, aid in identifying tone or intent in sentence correction or fill-in-the-blanks.
9. What are the common mistakes students make while solving factor-based questions?
Students often miss out on factor pairs or forget to check for divisibility. Another mistake is assuming primes or not verifying all factors up to the square root.
10. How should I practice these topics effectively on Day 5?
Dedicate time to revising multiplication tables, solve at least 20 factor-based questions, and review basic grammar rules related to conjunctions and interjections.
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Questions related to CAT
Have a question related to CAT ?
Hello Sahitya
For FMS Delhi, your percentile should be 99%+ and it should be 99.5%+ to be on the safer side.
Now coming to the academics:
1. 10th marks: 75%+ are given 10 out of 10
2. 12th marks: 75%+ are given 10 out of 10
3. Graduation marks: FMS doesn't considers graduation marks for screening.
So if you have 75%+ in both 10th and 12th, you will get full marks in academic score.
To know more about FMS: FMS
Hope this answer helps! Thank You!!!
Yash Teotia 13 July,2025
Hello Ayush
This is definitely a myth that with 0 work-ex you can't get IIM ABC because freshers still get into them although the competition is brutal but if you have good academics (9/9/9) and a good CAT (99.5%+), you have a chance.
These are some other good colleges except IIM ABC which you can aim for:
TIER 1:
- IIM Lucknow
- IIM Kozhikode
- IIM Indore
- IIM Shillong
- FMS Delhi
- SPJIMR Mumbai
- MDI Gurgaon
- IIFT Delhi & Kolkata
Tier 2:
- NMIMS Mumbai
- SIBM Pune
- SCMHRD Pune
- IMT Ghaziabad
- XIM Bhubaneshwar
- GIM Goa
- TISS Mumbai
To know more about CAT: CAT by Careers360
Hope this answer helps! Thank You!!!
Yash Teotia 13 July,2025
Hello Aspirant,
With an AIR (All India Rank) of 1,60,000 in NEET and in the OC (Open Category) there is a very slim chance of getting an MBBS seat in a government medical college, especially in General Category seats through All India Quota (AIQ), but here are some options:
- MBBS in Private Colleges: You could get a seat in a private medical college through the state quota, especially in Tier 2/3 states where the cutoffs are relatively lower. The fee would be high compared to government colleges.
- BDS Seats: You have fair chances for BDS in both government & private dental colleges under the state quota.
- Deemed Universities: Some deemed universities may offer MBBS seats at this rank but the fee is exorbitantly high (15 to 25 lakhs/year).
- Management/NRI Quota: If you can afford, you can explore MBBS through management/NRI quota seats in private colleges.
- Alternatives: You can think of allied health science courses such as BAMS, BHMS, B.Sc Nursing etc., which also have good career scope.
You can also participate in state counselling rounds, as sometimes, seats remain vacant/unfilled, including mop-up rounds.
gopi 13 July,2025
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
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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