# CAT Number System, Percentage Questions, LR & DI| Day 7

## Topic: Percentage

The percentage is the basic building block of Arithmetic. It is one of the most important topics for the CAT Exam.

The word “Percent” means “per 100” or “out of 100”.

To Ease your preparation for CAT 2022, divide the ‘cat percentage questions’ in 5 parts as below:

• Questions of the type where x% of y is to be calculated
x% of y = xy/100
Ex: 20 % of 30 = 20 * 30/100 = 6

• Questions of the type where x is what % of y is to be calculated
x is what % of y = x* 100/ y
Ex: 20 is what % of 30 = 20 * 100/30 = 66.66 %

• Questions of the type where x is what % more/ less than y is to be calculated
x is what % more/ less than y = (Difference between x and y) * 100/ y
Ex: 20 is what % less than 30 = 10 * 100/30 = 33.33 %

• Successive change:
Ex: Price of a commodity is increased by 10% first and then decreased by 5%. Find the net percentage change.
If the initial price is 100 then after the first change value will be 110. Now decrease this value by 5%. The final value after the second change will be 104.5. So, the Net percentage change will be 4.5%.

Such problems are to be dealt with separately.

• Expenditure-based questions
• Election-based problems.

### Prerequisite before practising cat percentage questions

To prepare percentages for the CAT exam, students must have knowledge of

• Fractions
• Ratios
• Simplification and Approximation

### Importance of the Percentage in the CAT Exam and Real Life:

Percentages are still relevant in day-to-day life and play an essential role in the quantitative aptitude for CAT.

• Important to understand the financial aspects.
• To analyze the large data in a small time with greater accuracy.
• Have importance in the business sector.
• Very important for statistical analysis.
• Percentage is the basics of topics like profit and Loss, Simple and Compound Interest etc. These topics are combinedly very important for CAT.

### Cat Percentage Questions From Cat Previous Year Papers

The two percentage questions for CAT exam are given below:

Q1. In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks but falls short of the pass mark by 68%. Which one of the following is then correct? [ CAT Question Paper]

1. 243 ≤ N ≤ 252.
2. N ≥ 253.
3. 201 ≤ N ≤ 242.
4. N ≤ 200.

Solution: (1)

Passing Marks = 45 % of N = 0.45 N

Also, passing marks = 36 + 68 % of (0.45 N) = 36 + 0.306N

So, 0.45N = 36 + 0.306N

N = 36/0.144 = 250

Percentage Questions For CAT Exam

Q2. In a class, 60% of the students are girls and the rest are boys. There are 30 more

girls than boys. If 68% of the students, including 30 boys, pass an examination, the

percentage of the girls who do not pass is [CAT Question Paper 2019, TITA]

Solution:

Let Total Students = 100x

Girls = 60x

Boys = 40x

Difference between girls and boys = 20x = 30

So, Number of boys = 40x = 60

Number of girls = 60x = 90

Total students = 150

Pass students = 68% of 150 = 102 (In which 30 are boys)

Girls who passed the exam = 102- 30 = 72

Girls who didn’t pass = 90- 72 = 18

Percentage of girls who didn’t Pass = 18*100/90 = 20%

### Tips to Prepare Percentage on CAT preparation

1. Learn the percentage to fractions conversion to solve the questions quickly.
For Ex: 50% of a number is calculated by dividing the number by 2.
33.33 % of a number is calculated by dividing the number by 3.
12.5% of a number is calculated by dividing the number by 8. etc
2. To find the net percentage change (In Successive Increase or Decrease), you can use the formula.
Net R% = R1 + R2 + (R1*R2)/100
Take the value of R1 and R2 positive if they are increasing and negative if they are decreasing.
3. Use Unitary Method.
4. CAT percentage questions generally combine more than one topic in the problems and will require you to use some degree of logic to make equations in the problems.
5. Practice different kinds of problems.

### References to Study (Theory):

1. Quantitative Aptitude book by Abhijit Guha.
2. 2iim Online Learning Classroom

### References to Study (Practice):

1. Arun Sharma: A Quantitative Approach for CAT (6th Edition)
3. CAT previous year papers

## Topic: Data Interpretation (Case let/ Case Study)

In previous articles-Day 6, strategies for DI based on Spider/ Radar Graph have been discussed. In this article, Case let/ Case Study will be discussed for the CAT exam. In the CAT Exam and other management entrance exams, data interpretation is a must-come topic.

Case let or case study consists of a set of information in the form of a passage. A set of questions based on it were asked.

No tables or graphs are given. You have to read the information to deduce the information and organize the given data to solve the questions.

Example:

Mr Sundar purchased a bike for Rs. 40,500. The bike is also available at Rs. 20,000 down payment and the monthly instalments of Rs. 1400 per month for 2 years or Rs. 16,000 down payment and a monthly instalment of Rs. 1100 per month for 3 years. Mr Sundar has with him Rs. 17,000 only. He took a loan equal to the balance money of the down payment from a private firm. The terms of that private firm are:

If Rs. 4500 is borrowed for a period of 12 months, the rate of interest is 10 %. The interest will be calculated on the whole amount for the whole year itself. Thus, the borrower needs to pay an amount of Rs. 412.5 per month for 12 months, because 4500 is the principal amount + 450 as the interest rate.

If more than Rs. 4500 is borrowed for 1 year, the rate of interest is 20 % and is calculated in exactly the same way as given above.

### Prerequisite:

To Prepare Data Interpretation (Caselet) for the CAT 2022, students must learn

• Percentage (Basic)
• Average
• Observational Skills
• Venn Diagram
• Profit And Loss (Basic)
• Interest (Basic)
• Ratio

### Importance of Caselet/ Case Study for the CAT Exam and in Real life:

Case let is important in following manner

• If we see patterns of questions asked in the DILR section of CAT, we will find that DI based on Caselet is asked. Caselet and problem solving are clubbed together.
• If data is coming from multiple sources, it is roughly collected in the form of a paragraph.
• Exact situation of a company/organization can be interpreted through Caselet.

### Questions Based On Caselet/ Case Study From Cat Previous Year Papers

Comprehension:

Twenty-four people are part of three committees which are to look at the research, teaching, and administration respectively. No two committees have any members in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:

1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.
[CAT Question Paper 2018]

Q1. Based on the given information, which of the following statements MUST be FALSE?

1. The size of the research committee is less than the size of the administration committee
2. In the teaching committee the number of educationalists is equal to the number of politicians
3. The size of the research committee is less than the size of the teaching committee
4. In the administration committee the number of bureaucrats is equal to the number of educationalists

Solution: (3)

No of Bureaucrats in teaching = No of Bureaucrats in Research = 75% of No of Bureaucracy in Administrative

So, No of Bureaucrats in Research: No of Bureaucrats in teaching: No of Bureaucrats in Administrative = 3: 3: 4

No of Politicians in administration = 60% of total politicians

No of Politicians in teaching = 20% of total politicians

No of Politicians in research = 20% of total politicians

No of politicians in Research: No of politicians in teaching: No of politicians in Administration = 1: 1: 3

 Research Teaching Administrative Total Bureaucrats 3x 3x 4x 10x Politicians Y y 3y 5y Educationalist

Possible values for the number of bureaucrats is 10, 20, 30….

(30 is not possible since total number of persons are 24 and 20 is not possible since in each committee there must be 1 politicians and 1 educationalist which will be 6 members at least, so the total will become more than 20)

From here we can say

 Research Teaching Administrative Total Bureaucrats 3 3 4 10

Possible values for number of Politicians is 5, 10 (Not more than 10 since 10 bureaucrats are there)

If politicians were 10 then the number of educationalists will be 4 which cannot be distributed according to the condition (point 2) given.

So, the number of Politicians = 5.

 Research Teaching Administrative Total Bureaucrats 3 3 4 10 Politicians 1 1 3 5 Educationalists 9

According to point (2) given in the question;

Educationalists in research are average of that in the remaining two committees.

Also, The number of educationalists in the teaching committee is less than the number of educationalists in the research committee.

According to this number of educationalists in Research = 3 (Average of 6)

In teaching, educationalists will be either 2 or 1. So,

 Research Teaching Administrative Total Bureaucrats 3 3 4 10 Politicians 1 1 3 5 Educationalist 3 1 or 2 5 or 4 9 Total 7 5 or 6 12 or 11 24

Option 3 is certainly false. Option 2 and option 3 can be true or false.

So, the answer will be (3)

Q2. What is the number of bureaucrats in the administration committee? [TITA - CAT question paper]

Ans: 4

See solution of Q1.

Q3. Which of the following CANNOT be determined uniquely based on the given information?

1. The total number of bureaucrats in the three committees
2. The size of the research committee
3. The size of the teaching committee
4. The total number of educationalists in the three committees

Ans: (3)

Since two possibilities are there.

### Tips to Prepare DI (Caselet) for CAT Preparation

• Convert Caselet into tables or other simpler forms of data representation.
• Use notations for names of things, people or places while solving the question.
• Solve small calculations mentally.
• Not down the important points separately.

### References to Study (Theory):

1. LRDI for CAT and GMAT by Nishit K Sinha.
2. ‘Feel Free to Learn’ (YouTube Channel)

### References to Study (Practice):

1. https://www.mockat.com/ (free Mock Test)
2. How to Prepare for Data Interpretation for CAT by Arun Sharma
3. CAT previous year papers

## Topic: Prepositions and its Uses

Prepositions are one of the entities in English grammar to define the relation between nouns and pronouns along with an object to form a meaningful sentence.

• Basic Prepositions: Prepositions that indicate time, direction, location etc.
Example: in, at, on, under, since, over, off, etc
• Prepositions using participles: These can be made using ‘ed, ing’ etc.
Example: during, regarding
• Phrase Prepositions: It defines the connection of an object with the object modifier.
Example: after dawn, etc

### Importance Of Prepositions and their uses for the CAT Exam and in Real life:

Prepositions are important in the following manner:

• It helps to improve sentence construction.
• Correct use of prepositions gives precise information about the connection of nouns with objects.
• With the knowledge of prepositions one can easily find grammatical errors.

### Prerequisite:

1. Basic Knowledge of Sentence Structure.
2. Basic Knowledge of Phrases.

### Practice Questions on prepositions to prepare for CAT Exam

Direction: Choose the correct preposition

Q1. What is the time __ your watch?

1. In
2. By
3. On
4. At

Ans. B

Q2. I will meet you __ airport/ bus station/ railway station.

1. At
2. In
3. Besides
4. Nearby

Ans. a

Q3. He entered __ the room.

1. Into
2. onto
3. in
4. No preposition required

Ans. d

Q4. The car was parked__ the shade of a tree.

1. Under
2. On
3. In
4. No preposition required

Ans. c

Q5. I have worked in academics __ 6 years.

1. For
2. Since
3. Of
4. From

Ans. A

### Tips to Prepare Prepositions and its Uses for CAT 2022

• Give special attention to confusing prepositions like beside, besides etc.
• Develop the habit of reading so that one can become aware of word collocation. For example- scared of, aware of, etc
• Practice error-based questions daily.
• Read newspapers so that you will get more clarity about the uses of prepositions.

### References to Study (Theory) for CAT preparation :

1. How to Prepare for Verbal Ability & Reading Comprehension for CAT by Meenakshi Upadhyay and Arun Sharma (9th Edition)
2. engvid.com (You Channel)

### References to Study for CAT exam preparation (Practice)

1. engvid.com (Web)
2. Oxford Practice Grammar (sixth edition)

We will be back with the Day-8 strategy tomorrow. Stay focused and keep practising.

Thank You

All the best.

Exam: CAT