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How To Prepare CAT Quantitative Aptitude Strategy | DI, VA and LR - Day 3
Edited By Team Careers360 | Updated on Nov 07, 2024 08:09 AM IST | #CAT
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CAT Application Date : 01 Aug' 2025 - 13 Sep' 2025
The CAT 2024 exam for MBA admissions will be conducted in November 2024, and we've prepared a 60-day study plan to help you qualify for the exam. The Common Admission Test (CAT) is difficult, and being acquainted with its ideas is critical to passing it. In this article, we will go over three important topics: divisibility laws, line graphs, and verbs. These topics are typically included in the CAT examination, so studying them will help you prepare. We will also go over some previous year's questions to help you prepare.
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Divisibility:
To solve the Divisibility and remainder CAT questions, you must know the divisibility rules for different prime and composite numbers.
Here are some rules:
Divisor | Divisibility condition | Examples |
2 | The last digit is even (0, 2, 4, 6, or 8). | 1,564: 4 is even. |
3 or 9 | Sum the digits. If the result is divisible by 3 (9), then the original number is divisible by 3 (9). | 405 → 4 + 0 + 5 = 9 and 699 → 6 + 9 + 9 = 24 which both are clearly divisible by 3. 405 is divisible by 9 also but 699 is not. |
4 | Examine the last two digits. | 46532: 32 is divisible by 4. |
5 | The last digit is 0 or 5. | 875: the last digit is 5. |
6 | It is divisible by 2 and by 3. | 1,368: 1 + 3 + 6 + 8 = 18, so it is divisible by 3 and the last digit is even, hence the number is divisible by 6. |
8 | Examine the last three digits. | 84176: Examine divisibility of just 176: 22 × 8 = 176 |
11 | Form the alternating sum of the digits. | 918,082: 9 − 1 + 8 − 0 + 8 − 2 = 22. |
Eg: (i) 369 is divisible by 3 since some of the digits are divisible by 3.
(ii) 678 is divisible by 6 since it is divisible by both 2 and 3.
How will you check whether a number is divisible by 18, 24, or 72 (composite numbers)?
Do the Co-prime factors of the divisor. And the given number must be divisible by co-prime factors.
18 = 2 and 9 (For 18, the number should be divisible by 2 and 9 both)
24 = 3 and 8 (For 24, the number should be divisible by 3 and 8 both)
72 = 8 and 9 (For 72, the number should be divisible by 8 and 9 both)
Remainders:
As we all know
Dividend = Divisor x Quotient + Remainders
Questions based on remainders are being asked in the CAT exam. You must prepare this topic separately as there are many rules to find the remainder. Some of them are listed below:
Binomial Theorem
Method of Cancellation
Fermat Little Theorem
Chinese Remainder Theorem
Wilson Theorem
CAT Quant Questions With Solutions (Number System) From CAT Previous Year Papers/ CAT questions on Divisibility Rules:
Question 1. The remainder when 292929 is divided by 9 is? [IPMAT 2019]
3
4
2
1
Solution: (A)
If we divide 29 by 9, the remainder is 2.
So, we now will divide 22929 i.e. 2841 to get the remainder.
2841 can be written as 2(3x280+1) = (8280)x2
When we divide 8 by 9, the remainder is -1.
When divided by 9, will give as the remainder of ((-1)280)x2 = 2
Question 2: If then x divided by 70 leaves a remainder of: [CATQuestion Paper 2005]
0
1
69
35
CAT remainders questions with solution
Solution: (A)
Rem (163/70) = Rem (4096/70) = 36
Rem (173/70) = Rem (4913/70) = 13
Rem (183/70) = Rem (5832/70) = 22
Rem (193/70) = Rem (6859/70) = 69
Net Remainder = 36 + 13 + 22 + 69 = 140.
When 140 is divided by 70, the remainder is 0.
Question 3. How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7? [CAT Question Paper 2020]
41
42
40
43
Ans: (A)
Number of multiples of 2= 2, 4, 6, 8, ………, 120 (Total of 60 numbers)
Number of multiples of 5 = 5, 10, 15, 20……….., 120 (Total of 24 numbers)
Number of multiples of 7 = 7, 14, 21, …….., 119 (Total of 17 numbers)
Number of multiples of 2 and 5 =10, 20, …., 120 (Total of 12 numbers)
Number of multiples of 2 and 7 = 14, 28, ………, 112 (Total of 8 numbers)
Number of multiples of 7 and 5 = 35, 70, 105 (Total of 3 numbers)
Number of multiples of 2, 5 and 7 = 70 (Total of 1 number)
Total Numbers divisible by any of 2, 5 or 7 =(1) + (2) + (3) – (4) –(5) –(6) +(7)= 60+ 24+ 17 – 12 - 8 – 3 + 1= 79
Therefore, Numbers divisible by none of 2, 5 and 7 = 120 – 79 = 41.
Prerequisite:
The CAT exam requires students to have knowledge of the basic elements that are given below.
Prime numbers, composites, and Co-Primes
Even and Odd numbers
Digit Sum
Binomial Expansion
Multiples and Factors
Expansion of (a+b)n and (a-b)n where n is any positive integer.
Tips On CAT Preparation For Number System:
Remainder is equal to sum of individual remainders.
Eg: If (72 + 37 + 89) is divided by 7
Remainder = Rem (72/7) + Rem (37/7) + Rem (89/7) = 2 + 2+ 5 =9
Since sum is greater than 7, again divide 9 by 7 to find the remainder i.e. 2.
A number is divisible by a composite number if only if it is divisible by its co-prime factors.
Learn Divisibility rules and apply them to different questions for better CAT Quant preparation.
CAT Quant Preparation Material Reference
References to Study (Theory):
Learn the concept of class 9 Mathematics NCERT (For Theory)
Arun Sharma: A Quantitative Approach for CAT Quant preparation(6th Edition)
YouTube Channel of 2iim
References to Study (Practice):
MASTER Number System for CAT and GMAT by Nishit K Sinha.
Question bank from CAT-Holic
Sample Papers
CAT previous year papers
Part-2: Logical Reasoning And Data Interpretation
Topic: Data Interpretation (Line Graph)
As discussed in the previous article, Data interpretation is the most important topic for CAT Exam and other management entrance Exams. We have discussed the strategies to prepare Bar graphs and Pie charts previously.
In this section, we will learn about line graphs. Similar skills like Skills of observation, doing calculations quickly, analyzing things, and comparison of values will be required while solving the problems of DI based on Line graphs.
What is a Line Graph?
In this section, we will focus on the most basic aspects of a line graph and how to solve line graph questions.
On the y-axis, a dependent variable is taken while on the x-axis, an independent variable is taken.
Dots represent the values of x and y variables at that point.
Line gives a visual representation of the data and its variation.
Vertical Label: Name of Dependent Variable
Horizontal Label: Name of Independent Variable
Slope of the line gives the variation of data i.e. if slope is positive then growth is positive and if slope is negative then growth is negative
Questions On-Line Graph From CAT Previous Year Papers/ Line graph questions for CAT
Direction: The following graphs give the revenue and growth rates (yoy) of 4 divisions of Garbage Inc., a company that specializes in waste management:
Question 1. What were the total revenues in 2011?
Rs. 640 Crores
Rs. 725 Crores
Rs. 760 Crores
Rs. 680 Crores
Solution: (B)
Division | Revenue (2010) | Growth Rate (2011) | Revenue (2011) Approx. |
Leather | 230 | -10.9 % | 205 |
Paper | 155 | -1.9 % | 248 |
Pharma | 225 | 10.2 % | 152 |
Technology | 92 | 30.4% | 120 |
Total | 702 | 725 |
Question 2. In the year 2013, what was the share of revenues of the division Pharma?
27%
35%
19%
22%
Solution: (D)
Division | Revenue (2012) | Growth Rate (2013) | Revenue (2013) Approx. |
Leather | 232 | 7.8 % | 250 |
Paper | 145 | -5.4 % | 140 |
Pharma | 195 | -20% | 156 |
Technology | 145 | 10.3% | 160 |
Total | 720 | 706 |
Revenue of Pharma Sector in 2013 = Rs 156 Crore
Total Revenue of company in 2013 = Rs 706 Crore
Share of Pharma = 156x100/706 = 22 %.
Question 3. Which year saw the highest percentage growth in revenues overall?
2009
2011
2012
2013
2014
Solution: (A)
From the solutions of Q1, Q2, and Graphs:
Total Revenue in 2008 (In Crores) = (62 + 88 + 156 + 212) = 518
Total Revenue in 2010 (In Crores) = 702
Total Revenue in 2011 (In Crores) = 725
Total Revenue in 2012 (In Crores) = 720
Total Revenue in 2013 (In Crores) = 706
Total Revenue in 2014 (In Crores) = (130 + 172 + 180 + 262) = 744
We need to Calculate Revenue in 2009 and 2015.
Division | Revenue (2008) | Growth Rate (2009) | Revenue (2009) Approx. | Revenue (2014) | Growth Rate (2015) | Revenue (2015) Approx. |
Leather | 212 | 6.1 % | 225 | 262 | 3.1% | 270 |
Paper | 156 | 2.6 % | 160 | 130 | -7.7% | 120 |
Pharma | 88 | 72.7% | 152 | 180 | 4.7% | 188.5 |
Technology | 62 | 21% | 75 | 172 | 5% | 180.5 |
Total | 518 | 612 | 744 | 759 |
Year | Revenue | Growth (Current year- Previous Year) |
2008 | 518 | |
2009 | 612 | 612- 518 = 94 |
2010 | 702 | 702- 612 = 90 |
2011 | 725 | 725 – 702 = 23 |
2012 | 720 | 720 – 725 = -5 |
2013 | 706 | 706- 720 = -14 |
2014 | 744 | 744- 706 = 38 |
2015 | 759 | 759- 744 = 15 |
If we observe the data in the above table, the growth rate is maximum for the year 2009 since it shows maximum growth (94) on minimum value (518). So, we need not to calculate the growth rate separately for every year.
Our answer is option A.
Prerequisite:
To Prepare Data Interpretation (Line graph) for the CAT exam, a student must learn
The Basics of Coordinate Geometry
Percentage (Basic)
Knowledge of fractions and Ratio
Basics of statistics
Tips On CAT Preparation For Data Interpretation Line Graph questions (Line Graph questions for CAT):
Practice questions on Simplification and Approximation, Percentage .
Identify the trend of graphs.
Compare values to find the growth rate instead of calculating percentage.
Use the tables to interpret the data instead of writing long sentences (It will save your time).
Practice solving the questions of percentages with the help of fractions.
References To Study (Theory):
LRDI for CAT and GMAT by Nishit K Sinha.
To learn the basics of bar graphs read statistics of class 9 and Class 10 Mathematics from NCERT (For Theory)
Kailasha Online Learning Classroom YouTube Channel
References To Study (Practice):
Sample Papers
Question bank from CAT-Holic
How to Prepare for Data Interpretation for CAT by Arun Sharma
CAT previous year's papers
Part-3: VARCTopic: Verb and its Uses:
Verbs are part of “parts of speech,” which express an action or the state of being.
Examples:
He missed the train. (Here, "missed" describes the action.)
The dog is sleeping. (In this, "sleeping" expresses the state.)
Further, verbs can be classified as
Transitive,
Intransitive
Helping verbs.
In the above example 1, "missed" is a transitive word.
In example 2, ‘sleep’ is an intransitive verb.
In example 2, "is" is a helping verb, while "sleeping" is the main (action) verb.
Questions On Verb from CAT Previous Year Papers
Q.1 Direction: Choose the option with the wrong use of the verb
- This has slowed the process
- of reforms in many countries
- because the choice of either of the extreme
- positions inevitably invites criticism.
Ans: D
“Invites” should come instead of invite (for singular noun: “either of extreme positions” forms singular clause)
Q2. Whether or not the rumours are true is beside the point.
the rumours are true are beside the point.
the rumours are true is beside the point.
the rumours are true are beside the point.
No correction required
Ans: B
‘the rumours are true’ is a noun clause, so ís’ should come in place of áre’.
Q3. Just as every generation believes it’s better than the others, so too does every country.
- believe they’re better than the others, every country believes it’s better too.
- believe they’re better than the others, so too does every country.
- believes it's better than the others, every country believes so too.
- No correction required
Ans: D
Correct use of pronouns and verbs is there.
Prerequisite:
Basic Knowledge of Tenses
Basic Knowledge of Sentence Formation
Knowledge of Nouns and Pronouns
Tips On CAT Preparation for Verbal Ability (Verb and its Uses):
Practice sentence formation by using different forms of the verb and analyze the change in the meaning of the sentence. In this way, you will learn the correct use of verbs.
Learn the rules for the use of verbs.
Reading Novels and newspapers (The Hindu) will certainly help you to learn the correct uses of Verbs.
References for Study (Theory):
Advanced English Grammar by Martin Hewings
2iim YouTube Channel
References for Study (Practice):
Question bank from CAT-Holic
CAT previous year's papers
How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
Free PDFs for CAT 2024
Top Executive MBA Programmes in India | CAT Verbal Ability |
Frequently Asked Questions (FAQs)
1. What is Line Graph?
A line graph is an easy method to demonstrate how something evolves over time or how two items are connected. To show these changes, it draws a line connecting points on the graph.
2. What is a Binomial Theorem?
The Binomial Theorem simplifies the expansion of formulas like (x+y)^n, particularly when n is large. Normally, expanding these equations would take a long time, but the Binomial Theorem gives a formula that makes the process faster and simpler. This involves learning how to compute binomial coefficients, grasping the elements of the theorem, and applying it to various applications. It's a handy tool for managing lengthy, complex expansions.
3. What does the X and Y axis represent on a Line Graph?
The X-axis (bottom line) usually depicts time or categories such as days, months, or types of item.
Y-axis (side line): Displays numbers such as sums, temperatures, or scores.
4. What is Verb and its uses?
A verb is a term that expresses what someone or something is doing or indicates a state of being. Verbs may describe activities, such as running or eating, or they can refer to additional information, such as stating that someone is satisfied. Some verbs, such as has and will, also aid in the expression of time. In layman's words, verbs are vital because they inform us what is occurring in the sentence, whether it's an action, an emotion, or a situation.
5. What is Total revenue?
Total revenue is the entire amount of money a firm earns by selling its goods or services. It is determined by multiplying the price of each item by the quantity sold. It refers to the company's sales profits before removing any expenses.
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Have a question related to CAT ?
Hello Aspirant,
Yes, if your caste is listed under Central OBC and you come under the category of Non-Creamy Layer, then you shall be eligible for the OBC-NCL reservation in the CAT exam and IIM admissions, irrespective of its being categorized as OEC in Kerala. Remember to get a valid OBC-NCL certificate obtained as per the format prescribed by the Government of India.
gopi 30 July,2025
Hey Vijay:)
Thanks for reaching out!
OEC,(Other Eligible Communities) is a state-specific reservation category used in Kerala,and it is not recognised as a separate category in central-level exams like the CAT.
For Central govt exams candidates must choose from the recognised categories: General,SC,ST,OBC-NCL,EWS or PwD.If your community is listed under OEC-SC or OEC-ST in Kerala,you should check whether it falls under SC or ST in the central list and apply accordingly.
Similarly,If your OEC community is in the central OBC list and you meet the non-creamy layer(NCL)rules,you can apply as OBC-NCL, otherwise you need to apply under the general category.
You can verify caste's status in the central list on the National Commission for Backward Classes (NCBC) website.
Hope this clears your doubt!
Taabia Fathima 30 July,2025
Hi dear candidate,
The score of your CAT exam is valid for one year from the date of exam.
For example: If your CAT exam was held on 24th November 2024 then your score is valid till 31st December 2025 meaning that you can take admission in the academic year 2025 - 27.
BEST REGARDS
Aryan 27 July,2025
With a Telangana EWS state rank of 2000 in NEET 2025, you have a decent chance of getting an MBBS seat under Category A (Convener quota) in government or semi-government medical colleges, especially during the later rounds of counselling. Your chances are higher in newer or peripheral colleges.
Abhilasha Agrawal 28 July,2025
CAT ( Common Addmission Test ) is for those students who want to study MBA or other post-graduation program in mangement field. Who have Bachelor's degree with minimum 50% recognised university can apply for CAT .final year graduation students are also eligible to apply for CAT exam .
Supriya 25 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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