CAT Averages Questions & Solutions

A sample of real CAT Averages past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 30 Averages questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   The average salary of 5 managers and 25 engineers in a company is 60000 rupees. If each of the managers received 20% salary increase while the salary of the engineers remained unchanged, the average salary of all 30 employees would have increased by 5%. The average salary, in rupees, of the engineers is

   • 45000

   • 50000

   • 54000

   • 40000

2. Q2.CAT 2024

   There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is

   Answer: 15

3. Q3.CAT 2023

   In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employees is

   • 6:5

   • 4:5

   • 5:4

   • 5:6

4. Q4.CAT 2022

   The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

   • 3

   • 4

   • 5

   • 1

5. Q5.CAT 2022

   Five students, including Amit, appear for an examination in which possible marks are integers between 0 and 50, both inclusive. The average marks for all the students is 38 and exactly three students got more than 32. If no two students got the same marks and Amit got the least marks among the five students, then the difference between the highest and lowest possible marks of Amit is

   • 22

   • 21

   • 24

   • 20

6. Q6.CAT 2021

   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

   • 26

   • 18

   • 16

   • 20

7. Q7.CAT 2020

   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

   • 4

   • 3

   • 2

   • 1

8. Q8.CAT 2019

   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

   • 53

   • 51

   • 48

   • 49

9. Q9.CAT 2017

   An elevator has a weight limit of 630 kg. It is carrying a group of people of whom the heaviest weighs 57 kg and the lightest weighs 53 kg. What is the maximum possible number of people in the group?

   Answer: 11

10. Q10.CAT 2017

    The average height of 22 toddlers increases by 2 inches when two of them leave this group. If the average height of these two toddlers is one-third the average height of the original 22, then the average height, in inches, of the remaining 20 toddlers is

    • 30

    • 28

    • 32

    • 26

11. Q11.CAT 2002

    Amol was asked to calculate the arithmetic mean of 10 positive integers, each of which had 2 digits. By mistake, he interchanged the 2 digits, say a and b, in one of these 10 integers. As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. Then |b - a| equals

    • 1

    • 2

    • 3

    • None of these

12. Q12.CAT 2000

    Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is:
    

    • n

    • n+1

    • kn, where k is a function of n

    • n+($\frac{2}{7}$)

CAT Averages previous year questions with solutions — AthenaPrep