How To Prepare CAT Quantitative Aptitude Strategy | DI, VA and LR - Day 3

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.

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:

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]

1. 3

2. 4

3. 2

4. 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]

1. 0

2. 1

3. 69

4. 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]

1. 41

2. 42

3. 40

4. 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:

1. 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.

2. A number is divisible by a composite number if only if it is divisible by its co-prime factors.

3. 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?

1. Rs. 640 Crores

2. Rs. 725 Crores

3. Rs. 760 Crores

4. Rs. 680 Crores

Solution: (B)

Question 2. In the year 2013, what was the share of revenues of the division Pharma?

1. 27%

2. 35%

3. 19%

4. 22%

Solution: (D)

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?

1. 2009

2. 2011

3. 2012

4. 2013

5. 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.

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)

• Average

• Knowledge of fractions and Ratio

• Basics of statistics

Tips On CAT Preparation For Data Interpretation Line Graph questions (Line Graph questions for CAT):

1. Practice questions on Simplification and Approximation, Percentage .

2. Identify the trend of graphs.

3. Compare values to find the growth rate instead of calculating percentage.

4. Use the tables to interpret the data instead of writing long sentences (It will save your time).

5. Practice solving the questions of percentages with the help of fractions.

References To Study (Theory):

1. LRDI for CAT and GMAT by Nishit K Sinha.

2. To learn the basics of bar graphs read statistics of class 9 and Class 10 Mathematics from NCERT (For Theory)

3. 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'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

1. This has slowed the process
2. of reforms in many countries
3. because the choice of either of the extreme
4. 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.

1. the rumours are true are beside the point.

2. the rumours are true is beside the point.

3. the rumours are true are beside the point.

4. 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.

1. believe they’re better than the others, every country believes it’s better too.
2. believe they’re better than the others, so too does every country.
3. believes it's better than the others, every country believes so too.
4. 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):

1. 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.

2. Learn the rules for the use of verbs.

3. Reading Novels and newspapers (The Hindu) will certainly help you to learn the correct uses of Verbs.

References for Study (Theory):

1. Advanced English Grammar by Martin Hewings

2. 2iim YouTube Channel

References for Study (Practice):

1. Question bank from CAT-Holic

2. CAT previous year's papers

3. How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)