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Cracking CAT 2024: Your Guide to Understanding Factors, Tables, Conjunctions, and Interjections - Day 5
Edited By Team Careers360 | Updated on Aug 26, 2024 08:38 AM IST | #CAT
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.
Free Study Material: VARC | Chapter-wise Practice MCQs
Practice Questions: DILR | Quant | Most Scoring Concepts
Test: 20 Free Mock Test | 10 Year PYQs
This Story also Contains
Part-1: Quantitative Aptitude for CAT 2024
Topic: CAT Number System-4 (Factors and Trailing Zeroes)
Factors:
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 2024 Most Scoring Concepts- VARC, DILR & QUANT
Start your CAT journey today and download CAT 2024 most scoring concepts PDF, including study materials based on CAT previous year papers, CAT question papers, and CAT exam sample questions.
Download EBookSolution: 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 2024
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 2024
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 2024
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 aspirant,
The CAT authorities may initiate a verification process to ensure the accuracy of your caste information. This could involve contacting the issuing authority of your EBC certificate or requesting additional documents.
If the verification process confirms your EBC status, your category might be changed to EBC. This could potentially affect your eligibility for certain seats or scholarships.
If your EBC certificate is not accepted as proof of OBC status, you might be ineligible for OBC reservations. However, you would still be eligible to appear for the CAT exam as a General category candidate.
It's crucial to:
- Monitor your application status: Keep an eye out for any communications from the CAT authorities regarding your application and caste verification.
- Provide necessary documents: If requested, promptly submit any additional documents that might be required to verify your caste status.
- Contact CAT authorities: If you have any concerns or questions, don't hesitate to reach out to the CAT helpline or support team.
Remember: The final decision regarding your eligibility for OBC reservation will depend on the specific policies and procedures of the CAT authorities.
I hope this information helps you.
kanishkakaushikii2004 02 September,2024
Hello Aspirant,
Common Aptitude Test (CAT) is a national-level exam, for MBA Programmes to get admissions in top management institutions in the country such as IIM's. Filling CAT Form is very crucial as the IIM selection and admission process will depend on this form. The IIM CAT 2024 registration process has started and the last date to apply is September 13.
The important point to note here is that the CAT application form cannot be edited once it is submitted.
Only certain fields can be edited that too when the CAT form correction window opens. Candidates can make changes in their CAT 2024 application form for free of cost when the form correction window opens. Candidates can only edit three fields photograph, signature and test city preference.
Once the CAT application form is submitted, candidates are not allowed to make changes in it. In case, you've made errors, you need to fill a fresh CAT application form and pay the fees again.
Thankyou.
Common Aptitude Test (CAT) is a national-level exam, for MBA Programmes to get admissions in top management institutions in the country such as IIM's. Filling CAT Form is very crucial as the IIM selection and admission process will depend on this form. The IIM CAT 2024 registration process has started and the last date to apply is September 13.
The important point to note here is that the CAT application form cannot be edited once it is submitted.
Only certain fields can be edited that too when the CAT form correction window opens. Candidates can make changes in their CAT 2024 application form for free of cost when the form correction window opens. Candidates can only edit three fields photograph, signature and test city preference.
Once the CAT application form is submitted, candidates are not allowed to make changes in it. In case, you've made errors, you need to fill a fresh CAT application form and pay the fees again.
Thankyou.
Hridaya Rao 01 September,2024
Hello there,
Amrita Common Aptitude Test (ACAT), is a national level management enterance exam which is conducted by
Amrita Vishwavidyapeetham for MBA programmes offered at Amrita School of Business at Amaravati, Amritapuri, Bengaluru, Coimbatore and Kochi campuses.
The eligible students who wish to study MBA at Amrita School of Business can also avail up to 100 per cent scholarships. Apart from ACAT, the university also acceptsCAT,MAT,XAT,CMATandNMATscores for admission to its MBA programme.
Syllabus for ACAT:
Verbal Reasoning and LanguageData Interpretation and Analysis
General Knowledge on Indian and Global Scenarios
Quantitative Aptitude
Exam mode: Computer Based Test mode, 100 Questions
Type of Questions : 100 Questions
Marking Scheme : +3 marks for correct answers , -1 mark for an incorrect answer
Language : English
Duration of Exam : 150 Minutes or 3 hrs.
Total Seats in MBA Programmes are 360 Amrita School of Business, Coimbatore
180 Seats : Amrita School of Business, Amrita Vishwa Vidyapeetham - Kochi Campus
60 Seats : Amrita School of Business, Amrita Vishwa Vidyapeetham - Amritapuri Campus
60 Seats : Amrita School of Business, Amaravati campus
Comparing ACAT with CAT: CAT is more difficult than ACAT, Because it has much more higher competition compared to ACAT.
Thankyou. I hope this helps you.
For detailed information kindly visit to the given link.
https://bschool.careers360.com/articles/acat-preparation-tips
Amrita Common Aptitude Test (ACAT), is a national level management enterance exam which is conducted by
Amrita Vishwavidyapeetham for MBA programmes offered at Amrita School of Business at Amaravati, Amritapuri, Bengaluru, Coimbatore and Kochi campuses.
The eligible students who wish to study MBA at Amrita School of Business can also avail up to 100 per cent scholarships. Apart from ACAT, the university also acceptsCAT,MAT,XAT,CMATandNMATscores for admission to its MBA programme.
Syllabus for ACAT:
Verbal Reasoning and LanguageData Interpretation and Analysis
General Knowledge on Indian and Global Scenarios
Quantitative Aptitude
Exam mode: Computer Based Test mode, 100 Questions
Type of Questions : 100 Questions
Marking Scheme : +3 marks for correct answers , -1 mark for an incorrect answer
Language : English
Duration of Exam : 150 Minutes or 3 hrs.
Total Seats in MBA Programmes are 360 Amrita School of Business, Coimbatore
180 Seats : Amrita School of Business, Amrita Vishwa Vidyapeetham - Kochi Campus
60 Seats : Amrita School of Business, Amrita Vishwa Vidyapeetham - Amritapuri Campus
60 Seats : Amrita School of Business, Amaravati campus
Comparing ACAT with CAT: CAT is more difficult than ACAT, Because it has much more higher competition compared to ACAT.
Thankyou. I hope this helps you.
For detailed information kindly visit to the given link.
https://bschool.careers360.com/articles/acat-preparation-tips
Hridaya Rao 01 September,2024
Hello there,
It is beneficial to submit the EWS certificate in CAT format, or Central Government Authorized EWS Certificate will only be considered for CAT or there might be chance of rejection your certificate. You may contact the authority for more clarification.
Thankyou
It is beneficial to submit the EWS certificate in CAT format, or Central Government Authorized EWS Certificate will only be considered for CAT or there might be chance of rejection your certificate. You may contact the authority for more clarification.
Thankyou
Hridaya Rao 31 August,2024
When filling out the CAT (Common Admission Test) application form, you typically need to provide the aggregate percentage of marks obtained in your graduation. This usually includes the average of all the years of your degree program, not just the final year.
Some universities mention 4 year aggregate on degree certificate. Some metions just final year aggregate.
So you just have to put the mentioned percentage of degree certificate.
sadafreen356 31 August,2024
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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