Basics of Average — CAT Previous-Year Questions

14 previous-year questions on Basics of Average from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.

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14 questions

Basics of Average · CAT PYQs

CAT 2024 Slot 1 · QA

Q1.

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

CAT 2023 Slot 1 · QA

Q2.

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

CAT 2022 Slot 3 · QA

Q3.

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

CAT 2020 Slot 1 · QA

Q4.

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

CAT 2020 Slot 1 · QA

Q5.

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

CAT 2020 Slot 3 · QA

Q6.

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

CAT 2017 Slot 1 · QA

Q7.

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?

CAT 2007 · QA

Passage / Data

Answer the next 2 questions based on the information given below.

Let a₁ = p and b₁ = q, where p and q are positive quantities.

Define:
a_n = pb_n−1 b_n = qb_n−1, for even n > 1 and
a_n = pa_{n − 1} b_n = qa_{n − 1}, for odd n > 1.

Q8.

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?

CAT 2002 · QA

Passage / Data

Sum of first n natural numbers = S(n)

Sum given by student = 575

S(10) = $\frac{10 \times 11}{2} =$ 55

S(20) = $\frac{20 \times 21}{2} =$ 210

S(30) = $\frac{30 \times 31}{2} =$ 465

S(40) = $\frac{40 \times 41}{2} =$ 820

∴ The student stopped counting somewhere between 30 and 40.

Consider S(35) = $\frac{36 \times 35}{2} =$ 630

The student stopped somewhere before 35.

∴ S(31) = 496, S(32) = 528, S(33) = 561 and S(34) = 595

But the student gave 575 as the sum, so the student missed on the number 20.

Hence, option 4.

Q9.

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?

CAT 2002 · QA

Passage / Data

Answer the following question based on the information given below.

A boy is supposed to put a mango into a basket if ordered 1, an orange if ordered 2 and an apple if ordered 3. He took out 1 mango and 1 orange if ordered 4. He was given the following sequence of orders.

12332142314223314113234

Q10.

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.

CAT 2001 · QA

Passage / Data

Answer the following question based on the information given below.

The batting average (BA) of a test batsman is computed from runs scored and innings played-completed innings and incomplete innings (not out) in the following manner:

r₁ = number of runs scored in completed innings; n₁ = number of completed innings

r₂ = number of runs scored in incomplete innings; n₂ = number of incomplete innings

BA = $\frac{r_{1} + r_{2}}{n_{1}}$

To better assess batsman's accomplishments, the ICC is considering two other measures MBA₁ and MBA₂ defined as follows:

MBA₁ = $\frac{r_{1}}{n_{1}} + \frac{n_{2}}{n_{1}} \times m a x [0, (\frac{r_{2}}{n_{2}} - \frac{r_{1}}{n_{1}}])$

MBA₂ = $\frac{r_{1} + r_{2}}{n_{1} + n_{2}}$

Q11.

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

CAT 2000 · QA

Q12.

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

CAT 1999 · QA

Passage / Data

Directions: Answer the questions based on the following information.
Recently, Ghosh Babu spent his winter vacation on Kyakya Island. During the vacation, he visited the local casino where he came across a new card game. Two players, using a normal deck of 52 playing cards, play this game. One player is called the ‘dealer’ and the other is called the ‘player’. First, the player picks a card at random from the deck. This is called the base card. The amount in rupees equal to the face value of the base card is called the base amount. The face values of ace, king, queen and jack are ten. For other cards the face value is the number on the card. Once the ‘player’ picks a card from the deck, the ‘dealer’ pays him the base amount. Then the ‘dealer’ picks a card from the deck and this card is called the top card. If the top card is of the same suit as the base card, the ‘player’ pays twice the base amount to the ‘dealer’. If the top card is of the same colour as the base card (but not the same suit), then the ‘player’ pays the base amount to the ‘dealer’. If the top card happens to be of a different colour than the base card, the ‘dealer’ pays the base amount to the ‘player’.
Ghosh Babu played the game four times. First time he picked eight of clubs and the ‘dealer’ picked queen of clubs. Second time, he picked ten of hearts and the ‘dealer’ picked two of spades. Next time, Ghosh Babu picked six of diamonds and the ‘dealer’ picked ace of hearts. Lastly, he picked eight of spades and the ‘dealer’ picked jack of spades. Answer the following questions based on these four games.

Q13.

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.

CAT 1997 · QA

Passage / Data

Answer the next 3 questions based on the following information.

There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D.

Q14.

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