In CAT average is a concept that is covered in Arithmetic topics like mixtures and allegations and it is an important concept since it forms the base of many other topics in the Quantitative ability section. Out of the total questions from arithmetic concepts, average concept forms around 10% of the questions. Other than the Quant section, this topic becomes of use in solving the Data interpretation and Logical reasoning questions also.
CAT
Averages 

Year 
No 
Good 
Difficulty 






2019 
Slot 1 
1 
1 
Easy to Moderate 
Slot 2 
1 
1 
Easy to Moderate 






2018 
Slot 1 
2 
1 to 2 
Moderate 
Slot 2 
2 
1 
Moderate to Difficult 






2017 
Slot 1 
1 
1 
Moderate 
Slot 2 
1 
1 
Moderate 
Averages:
Averages are a simple but effective way to determine the complete group by a single value. The formula for the calculation of averages is:
Average = (Sum of All Items in the group) / (Total number of items in the group)
Points to remember:
Some important CAT questions on averages from previous year papers are given below which can help in the preparation of CAT 2021
Averages:
1. Ramesh and Gautam are among 22 students who write an examination. Ramesh scores 82.5. The average score of the 21 students other than Gautam is 62. The average score of all the 22 students is one more than the average score of the 21 students other than Ramesh. The score of Gautam is? (CAT 2019 Slot 1)
Let the score of Gautam =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 Ramesh,
Or (21*62 +x)/22 1 = (21*62 +x – 82.5)/21
(21*62 + x 22)/22 = (21*62 +x – 82.5)/21 On solving x =51
2. The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers? (CAT 2019 Slot 2)
3. In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years? (CAT 2018 Slot 1)
Let the average age of people aged 51 years and above be x years. Let the average age of people aged below 51 years be y years.
Let the number of people aged below 51 years be N.
Given, the average age of all the people in the apartment complex is 38 years.
Therefore,
(X*30 + y*N)/ 30*N = 38 ….(1)
We want to maximize y, which occurs when x is minimum i.e. for x=51. Substituting the value of x in (1) we get
390=N*(38y)
Again, when y is maximum, N is also maximum i.e. 39
Therefore, the maximum value of y = 28.
4. A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is? (CAT 2018 Slot 1)
For the understanding of the candidate, we have divided the preparation into 3 levels for the upcoming CAT 2021.
Level 1
Level 2
Level 3
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