Basics of Average — CAT Previous-Year Questions

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

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

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 mean of all 4-digit even natural numbers of the form ‘aabb’, where a > 0, is

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

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

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?

Consider the set S = {2, 3, 4, ..., 2n + 1}, where n  is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?

Three friends went for a picnic. First brought five apples and the second brought three. The third friend however brought only Rs. 8. What is the share of the first friend?

Each question is followed by two statements A and B. Answer each question using the following instructions:

Answer (1) if the question can be solved by any one of the statements, but not the other one.
Answer (2) if the question can be solved by using either of the two statements.
Answer (3) if the question can be solved by using both the statements together and not by any one of them.
Answer (4) if the question cannot be solved with the help of the given data and more data is required.

Is 500 the average (arithmetic mean) score of the GMAT?

A. Half of the people who take GMAT score above 500 and half of the people score below 500.
B. The highest GMAT score is 800 and the lowest score is 200.

Based on the information provided which of the following is true?

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

Directions: Each question is followed by two statements I and II. Mark:
1. if the question can be answered by any one of the statements alone, but cannot be answered by using the other statement alone.
2. if the question can be answered by using either statement alone.
3. if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
4. if the question cannot be answered even by using both the statements together.

The average weight of students in a class is 50 kg. What is the number of students in the class?
I. The heaviest and the lightest members of the class weigh 60 kg and 40 kg respectively.
II. Exclusion of the heaviest and the lightest members from the class does not change the average weight of the students.

If all the students of the class have the same weight, then which of the following is false?