FREE IMO Integers and Data Handling Questions and Answers
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.
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.
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?
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.
Tap A can fill a tank in 4 hours, while tap B can empty the full tank in 5 hours. If both taps are open together, how long will it take to fill an empty tank?
Explanation:
Tap A fills the tank in 4 hours, so in 1 hour it fills 1/4 of the tank. Tap B empties the tank in 5 hours, so in 1 hour it empties 1/5 of the tank. When both taps are open together, they work simultaneously, so the net filling rate is (1/4)−(1/5)=1/20 of the tank per hour. Therefore, it takes 20 hours to fill the tank.
Find the mean of the first 17 natural numbers.
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.
While doing a science experiment in the physics lab, Pranav took 5 measurements of the temperature and wrote the average of those as an answer. If the measurements of the temperature are -3, 2, 1, -1 and -3 then what is the final answer of his experiment?
Explanation:
To find the average temperature, we add up all the measurements and then divide by the total number of measurements.
Sum of measurements: (−3+2+1−1−3)=−4
Total number of measurements: 5
Average temperature: (−4)/5=−0.8
What is the product of the first 8 prime numbers?
Explanation: The first 8 prime numbers are 2, 3, 5, 7, 11, 13, 17, and 19. To find their product, we simply multiply them together: 2×3×5×7×11×13×17×19=9,699,690. Therefore, the correct answer is 9,700.
The temperature in Thrissur was 27°C in the morning which dropped to 17°C in the evening. Find the temperature difference.
Explanation:
To find the temperature difference, we subtract the initial temperature from the final temperature.
Temperature difference = Final temperature - Initial temperature = 17°C - 27°C = -10°C
However, since the temperature dropped, we consider the difference as positive, so the temperature difference is 10°C.
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.
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.
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.
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.
While doing a science experiment in the physics lab, Sanjana took 7 measurements of the temperature and wrote the average of those as an answer. If the measurements of the temperature are -2, 1, 2, 0, -4, 2 and 2 then what is the final answer of her experiment?
Explanation:
To find the average temperature, we add up all the measurements and then divide by the total number of measurements.
Sum of measurements: −2+1+2+0−4+2+2=1
Total number of measurements: 7
Average temperature: 1/7=0.14
So, the final answer to her experiment is 0.14.
If a is an odd integer and b is an even integer, what is the product of a and b?
Explanation:
When we multiply an odd integer (odd) by an even integer (even), the result is always an even integer.