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

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

Edited By Irshad Anwar | Updated on Sep 15, 2023 06:29 PM IST | #CAT

Hello Aspirants,

Many of you will be wondering how to prepare for quantitative aptitude. Hopefully, you have kick-started your preparation for CAT-2023 to fulfill your dream of getting your master's in management from reputed institutes like IIMs. In the previous article -CAT Quant preparation, DI, VA and LR- Day 2-, we discussed preparing Numbers (Unit digit and Last two digits) from the CAT Quant Syllabus. According to the previous year's questions of CAT, about 36% constitute of arithmetic problems including divisibility questions for CAT and Remainder problems. QA is considered to be one of the most important sections in which the candidates need thorough preparation in. Therefore, CAT quant preparation is really recommended for students to do it rigorously as the CAT quant syllabus is really vast and needs proper time management as well. So, we are ready to discuss a strategic plan (day 3) for how to prepare for quantitative aptitude to crack the CAT Exam on our own. In this article, we are proceeding with the Divisibility and Remainders for CAT Quant preparation.

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]

  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

1694779517972

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.

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

  2. 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.

1694779518305

  • 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:

1694779518464

1694779518721

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)

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?

  1. 27%

  2. 35%

  3. 19%

  4. 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?

  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.

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

Technol-ogy

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)

  • Averages

  • Knowledge of fractions and ratios

  • 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 to solve the questions of percentage 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 graph 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 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 papers

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

We are done with our strategy for Day 3 preparation. See you tomorrow with Practice Set 1 on the topics from Day 1 to Day 3.

Thank You

All the best.

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For VARC, read daily from diverse sources (newspapers, novels, journals) to improve comprehension and vocabulary. Practice RC passages and verbal ability questions regularly. For DILR (Data Interpretation and Logical Reasoning) and QA (Quantitative Aptitude), solve previous years' papers and take mock tests to identify weak areas. Join a coaching institute or online courses for guidance and stay consistent with your study schedule. Review and analyze your performance in mocks to understand mistakes and improve. Maintain a positive mindset and stay disciplined in your preparation.

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View All

1-radian measures 600. (True/False)

Option: 1

True


Option: 2

False


$111111^2$ = 

Option: 1

123456654321


Option: 2

123454321


Option: 3

123454321


Option: 4

12345654321


1111112 =___________ 

Option: 1

 123456654321


Option: 2

1234554321


Option: 3

123454321


Option: 4

12345654321


159702 is divisible by

Option: 1

7


Option: 2

9


Option: 3

11


Option: 4

6


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What best can be said about the number of satellites serving C? 

Option: 1

Must be between 450 and 725 

 


Option: 2

Cannot be more than 800 
 


Option: 3

Must be between 400 and 800 

 


Option: 4

Must be at least 100 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

What is the minimum possible number of satellites serving B exclusively? 

Option: 1

100


Option: 2

200


Option: 3

500


Option: 4

250


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S? 

Option: 1

At most 475 

 


Option: 2

Exactly 475 
 


Option: 3

At least 475 

 


Option: 4

No conclusion is possible based on the given information 


1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O. 

The following facts are known about the satellites: 

1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2: 1:1. 

2. The number of satellites serving all three of B, C, and S is 100. 

3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B. 

4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B. 

Question:

 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE? 

Option: 1

The number of satellites serving C cannot be uniquely determined 

 


Option: 2

The number of satellites serving B is more than 1000 
 


Option: 3

All 1600 satellites serve B or C or S 

 


Option: 4

The number of satellites serving B exclusively is exactly 250 


2839155 is divisible by

Option: 1

2


Option: 2

7


Option: 3

55


Option: 4

None of the above


'a' for which x^{2}-ax+9= 0 can be written as square of a linear factor is

Option: 1

6


Option: 2

-6,6


Option: 3

\left ( 6,\infty \right )


Option: 4

\left ( -\infty,-6 \right )


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