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The CAT 2025 exam for MBA admissions is expected to be scheduled for 30th 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.
CAT 2025: VARC, DILR, and Quant: MCQs & Weightages | Chapter-wise MCQs
CAT 2025 Study Material: VARC | Quantitative Aptitude | 60 Days Study Material by Experts
Online MBA: Complete Guide | Universities That Redefine Online MBA in India
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. They are hard to solve and often very tough to crack with proper guidance and strategy. To aid your preparation, we've included permutation and combination examples with answers, as well as previous years' questions (PYQs) for practice.
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?
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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
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
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
MASTER Number System for CAT and GMAT by Nishit K Sinha.
Sample Papers
CAT previous year papers
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.
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
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
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.
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.
CAT 2023 Official Question Paper and Answer Key (Slot 1) | |
CAT 2023 Official Question Paper and Answer Key (Slot 3) |
CAT 2025 is likely to be held in November 2025, tentatively on the last Sunday of the month.
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.
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.
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.
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.
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Although, it's very unlikely that you will secure a seat in top ABM with CAT 67 percentile. Here's is a breakdown to your question:
· CAT Percentile vs. Score: A CAT score of 67 typically translates to a percentile in the range of 90-95 percentile based on the provided data from previous years. While this is a decent score overall, it falls short of the cutoffs for most top-tier ABM programs.
· Cutoffs for Top ABM Institutes:
· Overall Good CAT Score: Generally, a CAT percentile of 90 and above is considered a good score for securing admission to decent MBA programs in India. For top-tier institutes, a percentile of 95 and above is often preferred.
· MBA Colleges Accepting 60-70 Percentile: While there are MBA colleges that accept CAT scores in the 60-70 percentile range, these are generally not the top-ranked or most sought-after ABM programs. The focus of those lists is on general MBA programs, not specifically ABM.
While securing a seat in ABM can be tough, you can research about other colleges, consider other examinations, to improve your application profile.
You Got This !
Hello,
achieving a 99.99 pecentile in the CAT exam significantly enhances your prospects for admission to JBIMS, which evaluates candidates using an application rating(AR) score, which includes
-entrance exam score (CAT/MH-CET/CMAT) : 60% weightage
-Past Academic Record (PAR) : 15% weightage (https://cracku.in/colleges/jbims/admission-process/?utm_source=chatgpt.com)
-Extra-curricular Activities/Work Experience : 20% weightage (https://jbims.edu/uploads/announcement/Revised_M_Sc__Finance_Admission_Procedure_Batch_2024-26.pdf?utm_source=chatgpt.com)
-Diversity (Academic/Gender): 5% weightage
while ahigh CAT percentile is crucial, a lower academic record may impact your overall AR score. Nonetheless, exceptional performance in other areas, such as entrance exams and extracurricular activities, can help offset weaker academic credentials. it's advisable to review JBIMS's detailed admission criteria and consider strengthening other aspects of your application to enhance your chances
To find the 2024 MHT CET answer key, you'll need to check the official Maharashtra State Common Entrance Test Cell website. This is the primary source for all official announcements and documents related to the MHT CET exam. After the exam concludes, the CET Cell typically releases a provisional answer key.
Once released, the provisional answer key will likely be available as a downloadable PDF file. You'll need to navigate to the official website, look for the MHT CET section, and find the link related to the answer key. This link might be labelled "MHT CET 2024 Answer Key" or something similar.
After downloading the answer key, you can compare your responses with the official answers. If you find any discrepancies or have objections, the CET Cell usually provides a window for raising objections. You'll likely need to pay a specified fee for each objection raised. The official website will provide instructions on how to submit your objections, which may involve logging into your candidate portal and following the provided steps.
Finally, after considering all objections, the CET Cell will publish a final answer key. This final version is considered definitive, and the MHT CET results will be based on it. Keep an eye on the official website for all updates and announcements regarding the 2024 answer key.
I hope this helps.
Greetings! Here's a detailed response to your query
Okay, so you're a bit confused about what to put in those CAT, FMS, DSE, and IIFT forms regarding your 12th scores. Since you did CBSE, they usually only consider your final 12th standard marks.
Even though you did great in 11th, scoring 495 out of 500, for these entrance exam forms, they're specifically asking about your 12th board exam marks .You mentioned you got 400 out of 500 in 12th, which comes out to 80%.
Therefore, when filling out the forms for CAT, FMS, DSE, and IIFT, you should enter 80% as your 12th percentage. The aggregate of 11th and 12th isn't typically what they're looking for in these sections. They want to know how you performed in your final board exams. So, stick with the 80% from your 12th results. Good luck with your applications!
Greetings! Here's a detailed response to your query:-
Determination of the best time to start the journey of CAT examination is based on individual factors like your current skill level, knowledge ,potential, learning pace and availability. To give yourself the best chance of success on the CAT exam , which usually takes place in November, it's advisable to begin studying between January and March of that same year. This 8 to 12-month preparation window is widely recommended by experts. But if you're managing your college along with the CAT preparations make sure you start from 2nd year onwards. It will hep you manage stress and you'll have ample amount of time to get along with the syllabus , pattern and various practice and mocks .
You'll be able to build a strong foundation in each sections and be able to know your strengths and weaknesses in different topics. The CAT syllabus is extensive, and early preparation allows for thorough coverage. Assess your learning speed and adjust your preparation timeline accordingly.
Essentially, while the ideal start time is subjective, beginning your CAT preparation well in advance is generally considered the most effective strategy for achieving optimal results.
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