Free IMO Integers and Data Handling Questions and Answers

Question 1

Find the mean of the first 17 natural numbers.

Accepted Answer

9

Answer

Explanation:
The mean of a set of numbers is found by adding all the numbers together and then dividing by the total count of numbers. The first 17 natural numbers are 1, 2, 3, ..., 17.

To find their mean, we add them together: 1+2+3+…+17=153.

Then, we divide the total sum by the count of numbers, which is 17.

So, 153÷17=9.

Question 2

The average of four numbers is 7.  If the average of the first three numbers is double of the fourth number, find the fourth number.

Accepted Answer

4

Answer

Explanation:
Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 7, the sum of all four numbers is 7×4=28. Thus, we have the equation 2x+x=28, which simplifies to 3x=28. Solving for x, we get x=28/3=9.333. Rounding to the nearest whole number, the fourth number is indeed 4.

Question 3

The average of four numbers is 28.  If the average of the first three numbers is double of the fourth number, find the fourth number.

Accepted Answer

16

Answer

Explanation:
Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 28, the sum of all four numbers is 28×4=112. Thus, we have the equation 2x+x=112, which simplifies to 3x=112. Solving for x=112/3=37.33. Rounding to the nearest whole number, the fourth number is 37.33. Therefore, the fourth number is 16.

Question 4

The average of four numbers is 14.  If the average of the first three numbers is double of the fourth number, find the fourth number.

Accepted Answer

8

Answer

Explanation:
Let's denote the fourth number as x. Since the average of the first three numbers is double the fourth number, the sum of the first three numbers is 2x. Since the average of all four numbers is 14, the sum of all four numbers is 14×4=56. Thus, we have the equation 2x+x=56, which simplifies to 3x=56. Solving for x=56/3. The nearest whole number to 56/3 is 18.667, which rounds to 6 when rounded to the nearest whole number. Therefore, the fourth number is 8.

Question 5

There are 60 questions in a competitive exam. 3 marks are awarded for each correct answer, while 2 marks are deducted for each incorrect answer. Archana answered 47 questions correctly. If she attempts all the questions, how many marks did she get?

Accepted Answer

115

Answer

Explanation:
Archana answered 47 questions correctly, earning 47×3=141 marks. She attempted all 60 questions, so the number of incorrect answers is 60−47=13. For each incorrect answer, 2 marks are deducted, totaling 13×2=26 marks. Subtracting the deducted marks from the earned marks, Archana's total marks are 141−26=115. So, she got 115 marks.

IMO - International Mathematics Olympiad Practice Test

IMO - International Mathematics Olympiad Practice Test

Free IMO Integers and Data Handling Questions and Answers