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

Part 1: Quantitative Aptitude For CAT 2024

Topic: 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; 2 ⁵= 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.

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

Ans: (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 the 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 is (1+ 2 + 6 + 24 + 20 + 20 + 40 + 30 + 80). On dividing this result by 100, we get 13 as the remainder.
Product of digits of 13 = 1 × 3 = 3.

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

1. 21

2. 61

3. 01

4. 41

Ans: (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
So, the 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

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. The 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. Odd^20k = 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. Even^20k= 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 2024

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 calculations quickly, analyzing things, and comparison of values will help you in solving 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 below as well.

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

Sample pie charts of distribution of 6 parameters.

In the pie chart, data is distributed in a circle, which forms 360 degrees at its centre and comprises 100% of its area. Students must know how 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 is 18% of total students.

So, 18% = 225

Major in Chemistry

14% = (225/18) x 14 = 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 is 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 are students from Delhi with Engineering major)

⇒ 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 majors = 225
Total number of students = 225 x 100/18 = 1250
Students from Chennai = 12% x1250 = 150
Number of Physics majors from Chennai (from graph) = 40
Maximum possible number of Economics majors from Chennai = 150 - 40 = 110
Maximum Percentage of Economics Major from Chennai = 110 x 100/150 = 73.33%.

Prerequisite:

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

• The Basics of Trigonometry

• Percentage (Basic)

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

• Knowledge of fractions and Ratio

• Must know to find Average

• 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's papers

2. Question bank from CAT-Holic

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

Part-3: VARC for CAT 2024 Exam

Topic: 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:

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

Direction- 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 for "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. However 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 Papers 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's previous year's papers

2. Objective General English (Arihant)

Free PDFs for CAT 2024 preparation

• Mistakes to avoid during GD and PI

• Topper's tips for GD-PI & WAT