CAT QA AVERAGES QUESTIONS

The average of three distinct real numbers is 28. If the smallest number is increased by 7 and the largest number is reduced by 10, the order of the numbers remains unchanged, and the new arithmetic mean becomes 2 more than the middle number, while the difference between the largest and the smallest numbers becomes 64. Then, the largest number in the original set of three numbers is

A company has 40 employees whose names are listed in a certain order. In the year 2022, the average bonus of the first 30 employees was Rs. 40000, of the last 30 employees was Rs. 60000, and of the first 10 and last 10 employees together was Rs. 50000. Next year, the average bonus of the first 10 employees increased by 100%, of the last 10 employees increased by 200% and of the remaining employees was unchanged. Then, the average bonus, in rupees, of all the 40 employees together in the year 2023 was

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

There are three persons  and  in a room. If a person  joins the room, the average weight of the persons in the room reduces by . Instead of , if person  joins the room, the average weight of the persons in the room increases by . If the weight of  is  more than that of , then the value of  is

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 non-manufacturing employees is

In an examination, the average marks of 4 girls and 6 boys is 24. Each of the girls has the same marks while each of the boys has the same marks. If the marks of any girl is at most double the marks of any boy, but not less than the marks of any boy, then the number of possible distinct integer values of the total marks of 2 girls and 6 boys is

In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference between the maximum and minimum possible number of students in section A is

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Consider six distinct natural numbers such that the average of the two smallest numbers is 14, and the average of the two largest numbers is 28. Then, the maximum possible value of the average of these six numbers is

The average of all 3-digit terms in the arithmetic progression 38, 55, 72, ..., is

The average of a non-decreasing sequence of  numbers  is 300 . If  is replaced by , the new average becomes 400 . Then, the number of possible values of  is

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

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

The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is

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

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

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

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

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 by

Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

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?

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

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 [TITA]

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? 

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

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? (TITA)

Manu earns ₹4000 per month and wants to save an average of ₹550 per month in a year. In the first nine months, his monthly expense was ₹3500, and he foresees that, tenth month onward, his monthly expense will increase to ₹3700. In order to meet his yearly savings target, his monthly earnings, in rupees, from the tenth month onward should be

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

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

If a man weighing 80 kg joins a group of n people, the average weight of the group increases by 2. But if a man weighing 60 kg joins the group, the average weight drops by 3. Find n.

The 'Raging Bulls' Kabaddi team had a rollercoaster season. Across eight hard-fought matches, their scores were 36, 29, 30, 35, 26, 22, 27, and 25. They managed to clinch victory in four of those matches, showcasing their dominance by scoring double the points of their defeated opponents. However, the other four matches ended in losses. Three of those losses were by a slim 4-point margin, while the final loss was a more decisive 7-point defeat. What was the average score of the opposing teams that faced the Raging Bulls in these eight matches?"

The average of 50 integer is 8. Out of the 50 integers, exactly 35 numbers are less than or equal to 7. What is the highest possible value of the average of these 35 integers?

Ram and Reena can travel from P to Q in 5 hours and 10 hours, respectively. They both start from P, go towards Q, reach Q and return to P. If they both start at 10: 00 a.m. from P,when will they cross each other.

The average number of pages read by Sarah in 12 days is 2.5 more than the average number of pages read by John in 11 days. John and Sarah read 79 and 93 pages, respectively, on the 12th day. If the average number of pages read by John in 12 days is 24, what is the average number of pages read by Sarah in 11 days?

The average of p, q and r is 12, and the average of  s, t and u is 20, where p, q, r, s, t ,u are distinct positive integers. What is the difference between the maximum and minimum possible values of the average of p and u?

The average weight of a class of 25 students is 30 Kg. The average weight of girls is 5 kg more than that of the boys. If the class teacher’s weight which is male and between 64 Kg and 106 Kg is also included, then the average weight of the male members of the class equals the female members of the class. What is the number of boys in the class, if the average weight of the boys (in Kg) is an integer?

If 20 distinct natural numbers are arranged in ascending order. The average of the first 10 least numbers is 45. What can be the minimum average for the next 10 numbers.

A player scored 30, 34, 36 and 40 runs in his fifth, sixth, seventh and eighth innings respectively. He noticed that his average runs per inning for the first eight innings became less than his average runs for the first four innings. If his average runs for the first nine innings turned out to be exactly 41, then what is the maximum number of runs he could have scored in the ninth inning?

The average weight of Arjun’s family increases by 6 kg from 71 kg, when his maternal uncle joins the family If the weight of his uncle is 113kg then find the initial number of members in his family.

There are five students in a class, have average marks of Z. If marks of two students 72 and 48 are excluded, then average marks of rest students are 12 marks less than that of average marks of all five students. Find the value of (Z + 18)?

The average of a series S1 of 7 consecutive odd numbers is 17 and average of the series of S2 of 7 consecutive even numbers is 30. What is the sum of smallest and highest number of series S1 and S2?

There are 8 numbers given. The average of the first two numbers is 75 and that of the next four numbers is 40/3% more than the average of the first two numbers. If the 2nd number from last is 500/21% less than the last number and the average of all 8 numbers is 84.375, then what is the last number?

The average weight of 20 students in a class is 50 kg. when one student leaves the class, the average weight becomes 49 kg. What is the weight of the students who left the class?

The batting average of Rohit for 21 innings is 43 runs. His highest score in an innings exceeded his lowest score by 64 runs. If these two innings are excluded, the average score of the remaining 19 innings is 39 runs. Find his highest score in an inning?

The average score in social science of 9 students of 9th and 10th together is 98. The number of students in class 9th was 25% more than that of the class 10Th  and the average score of students in 10th class was 20% higher than that of students of class 9th. What is the average score of the student of class 9th.

The number of students who took biology and math in 11th class are 40 and 52 respectively. The average score of all the students is 150. If the average score of a student in biology is 40% more than that of students in maths, then what is the average score of students [nearest to the integer] who took maths Solution Concept used

A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is?

The average weight of Arjun’s family increases by 6 kg from 71 kg, when his maternal uncle joins the family If the weight of his uncle is 113kg then find the initial number of members in his family.