# Average

Ready to master your way to CAT exam success? At Quantifiers, we’ll make the world of averages not only understandable but also as easy as pie! Join us on this journey of mastering the Average concept with a sprinkle of wit and a dash of fun. This section will explore the idea of Average, how important it is to the CAT exam’s Quantitative Aptitude section, and how you can succeed with our experienced assistance.

## Understanding Average

Averages are like the unsung heroes of data analysis. They help us make sense of numbers, providing a single representative value that simplifies complex data sets. But what’s the deal with averages? In a nutshell, it’s the “middleman” of data, a value that stands right in the middle, telling us what’s typical and expected. How do averages relate to the CAT exam? Well, they’re an essential ingredient in the Quantitative Aptitude section. This section throws a variety of number sets, scores, and data points at you, and it’s your job to calculate and interpret averages. Here’s why mastering averages is crucial:

• Score Analysis: CAT exam scores? Yep, they’re all about averages. Understanding how they’re calculated can help you set realistic goals and track your progress.

• Data Interpretation: Averages are your secret weapon in understanding large data sets quickly, which is vital for solving data interpretation problems.

• Problem Solving: From group questions to individual scores, CAT problems often involve finding or working with averages.

• Logical Reasoning: Averages are also integral to logical reasoning problems, where you’ll need to deduce information based on averages.

At Quantifiers, we’re not just about numbers; we’re about making them work for you. Master the art of averages with us, and you’ll not only understand this concept but also learn to appreciate its importance in the CAT exam.

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## Practice Questions for CAT with Solutions

#### 1. CAT - Average

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to (CAT 2021)

1. 26
2. 16
3. 18
4. 20

3. 18

#### 2. CAT - Average

In a football tournament, a player has played a certain number of matches and 10 more matches are to be played. If he scores a total of one goal over the next 10 matches, his overall average will be 0.15 goals per match. On the other hand, if he scores a total of two goals over the next 10 matches, his overall average will be 0.2 goals per match. The number of matches he has played is: (CAT 2021)

10

#### 3. CAT - Average

The arithmetic mean of scores of 25 students in an examination is 50. Five of these students top the examination with the same score. If the scores of the other students are distinct integers with the lowest being 30, then the maximum possible score of the toppers is: (CAT 2021)

92

#### 4. CAT - Average

Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is 1 year less than the average age of all three, then Harry’s age, in years, is: (CAT – 2020)

18

#### 5. CAT - Average

A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs and he scored 38 and 15 runs in the last two innings. The batsman scored less than 38 runs in each of the first n innings. In these n innings, his average score was 30 runs and lowest score was x runs. The smallest possible value of x is (CAT 2020)

1. 1
2. 2
3. 3
4. 4

2. 2

#### 6. CAT - Average

There are three categories of jobs P.R.T., T.G.T. and P.G.T. The average salary of the teachers who got the job in P.R.T and T.G.T. categories is 26 lakhs per annum. The average salary of the teachers who got the job in T.G.T. and P.G.T. categories is 44 lakhs per annum and the average salary of those teachers who got the job of P.R.T and P.G.T categories is 34 lakhs per annum. The most appropriate range of average salary (in lakhs per annum) of all the three categories (if it is known that each teacher gets only one category of job i.e. P.R.T. or T.G.T. or P.G.T.):

30 < A < 39

#### 7. CAT - Average

Aman and eight of his friends took a test of 100 marks. Each of them got a different integer score and the average of their scores was 86. The score of Aman was 90 and it was more than that of exactly three of his friends. What could have been the maximum possible absolute difference between the scores of two of his friends?