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Unlocking CAT Exam Essentials: Exploring Unit Digits, Pie Charts, and Pronouns - Day 2

Unlocking CAT Exam Essentials: Exploring Unit Digits, Pie Charts, and Pronouns - Day 2

Edited By Irshad Anwar | Updated on Sep 09, 2023 06:24 PM IST | #CAT

In the previous article, we talked about CAT Preparation Strategy On Quants for Day 1 in which students were given a brief introduction to the number system and its sub-parts i.e. classification, decimal to fraction digits, base system, etc. along with the CAT quant questions i.e. number system questions.

Unlocking CAT Exam Essentials: Exploring Unit Digits, Pie Charts, and Pronouns - Day 2
Unlocking CAT Exam Essentials: Exploring Unit Digits, Pie Charts, and Pronouns - Day 2

In this article, we are going to discuss the unit digit and last two digits of a number from the CAT Quant syllabus 2023 along with the previous year's CAT questions on the number system. These types of questions are about 3-4 expected questions that come in exams as seen in the previous CAT quant questions in the PYQs.

For example, the number 234432 is given. How will you find the digit's unit place?

How will you find the last two digits of the number?

What is “Cyclicity”?

Cyclicity is used to determine the unit digit. Cyclicity is the power of a number after a multiple in which a unit digit is repeated.

For example, 21=2; 22= 4; 23= 8; 24= 16; 25= 32 and so on

As it is shown in the above example, after every fourth power of 2, the unit digit is repeated. So, 4 is cyclicity of 2.

So, you have to learn the cyclicity of every digit.

Digit

Cyclicity (Power Cycle)

Digit

Cyclicity (Power Cycle)

0

1 (Gives always 0 at unit place)

5

1 (Gives always 5 at unit place)

1

1 (Gives always 1 at unit place)

6

1 (Gives always 6 at unit place)

2

4 (2, 4, 6, 8)

7

4 (7, 9, 3, 1)

3

4 (3, 9, 7, 1)

8

4 (8, 4, 2, 6)

4

2 (4, 6)

9

2 (9, 1)

CAT quant questions based on the last two digits of a number are asked frequently in the CAT Exam.

Eg: Find the last two digits of 3737.

It is practically not so easy to solve this power. So, you need to learn the tricks to find the last two digits without actually solving this problem. Some of the tricks will be discussed later in this article, like dividing a number by 100 so that the remainder is the last two digits.

CAT Quant Questions From CAT Previous Year Papers

Question 1: The product of the last two digits of (1! + 2! + 3!….. 50!) is?

  1. 3

  2. 4

  3. 5

  4. 6

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Solution: (A)

Divide the given number by 100 to find the last two digits.

Number 10! And greater than 10! are divisible by 100.

So, find (1! + 2! + 3!….. +9!) and divide the result by 100 to get the remainder and hence last two digits of the number.

So, 1! + 2! + 3!….. +9! = 1+ 2+ 6+ 24+ 120+ 720+ 5040+ 40230+ 362880

So, the sum of the remainder are (1+ 2+ 6+ 24 + 20+ 20+ 40+ 30 + 80). On dividing this result by 100, we get 13 as remainder.

ANS. Product of digits of 13 = 1x3 = 3.

Question 2: What are the last two digits of 72008? [CAT Question Paper 2008]

  1. 21

  2. 61

  3. 01

  4. 41

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Solution: ( C )

(1,3,7,9)20k = 01 (Last two digits) where k is a positive integer.

So, 72008 = 72000 x 74 x 74= 01 x 01 x 01 (Taken last two digits only) = 01

ANS. So, Answer is 01.

Prerequisite:

While preparing for the number system, a student must learn:

  • Squares of the first 25 natural numbers

  • Cubes of natural numbers till 15

  • Knowledge of Prime and Composite

  • Knowledge of powers

  • Knowledge of factorial

  • Knowledge of Even and Odd Numbers

  • Basic Knowledge of Multiples and Factors

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Tips On CAT Preparation For the Number System (Unit Digit And Last Two Digits):

  1. Learn Cyclicity to find the unit digits as discussed in this article.

  2. Use the Concept of cyclicity in Practice Problems.

  3. To find the last two digits, the following tips may help you

    1. Last two digits of x2, (50+ x)2, (50- x)2, (100+ x)2, (100- x)2 are the same.

      Eg: 022 = 04
      522 = 04
      482 = 04
      1022 = 04
      982 = 04

    2. Odd20k = 01(last two digits) except for 5. Where k is a positive integer.
      Eg. 2342 = 01

    3. (a5)even = 25 (last two digits)
      (a5)odd = 75 (last two digits); where can be any digit.
      Eg: 13572 = 25
      13523 = 75

    4. Even20k= 76(last two digits) where k is a positive integer.
      Eg: 48200 = 76 (last two digits)

  4. Practice Mock Tests and CAT Question Paper


References for Study (Theory):

  1. Learn the concept of class 9 Mathematics NCERT (for theory)

  2. Arun Sharma: A Quantitative Approach for CAT (6th Edition)

  3. YouTube Channel of 2iim

References for Practice(Number System Questions And Answers):

  1. Master Number System for CAT and GMAT by Nishit K Sinha.

  2. CAT previous year papers: practice previous year CAT questions on number system

  3. Question bank from CAT-Holic


Part-2: Data Interpretation And Logical Reasoning For CAT 2023

Topic: Data Interpretation (Pie Graphs)

As discussed in the previous article, Data interpretation is the most important topic for the CAT exam and other management entrance Exams.

Skills of observation, doing the calculations quickly, analyzing the things, and comparison of values will help you in solving the questions based on Data interpretation (Pie Charts).

In this topic, we are going to discuss strategies to prepare Data Interpretation based on Pie Charts. We will discuss some Pie chart questions on CAT belowas well.


What is a Pie Chart (Pie chart basic concept for CAT Exam)?


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Sample pie charts of distribution of 6 parameters.

In the pie chart, data is distributed in a circle, which forms 360 degrees at its center and comprises 100% of its area. Students must know to derive the relation between angle and percentage to calculate the parameter’s value.

Pie chart questions and concepts for CAT preparation from CAT Previous Year Papers:

Direction: The break-up of the students in a university by subject major is given in the polar pie chart. The bar chart shows the number of students who major in physics by geographic location. [XAT 2019, based on CAT PYQ]

Question 1. How many students major in chemistry?

  1. 200

  2. 175

  3. 170

  4. 190

  5. 180

Solution: (B)

Students major in physics = 18+ 36+ 80+ 40+ 23+ 28 = 225 which 18% of total students.

So, 18% = 225

Major in Chemistry

14% = (225/18) x14 = 175

Question 2. If the proportion of physics majors who are from Delhi is the same as the proportion of engineering majors who are from Delhi, how many engineering majors are from Delhi?

  1. 22

  2. 26

  3. 18

  4. 20

  5. 24

Solution: (D)

Students major in physics = 18+ 36+ 80+ 40+ 23+ 28 = 225 which 18% of total students.

So, 18% = 225

So, Total students in Engineering major = 225*20/18 = 250

According to question

18/225 =x/250 (where x is students from Delhi in Engineering major)

ANS. x = 20.

Question 3. 12% of all students are from Chennai. What is the largest possible percentage of economics students that can be from Chennai, rounded off to the nearest integer?

  1. 73%

  2. 77%

  3. 75%

  4. 71%

  5. 69%

Solution: (A)

Total number of Physics major = 225

Total number of students = 225x100/18 = 1250

Students from Chennai = 12% x1250 = 150

Number of Physics majors from Chennai (from graph) = 40

Maximum possible number of Economics major from Chennai = 150-40 = 110

Maximum Percentage of Economics Major from Chennai = 110x100/150 = 73.33%.

Prerequisite:

To prepare Data Interpretation (Pie Chart), a student must learn

  • TheBasics of Trigonometry

  • Percentage (Basic)

  • Squares and Cubes of 20-30 first natural numbers.

  • Knowledge of fractions and ratios

  • Must know to find averages

  • Knowledge of mean, mode, and median.

Tips On CAT Preparation For DI (Pie Chart):

  1. Practice questions on simplification and approximation.

  2. Practice questions on the basics of percentages.

  3. Try to solve addition, subtraction, and multiplications mentally.

  4. Understand the conversion of angles into percentages.

  5. Practice the questions on the basics of average.

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. 2iim YouTube Channel

References To Study (Practice):

1. CAT previous year papers

2. Question bank from CAT-Holic

3. How to Prepare for Data Interpretation for CAT by Arun Sharma


Part-3: VARCTopic for CAT 2023 Exam: Pronoun and Its Type

Pronouns are used in place of nouns to avoid repetition of the nouns to which they refer. Pronouns have different forms and are used in different ways.

Eg: I, me, he, she, they, each, few, many, etc

To understand them in a better way, they are categorized into different categories as shown:

Type

Example

Uses

Personal Pronoun

(Used in place of the name of a person)

I, Me, He, She, You, They, Her, Us etc

He is going to meet her.

Possessive Pronoun (Shows possession of something)

My, Mine, ours, your, its, hers, etc

This T-shirt is mine.

Relative Pronoun (used before describing the features or properties of the subject)

That, who, whom, whose, which etc

Thief who stole the money has been successfully punished.

Reflexive Pronoun (Used when the subject and the object of a sentence are the same)

herself, myself, yourself, yourselves, himself, oneself, etc

He used to believe in himself.

Intensive Pronoun (Similar to Reflexive pronoun but emphasise more intensely on Subject)

herself, myself, yourself, yourselves, himself, oneself, etc

I myself cook my food.

Indefinite Pronoun (Used when the subject is not certain)

nobody. anybody everybody, somebody Anyone, no one, everyone, someone etc.

No one is perfect in this world.

Demonstrative Pronoun (Used to show the closeness of the subject or its position)

This, that, these, such, those, etc.

I had the privilege to visit the Prime Minister’s office, that was worth remembering.

Interrogative Pronouns (used to ask questions)

What, which, whose, whom, who, etc.

Who is confident enough to clear the CAT this year?

Reciprocal Pronoun (Used when the sentence has the two actions are performed by two parties)

Each other, one other

The kids threw stones at one another.

Distributive Pronoun (refers to individuals in a group)

none, each, either, neither, any, everyone, no one etc.

None of our friends was involved in the fighting.


Questions on Pronouns From CAT Previous Year Papers (CAT VARC pronoun)

Direction-Q.1: Find the correct alternative for the underlined sentence:

Question 1. My mother bought ice creams for my brother and me, but she didn’t buy one herself.

  1. for my brother and me, but she didn’t buy one for herself.

  2. for my brother and myself, but she didn’t buy herself one.

  3. for my brother and I, but she didn’t buy one for her.

  4. for my brother and I, but she didn’t buy one for herself.

Ans. (A)

Option C and D are wrong because the use of ‘I’ does not make any sense, In place of I, ‘me’ should come (pronoun in place of a noun)

Option B is wrong since ‘myself’ (reflexive pronoun) refers to when I purchased the ice-cream but her mother purchased it.

Therefore, option A is correct because correct pronouns were used.

Question 2. He ____ saw the running Dog.

(a) himself (b) him (c) them (d) themselves

Ans: (a)

The correct pronoun of "he" is himself.

Question 3. Shreeti and ____ went to a movie.

(a) I (b) themselves (c) myself (d) ourself

Ans: (a)

Personal pronouns should be used here. So, the correct answer is option A.

Question 4. When a girl asked how I got _____ address, I told her that it was with the help of a relative of _____.

(a) my/ me (b) mine/ his (c) her/hers (d) she/ she

Ans: (c)


The address here is related to a girl, so "her" should come

Relative to mine or a relative of hers; both can be correct. But according to the options given, option (C) will be correct.

Tips On CAT Preparation for Verbal Ability (Pronoun):

  1. Learn the pronouns by categorizing them and their uses in different situations.

  2. Learn the basics of Grammar

  3. Practice different pronouns in different situations.

  4. Practice CAT Question Paper and Mock tests.

  5. Develop the habit of reading (Newspapers, Novels, Articles etc)

References To Study (Theory):

  1. Advanced English Grammar by Martin Hewings

  2. 2iim YouTube Channel

References To Study (Practice):

  1. CAT previous year papers

  2. Objective General English (Arihant)

We are done here for Day 2 and will be back with Day 3 strategy. Do not give a break to your preparation.

Till then, Take care and practice hard.

All the best.

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Hello aspirant,
The CAT exam syllabus is not officially prescribed, but it generally includes topics from the following sections:

1. Verbal Ability and Reading Comprehension (VARC)
2. Data interpretation and logical reasoning
3. Quantitative ability

  • Arithmetic

  • Algebra

  • Geometry and Mensuration

  • Number System

  • Modern Math

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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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