300+ Most Important Arithmetic Questions for CAT
Average
Average is a foundational and frequently tested topic in Arithmetic for CAT 2026, forming the base for several higher-order Quant problems. Practice curated CAT arithmetic important questions built around repeated average concepts, weighted averages, and data-based applications seen in recent CAT exams. These questions are designed to sharpen your calculation speed and conceptual accuracy for CAT 2026.
Arithmetic
Q1. Sindhu played ten games in the badminton tournament. Her scores in the sixth, seventh, eighth, and ninth games were 22, 16, 14, and 20 points respectively. Her points-per-game average was higher after nine games than it was after the first five games. If her average after ten games was greater than 19, what is the minimum number of points she could have scored in the tenth game?
31
30
29
28
Q2. The average of 8 numbers is 75. If the smallest number is deleted, then the average of the remaining numbers is A and if the largest number is deleted, then the average of the remaining numbers is B. If A + B = 90, then what is the average of the smallest and largest numbers?
275
355
315
285
Q3. A set of four positive integers a, b, c and d in any arrangement follow the condition that a + 1 = b – 2 = 3c = d/4. If the sum of the four numbers in the set is 58, then what is the average (up to one decimal place) of the largest and smallest number in the set?
18.5
18.2
19.3
19.5
Q4. The average of 20 whole numbers is 4.5. The maximum number of distinct numbers among these 20 whole numbers can be:
12
13
14
10
Q5. Girish finds the average of five two digits numbers. If one number is reversed and the average is taken again, then the average increases by 7.2. If all five numbers are consecutive multiples of four, then find the number which is reversed.
Q6. The average weight of a group of 28 students increases by 5 kg when four of them leave this group. If the average weight of these four students is one-fifth the average weight of the original 28, then what is the average weight, in kg, of the remaining 24 students?
47.5
42.5
37.5
32.5
Q7. There are 8 consecutive odd natural numbers. If the product of the 4th and the 5th numbers is 783, then find the average of all the numbers.
Q8. Team Alpha is planning to participate in a pizza baking competition, which has a time limit of 30 minutes. During last week, the average number of pizzas that they baked in an hour was 38, for the first four days the average was 32 and the average for the last four days was 40. Find out the number of pizzas baked by Team Alpha in the competition if they baked at the rate of the fourth day of the week.
Q9. Average of 3 numbers x, y and z is 35 where x: z = 2: 5 and y is greater than x by 15. Also, z is given by the equation z = ab – 25 where a and b are natural numbers, then what is the minimum possible average of a and b?
Q10. Let the set S = {5, 6, 7, ……., 2n + 1}, where n is a positive integer larger than 2023. If A is the average of the odd integers in S and B is the average of the even integers in S, then A – B is:
2024
n/2
1
0
Q11. There are nine distinct natural numbers such that the average of the three smallest numbers is 17, and the average of the three largest numbers is 32. The maximum possible value of the average of these nine numbers is:
26.33
26
25.33
24
Q12. The average height of a group of people increases by 0.375 inches when a few more people join them. If the average weight of the new people is 3 inches more than that of the original group, then the ratio of the number of people present originally to those who joined later is:
7: 1
11: 5
5: 1
13: 2
Q13. In a school, the average weights of students in the junior (5th to 7th grade) and senior (8th to 10th grade) divisions are 45 and 69, respectively, and the average weights of all the students in both divisions combined is an integer. If the number of junior students is 12 more than that of the senior students, then the difference between the maximum and minimum possible number of students in the school is:
Q14. A batsman played a total of 9 innings and his average score in these 9 innings was 35. He never scored more than 50 runs in a single innings. If in the first 5 innings his highest score was 31 then the largest possible difference between two lowest scores scored in these 9 innings is:
24
28
31
34
Q15. The warden of the boy’s hostel at National College of Engineering, Patna was trying to calculate the average age of the 35 boys living in the hostel. By mistake, he included himself with the group of boys, as a result, the average age increased by one year. If the warden is 57 years old, what is the average age of the boys living in the hostel?
Q16. 17 glass balls of distinct colours and distinct weights have been arranged in a row. The weight of the red ball is 17 kg. The average weight of all balls other than the green one is 8.5625 kg. The average weight of all the balls is 500 gm more than the average weight of 16 balls other than the red one. The weight of the green ball, in kg, is:
Q17. If M and N are two positive integers such that (2M + 3N) = 53, then the average of the maximum and minimum possible values of (M + N) is:
21
21.5
22
22.5
Q18. The ratio of the ages of A and B twelve years ago was 2: 3 and the ratio of the ages of B and C 12 years from now will also be 2: 3. If the average age of A and C at present is 57 years, the ratio of the ages of B and C was/will be 1: 2:
6 years ago
12 years ago
18 years ago
18 years from now
Q19. The average age of husband, wife and their child 3 years ago from now was 27 years and that of wife and child 5 years ago from now was 20 years. The age (in years) of the husband 5 years ago from now was:
Q20. If the average of nine consecutive even natural numbers, the greatest of which is y, is x, then what is the average of 17 consecutive natural numbers, the least of which is x?
y – 2
y
y – 1
y + 4
Q21. Heights of five students have distinct integer values when expressed in centimetres and can include any value from 135 to 170, both inclusive. Their average height is 150 cm and the heights of exactly two students are below this value. The difference between the highest and lowest possible height (in cm) of the second tallest person among them is:
13
14
15
10
Q22. The average age of three sisters is 17 years. If the age of the brother is included, the average age of the 4 persons remains an odd number. What can be the minimum age of the brother (in years) if his age is not less than 2 years?
3
5
9
13
Q23. In a team of 20 young adults, 8 are females and the rest are males. The average weight (in kg) of the female members in the group is an integer which is more than 50 but less than 55, and the average weight of the group of males is 1/3 kg more than that of the females. What is the average weight (in kg) of the female members in that group, if the total weight of the whole group (in kg) is a perfect square of a natural number?
Q24. The average of 10 distinct natural numbers is 31. What can be the maximum average of two largest numbers among these ten numbers?
Q25. Volleyball players of a club, all of distinct heights, are standing in the descending order of their heights from left to right. If we do not include the first 5 players from the right, the average height of the players increases by 2 cm, and if we do not include the first 5 players from the left, the average height of the players decreases by 2 cm. If the sum of the height of the first 5 players from the left is 920 cm and that from the right is 680 cm, then find the total number of players of the club.
Q26. If ‘x’ is the median of the integers {11, 13, 4, 9, 7, 19, 2, 5, 24, 17, x}, which of the following could possibly be average of all values of the set?
9
10
11
12
Q27. The average weight of 45 children is 8 kg. Out of these 45 children, exactly 30 have weights that are 8 kg or less. If all the children’s weights are in integral kilograms, what is the highest possible value for the average weight (in kg) of these 30 children?
7
7.25
7.5
7.75
Q28. There are 8 students in a group. When the heaviest student leaves the group the average weight of the new group reduces by 2 kg. When the lightest student leaves the group the average of the new group increases by 2 kg. If both of them leave the group, then the sum of the weights of the remaining students in the group was 270 kg. What is the weight (in kg) of the heaviest student in the original group?
Q29. Harish, a mathematics teacher, gave a test to his five students. He entered the scores in random order into an excel sheet, which recalculated the class average after each score was entered. Harish noticed that after each score was entered, the average was always an integer. The scores (listed in ascending order) were 62, 67, 71, 73, and 82. What was the last score Harish entered?
Q30. In a school, 50 students each took 6 subjects, and each subject was graded out of 100 marks. The students’ average percentage across all subjects is 75%. Two students want to re-evaluate their scores in one subject each. If their marks don’t decrease, and the new overall average becomes 75.05%, what is the maximum possible score increase for either of the two students?
Q31. The average marks of 6 students in a test is 72. All the students got different marks, one of the students obtained 80 marks and all other students scored 50 or above. The maximum possible difference between the second highest and the second lowest marks is:
50
54
48
44
Q32. A college cricket team has 11 players and out of them A, B, C, D, and E have scored runs at an average of 30, 40, 35, 45, and 50 respectively, in the first 20 matches of the season. In the next 5 matches, A and B scored 200 runs each whereas C’s score was 50% more than that of D. After 25 matches, if A’s new average score is 4/5th that of D, what is the average score of C?
Q33. The average weight of 24 students increases by 6 kg when four of them leave the group. If the average weight of these four students is one-fourth of the average weight of the original 24 students, then what is the average weight of the remaining 20 students, in kg?
Q34. In a group with a certain number of people, if one new person weighing 60 kg is added, then the average weight of the group increases by 3 kg. If one more person weighing 60 kg is added, then the average weight of the group increases by an additional 2 kg. What is the average weight (in kg) of the original group?
Q35. The height of the four brothers are non–zero distinct integral number of feet such that the average height of these brothers is 3.5 feet. The average height (in feet) of two elder brothers cannot exceed:
5
5.5
6
6.5
Q36. In a school, students of two classes: A and B participated in a Maths competition. The average score of the students of class A is 70, and the average scores of boys and girls of class A are 72 and 68 respectively. For class B: the average score of the class is 75; and the average score of the boys and girls are 78 and 72 respectively. If thrice the number of girls in class B is twice the number of boys in class A, what is the average score of the students of the two classes combined?
Q37. An examination consisted of 6 tests out of which 3 were Language and 3 were Core subjects. The marks obtained by Sudha in the 5 tests were 20, 30, 70, 80, 40, and 60. The average marks obtained by her in Language and Core subjects were the same. A student has to have a minimum cut off to be eligible for a scholarship. While calculating the ‘overall weighted average’ for the examination, the test with the minimum score among the Language tests was given twice the weight and the test with the maximum score among the Core subjects was given thrice the weight as compared to others. The maximum ‘overall weighted average’ would be closest to:
50.67
56.67
52.86
53.33
Q38. There are total ‘n’ students in a group. The average weight of these ‘n’ students along with their two teachers is 37 kg. The weights of the two teachers are 50 kg and 46 kg. The weight of none of the students is more than 37 kg. What can be the minimum weight of a student if the average weight of the ‘n’ students is 35 kg?
13 kg
15 kg
17 kg
19 kg
