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The CAT exam for MBA admissions 2025-2027 is scheduled for November 24, 2024. In this 60-day CAT 2024 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 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.
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:
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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
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
Tips On CAT Preparation For Number System (Factors and Trailing Zeroes)
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?
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?
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
References to Study (Theory):
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:
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) |
With a 59.95 percentile in CAT 2024 and ST category, you can expect calls from newer IIMs like IIM Bodh Gaya, IIM Jammu, and IIM Sirmaur, as they have lower cutoffs for reserved categories. Non-IIM options like IIT Madras (MBA), NIT Trichy (MBA), and state universities like Delhi School of Economics (DSE) might also consider your profile. Apply to institutions that prioritize diversity and offer ST reservation. Ensure your application highlights strong academics and achievements.
For more details you can visit the link given below
https://bschool.careers360.com/cat-percentile-predictor
Hi,
Based on the previous year analysis, According to your CAT 2024 percentile some of the best colleges offering MBA and PGDM course in Telangana in which you have chances to get a seat are the following
For more information about the colleges in which you have chances to get a seat you can predict using MBA college predictor tool provided below
https://bschool.careers360.com/cat-college-predictor
Hope this information will help you
Hi,
With a CAT 2024 score of 93.94 percentile, you have a good chance of getting calls from several IIMs. Here are some possibilities:
IIM Jammu
IIM Bodhgaya
IIM Udaipur
IIM Kashipur
IIM Vizag
Apart from IIMs, you can also consider other prestigious B-schools like:
Management Development Institute (MDI) Gurgaon
FMS Delhi
IIT Delhi
IIM Lucknow
IIM Indore
IIM Raipur
CAT exam is conducted every year for purpose of admission to various prestigious business school and management institutes in India. The exam is also considered among toughest entrance exams in India. The exam rats the logical skills of the candidates. You can get the college list based on your CAT score by simply visiting CAT College Predictor 2024
Hi Sonu,
Preparing for CAT 2025 through self-study requires the right study materials, a structured plan, and consistent effort. CAT Syllabus comprises of Quantitative Aptitude (QA), Data Interpretation and Logical Reasoning (DILR), Verbal Ability and Reading Comprehension (VARC).
You can get more detailed information in the mentioned website of Careers360, it will be helpful enough for preparation of CAT 2025.
If looking for online sources, you can go through few channels on YouTube like- Study Buzz, Takshzila, and Career Launcher. Apps like unacademy and Byju's can help as well.
All the best for your CAT preparation.
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