CAT refers to Common Aptitude Test. Which is a computer-based exam. This exam has three sections. Namely Quantitative, logical and data interpretation section. CAT Average is one of the important topics in the quantitative section. In this article, we would discuss a few important concepts of average.

The quantitative section contains 10% of the average questions. Average concepts are covered under arithmetic questions. Arithmetic questions are mixtures and allegations. In CAT exams Arithmetic questions are important as it is based self many other topics. Arithmetic topics help in solving many questions. Hence, this arithmetic topic is considered an important concept. So, let us recall the basic concepts of average that we are already aware of.

Also read: How to Prepare for CAT

Basic Concepts of average for CAT exams.

An average is one of the important concepts for the CAT in comparison to other competitive exams. Most aspirants have a basic understanding of the average. However, the questions that come in the exam from average are a little tricky. Even calculations are also a little intensive if we apply the standard approach. Average is mainly defined as the sum of observations divided by the number of observations.

An average or more accurately an arithmetic mean can be defined as the sum of n different data divided by n. The average of a group is mainly defined as the ratio of the sum of all the items. In the group to the number of items in the group.

CAT Average = (Sum of all items in the group)/ Number of items in the group

Average = Formula by Putting symbols, X =

Average Speed basic concepts for CAT exam

• If a person travels a distance at a speed of x km/hr. And the same distance at a speed of y km/hr. Then the average speed during the whole journey.
• If a person covers P km at x km/hr and Q km at y km/hr and R km at z km/hr, then the average speed in covering the whole distance. Hence, {(P+Q+R) / ( [P/x] + [Q/y] + [R/z] ) }

Question related to Concept: When a person leaves the group, and another person joins the group in place of that person. Then you can calculate answers from the below-mentioned points.

• If the average age of a person is increasing. Then the Age of the new person is equal to the Age of the separated person and the sum of (Increase in average × total number of persons).
• If the average age of a person is decreasing. The age of the new person is equal to the Age of the separated person and subtraction from (Decrease in average × total number of persons).

Question related to Concept: When a person joins the group.

• In case there is an increase in average: Age of new member = Previous average + (Increase in average × Number of members including new member)
• In case there is a decrease in average: Age of new member = Previous average – (Decrease in average × Number of members including new member)
• Average calculation of n natural no’s is (n+1)/2
• For Average of even N is (n+1)
• The average calculation of odd No is n
• At last General Formula is (1st number +Last number)/2

Must read: Section-wise CAT exam strategy

Basic Concept of weighted mean/average

The weighted arithmetic mean, usually denoted by

,

where x1, x2, x3, …, xn are averages and w1, w2, w3, .., we are their respective weight-ages

For Example: In a class of 25 boys and 15 girls, the average heights of the two groups of boys and girls are 150 cm and 140 cm respectively. Find the average height of the class.

Standard approach:

Total weight of the group of boys = and for the group of girls, the total weight =

Therefore, the average height of the class =

Deviation Approach:

Assume that each boy and each girl are carrying 150 and 140 chocolates respectively.

We have to distribute the total chocolates such that each boy and girl must carry an equal number of chocolates.

Since each boy carries 10 chocolates more than each girl, let us take away 10 chocolates from each boy so that now each boy and girl carries 140 chocolates. The excess chocolates we have is equal . These excess chocolates are to be equally distributed among the boys and the girls. so, everyone will be getting=6.25 more chocolates. Hence the average of the class = 140+6.25 = 146.25 cm.

Past year important questions for CAT exam.

Question 1. In a group of 10 students, the mean of the lowest 9 scores is 42 while the mean of the highest 9 scores is 47. For the entire group of 10 students, the maximum possible mean exceeds the minimum possible mean[CAT 2020]

Answer: Here a2 to a9 is common to both the terms

So, a1 + (a2 to a9) = 42 × 9

a10 + (a2 to a9) = 47 × 9

Solving this two a10 – a1 = 45

a1, a2, a3,……………, a9, (a1 + 45)

In one instance every number is 42

42, 42, …………………, 42, 42+45 (a1 to a9 are equal) ———–(1)

Another instance is every number is 47

47 – 45, 47, …………………, 47, 47 (a2 to a10 are equal) ———(2)

Mean of (1) = 46.5, Mean of (2) = 42.5. So, (1) – (2) = 4

Question 2. A batsman played n + 2 innings and got out on all occasions. His average score in these n + 2 innings was 29 runs 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 innings, his average score was 30 runs, and his lowest score was x runs. The smallest possible value of x is. [CAT 2020]

Answer: Let’s consider Tom’s age to be ‘x’ years.

Dick is thrice as old as Tom,

Dick’s age = 3 × x = 3x

Harry is twice as old as Dick,

Harry’s age = 2 × 3x = 6x

Dick’s age is 1 year less than the average age of all three,

3x = Average (x, 3x, 6x) – 1

3x = ((x + 3x + 6x)/3) – 1

Then, 3x = (10x/3) – 1

1 = (10x/3) – 3x

1 = (10x – 9x)/3

Hence, 1 = x/3. which means x = 1

Few More question Past year's important questions

Question 3. Dev and Om are among 22 students who write an examination. Dev scores 82.5. The average score of the 21 students other than Om is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Dev. The score of Om is. [CAT 2019]

Answer: Let the score of Om =x

Total marks of all the students = 21*62 +x

As per the question, The average score of all the 22 students is one more than the average score of the 21 students other than Dev,

Or (21*62 +x)/22 -1 = (21*62 +x – 82.5)/21

(21*62 + x -22)/22 = (21*62 +x – 82.5)/21. Therefore, x =51

Question 4. The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed What is the highest possible value of the average of these 20 integers? [CAT 2019]

Answer: Sum of all 30 integers =5*30 = 150

The minimum possible sum of the remaining 10 integers = 10*6 = 60

(as all remaining 10 integers are greater than 5 so their sum will be minimum when they all are equal and each has a value =6)

So some of the 20 numbers = 150 – 60 = 90

Thus required average = 90/20 = 4.5

Also read: CAT exam motivation

Few questions for CAT exam practice.

For Example 1: The average weight of a class of 24 students is 36 years. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?

Answer: 61

For Example2: Find the average of the first 30 natural numbers.

Answer: 15.5

For Example 3: A man buys spirit at Rs. 60 per litre, adds water to it and then sells it at Rs. 75 per litre. What is the ratio of spirit to water if his profit in the deal is 37.5%?

A. 9:1 B. 10:1 C. 11: 1 D. None of the above

Answer: B

For Example 4: A car rental agency has the following terms. If a car is rented for 5 hr. or less, then the charge is Rs. 60 per hour or Rs. 12 per kilometre whichever is more. On the other hand, if the car is rented for more than 5 hr., the charge is Rs. 50 per hour or Rs. 7.50 per kilometre whichever is more. om rented a car from this agency, drove it for 30 km and ended up paying Rs. 300. For how many hours, did he rent the car?

1. 4 hr. B. 5 hr. C. 6 hr. D. None of these

Answer: C

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