# CAT Preparation Strategy on Quant (QA), DI, VA and LR - Day 1 ## Topic: Basics of the Number System-1

A number is a mathematical value used for arithmetic calculations, counting purposes, etc. Numbers are broadly classified as Real and Non-Real Numbers, as shown.

Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value.

A number has another classification as even and odd numbers, prime and composite numbers.

The number system is a vast topic of QA, which has to be prepared in the division. So, we divide the number system into five parts. i.e.

• Classification of numbers, Base System, Conversion from Decimal to Fraction

• Unit digits and the last two digits

• Divisibility and Remainders

• Factors and Trailing Zeroes

• HCF and LCM

All the parts have to be prepared sequentially for CAT exam preparation in 2 months.

In this article, we are going to discuss strategies to prepare for the classification of Numbers, Conversion from decimal to fraction and Base System, as well as number system questions for cat exam.

### Prerequisite:

To prepare for the number system for the CAT exam, a student must learn

• Tables up to 30

• Squares up to 30

• Cubes up to 20

• Make sure you learn all prime numbers until 100.

• Knowledge of Fractions

Importance of the Number System in the CAT Exam and Real Life:

Number System questions are still relevant and play an essential role in the quantitative aptitude for CAT. The topic is quite vast and is full of tricks and shortcut formulas that help the students solve the questions quickly.

Knowledge of Number Systems will help students in other areas of Quantitative Aptitude as well.

Numbers act as a foundation for human beings. People start their lives with a number and end with a number in the form of age, Human growth is un-measurable with the help of numbers.

Our day starts with numbers and ends with numbers, from buying household items to paying taxes to the government. If a person is able to understand numbers well, it acts as an added advantage to their overall growth.

Being a responsible manager, decision-making is the most important tool, and the manager takes decisions based on quantitative as well as qualitative aspects of the decision, and his understanding of numbers gives him an edge in comparison to others.

### Number System Questions From CAT Previous Year Papers

Question 1: Let m and n be natural numbers such that n is even and 0.2 < m/20, n/m, n/11< 0.5. Then m - 2n equals [CAT Question Paper 2020].

1. 4

2. 2

3. 1

4. 3

Solution:

0.2 < m/20, n/m, n/11< 0.5

1/5 < m/20, n/m, n/11< ½

Solve these 1 by 1:

1/5 < m/20 and m/20 < ½

So, m> 4 and m <10

Therefore, possible values of m 🡪 5, 6, 7, 8, 9

Now, 1/5 < n/11 and n/11 < ½ and n is even

So, n > 11/5 and n < 11/2

Therefore, a possible value of n is 4 (since 4 is the only even natural number between 11/5 and 11/2)

Since n/m > 1/5 and n/m <1/2

n/m <1/2 🡪 Since n is 4, m should be greater than 8 to satisfy the condition.

Therefore, m is 9.

m- 2n = 9- 2x4 = 1

Question 2: Convert the number 1982 from base 10 to base 12. The result is?

(CAT Question Paper 2000)

A. 1182

B. 1912

C. 1192

D. 1292.

Solution: C

For that, divide 1974 by 12 as shown

 Divisor quotient Remainders 12 1982 12 165 2 12 13 9 12 1 1 0 1

Write the remainders from bottom to top.

So, in base 12, 1982 is 1192.

### Tips On Cat Preparation For Number System (Basic):

1. Learn the classification of numbers (Natural, Whole, Integers, Prime, Composite, Co-prime etc.) thoroughly from NCERT books (9-10th standard).
2. Apply the concepts to practice Number System questions.
3. Do small problems first (based on classification)
4. Increase the difficulty level of the questions stepwise.
5. Following are some useful tips and number system cat formulas that can help in your preparation:
1. The sum of a two-digit number and a number formed by reversing its digits is divisible by 11. E.g., 24 + 42 = 66, this is divisible by 11.
At the same time, the difference between those numbers will be divisible by 9. e.g., 42- 24 = 18, this is divisible by 9.
2. ∑n = n(n+1)/2, ∑n is the sum of the first n natural numbers.
3. ∑n2 = n(n+1)(2n+1)/6, ∑n2 is the sum of the perfect squares of the first n natural numbers.
4. ∑n3 = n2(n+1)2/4 = (∑n)2, ∑n3 is the sum of the perfect cubes of the first n natural numbers.

6. Learn Recurring and Non- Recurring decimal numbers and their conversion to fractions.

• Number of the form of 0.a = a/9

Eg. 0.77777…. = 7/9

• Number in the form of 0.ab = ab/99

Eg. 0.73737373….. = 73/99

0.343343343…. = 343/999

• Number of the form of 0.0a = a/90

Eg. 0.07777….. = 7/90

• Number of the form of 3.0a = 3 + a/90

7. Learn the basics of the Base systems and Conversions from numbers in one base system to another. for example, fractions to decimals examples, how to remove decimal point in fraction, how to convert numbers to fractions, number system questions and answers,

8. Practice previous year CAT questions on number system.

References for Study (Theory):

1. Class 9 and Class 10 Mathematics NCERT

2. Arun Sharma CAT books: A Quantitative Approach for CAT

References to Study (Practice):

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

2. Question bank from CAT-Holic

3. Sample Papers - number system questions for cat exam

4. CAT previous year papers

## Topic: Data Interpretation (Bar Graph)

Data interpretation is a must-come topic in the CAT Exam and other management entrance exams.

Data interpretation involves skills of observation, with the help of which you have to analyze the graph, deduce the useful information, and apply that information to solve the given questions.

This section has to be studied in parts. i.e.

• Bar Graph

• Pie Chart

• Line Graph

• Tables

• Case Lett

• Spider

• Miscellaneous

In this article, we are going to discuss strategies to prepare Data Interpretation based on Bar Graph for the CAT exam.

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data. They are also known as bar charts.

### Prerequisite:

To prepare Data Interpretation (Bar Graph) for the CAT exam, a student must learn

• Tables up to 30

• Squares up to 30

• Cubes up to 20

• Basics of Percentage

• Must know to find averages

### Importance of Bar Graphs for the CAT Exam and in Real Life:

• Bar graphs are helpful in the comparison of different sets of data among different groups.

• The graph shows the changes in data over a time period as per our requirements to make analysis easier.

• Over the past years, questions on bar graphs have been repeatedly asked in the CAT Exam.

• These are also used in presentations, so knowledge of these graphs enhances your skills and effectiveness.

### Questions On Bar Graph From Cat Previous Year Papers

Question: The following chart gives the revenue share of different companies in the tech sector in Cuckoo Land:

Question 1: In 2001, the company that grew the quickest grew by 100%. What was the growth rate of the company that had the least growth rate?

A. 50%

B. 25%

C. 20%

D. 33%

Solution:

Let the total revenues of the entire industry be 100X in 2000 and 100Y in 2001.

 Company Share in 2000 (approx.) Share in 2001 (approx.) Share in 2001: Share in 2000 FINY 22.9x 21.1y 21.1y:22.9x PRIWO 17.1x 19.3y 19.3y: 17.1x SCT 25.7x 21.1y 21.1y: 25.7x GOCN 14.3x 14y 14y:14.3x BIM 8.6x 10.5y 10.5y: 8.6x CENTURE 11.4x 14y 14y: 11.4x

The company that grew the quickest would be the one that had the maximum ratio of 2001 revenue share to 2000 revenue share. Only the shares matter, X's and Y's do not matter.

Clearly, CENTURE saw the highest ratio and hence the highest growth, which is equal to 100%, and for that share in 2001: share in 2000 = 2: 1 (for CENTURE).

So, 14y/ 11.4x = 2/1

So, y/x = 11.4/7

The company that saw the least ratio, and hence the least growth rate, is SCT.

Share in 2001: Share in 2000 = 21.1y/25.7x = (21.1/25.7) * (11.4/7) = 1.33

So, the percentage change is 33%.

Question 2: In 2002, the growth rate of the overall sector was 39%. What was the growth rate seen by SCT?

A. 50%

B. 75%

C. 30%

D. 40%

Solution:

Let Revenue in 2001 is 100

Then Revenue in 2002 be 139.

Share of SCT in 2001 🡪 21.1 % of 100 = 21 (Approx)

Share of SCT in 2002 🡪 22.8 % of 139 = 32 (Approx)

Percentage Change = 11*100/21 = 52% = 50% (Approx)

Question 3: Total revenue in 2006 was $21.2 bn, and total revenue in 2005 was$18.1 bn. What was the growth rate seen in Centure?

A. 11%

B. 35%

C. 20%

D. 27%

Solution:

Growth rate = (8.5% of 21.2- 8.3% of 18.1) *100/18.1 = 20% (approx.)

Tips On Cat Preparation For DI (Bar Graph):

1. Learn the basics of simplification and approximation.

2. Learn to solve percentages quickly.

3. Do small calculations mentally.

4. Learn the basics of bar graphs.

5. Understand the components on both axes.

6. Interpret the necessary data requirements.

7. Practice CAT Question Paper

References for Study (Theory):

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

2. To learn the basics of bar graphs, read Class 9 and Class 10 Mathematics NCERT (For theory)

References For Study (Practice)

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

2.CAT previous year papers

3. Sample Papers

4. Question bank from CAT-Holic

## Topic: Noun and its Type

There are several definitions of Noun but since our childhood, we have been using an unornamented definition of it, i.e. Nouns are a part of speech that comprise words that are used to name people, places, animals, objects, and ideas.

Almost every sentence will definitely have a noun, and they perform different roles in a sentence. Nouns can act as the subject, an indirect object, a direct object, a subject complement, and an object complement. Nouns can also function as adjectives and verbs.

### Importance of Noun for the CAT Exam and in Real Life:

The primary (macro) communication skills required for any language are listening, speaking, reading, and writing. Being exceptionally skilled in just one of these abilities won't improve your communication. For example, you need to be able to read well before you can write well. Before you can speak, you must first have the ability to listen.

So, when it comes to grammar, first you have to understand the noun.

We all learned about the eight parts of speech during our school days. If you recall, these parts of speech form the building blocks of English grammar. But, how is it important for CAT exam preparation? Well, learning about the various parts of speech and the related rules will help you answer the grammar-based questions accurately. Such questions may feature in the form of error detection, sentence correction, fill-in-the-blanks and word usage. In the CAT verbal ability test, the grammar section thus carries significant weight.

### Questions On NOUN from Cat Previous Year Papers

Direction-Q.1 to 2 In each question, there are four sentences or parts of sentences that form a paragraph. Identify the sentence(s) or part(s) that is/are incorrect in terms of grammar, including, spelling, punctuation, and usage. Pick out the most appropriate option, out of the options that follow the question.

Question 1:

A. Either the parents or the child are going to talk.

B. to the principal on this issue, and I find many reasons

C. Why I can't help the child; please excuse me now as the principal

D. accompanied by the teachers, has to go to the auditorium.

1. A, B & D 2. B, C & D 3. A & D 4. B & C

Ans. 1. A, B & D – A- Either the parents of the child is going to talk- verb will follow the latter noun (subject);

B- “Many a” should be followed by a singular noun.

D- accompanied/as well as/ along with" do not make the plural or singular even if followed by the same. Therefore, the verb will have to be used in accordance with the first (former) subject.

Question 2:

A. Neither the high profile Manager nor the staff members were able

B. to calm the distressed customer. On the top of it, the

C. The working team at this FDI-funded store is always

D. fighting among themselves.

1. A & C 2. B & D 3. A only 4. D only

Ans. 1. A & C –

A - Nor the staff members were able (plural verbs with plural nouns should be used).

C - “are” should be used with “working team” plural noun).

### Tips On CAT Preparation for Verbal Ability (Noun):

• Preparation for verbal ability should involve regular practice. The fundamentals of the contextual usage of grammar and vocabulary should be well understood before the exam.

• Learn the rules of nouns.

• Correct usage of nouns should be learned.

• Dedicate time to solving crossword puzzles. This will help you gain experience in solving jumbled sentences and paragraphs.

• Reading newspaper articles will help to improve

• Practice CAT Question Paper

### References for Study (Theory):

1. Wren and Martin

### References for Study (Practice):

1. CAT previous year papers

2. Advanced English Grammar by Martin Hewings

3. The Pearson Guide to Verbal Ability and Reading Comprehension for CAT by Nishit Sinha (2020)

4. Question bank from CAT-Holic

This is all for Day 1 CAT exam preparation. We will come back to you for Day 2 CAT Exam preparation in our very next article. Till then, practice the CAT exam question paper more and more.

All the best

Exam: CAT