Free IMO Logical Reasoning Questions and Answers

Question 1

Harsh plays hockey every 4th day and plays squash every 6th day. He played both hockey and squash on 16th June. What is the next date when Harsh will play both games?

Accepted Answer

28th June

Answer

Explanation:
Harsh plays hockey every 4th day and squash every 6th day. The least common multiple (LCM) of 4 and 6 is 12. So, Harsh will play both hockey and squash every 12 days. Since he played both games on 16th June, the next date when he will play both games is 16 + 12 = 28th June.

Question 2

Ria is standing in a row. If she is 6th from the left and 20th from the right, how many people are standing in the row?

Accepted Answer

25

Answer

Explanation:
Ria is 6th from the left and 20th from the right. To find the total number of people standing in the row, we add Ria's position from the left and the right, and then subtract 1 because Ria is counted twice in the sum.

So, 6 + 20 − 1 = 25

Question 3

Aman is standing in a row. If he is 12th from the left and 16th from the right, how many people are standing in the row?

Accepted Answer

27

Answer

Explanation:
To find the total number of people standing in the row, we'll add Aman's position from the left and the right and then subtract 1 because Aman is counted twice in the sum.

So, 12+16−1=27

Question 4

Showing the man singing on the stage, Sarika says, "He is the brother of my uncle's daughter". How is Sarika related to the man?

Accepted Answer

Cousin

Answer

Explanation:
Sarika's uncle's daughter is her cousin. The man singing on the stage is stated to be the brother of Sarika's cousin, so he is also Sarika's cousin.

Question 5

A rectangular courtyard with a length of 3 m 25 cm and a breadth of 2 m 35 cm is to be paved with square stones of the same size. Find the least number of such stones required.

Accepted Answer

3055

Answer

Explanation:
To find the least number of square stones required, divide the area of the rectangular courtyard by the area of one square stone. The dimensions of the courtyard are 325 cm by 235 cm, so its area is 76,375 square centimeters. Assuming each stone is x cm by x cm, we want to maximize x. The greatest common divisor (GCD) of 325 and 235 is 5, so each stone is 5 cm by 5 cm, covering 25 square centimeters. Dividing the area of the courtyard by the area of one stone gives us 3,055 stones.

IMO - International Mathematics Olympiad Practice Test

IMO - International Mathematics Olympiad Practice Test

Free IMO Logical Reasoning Questions and Answers