International Mathematical Kangaroo

Description: The International Mathematical Kangaroo is a prestigious mathematics competition for students from all over the world. It is designed to challenge and inspire students, and to promote a love of mathematics. This quiz contains 15 questions from the International Mathematical Kangaroo competition.
Number of Questions: 15
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Tags: mathematics mathematical competitions international mathematical kangaroo
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What is the value of the expression $2^3 + 3^2 - 5^1$?

  1. 14

  2. 16

  3. 18

  4. 20


Correct Option: C
Explanation:

Using the order of operations, we have $2^3 + 3^2 - 5^1 = 8 + 9 - 5 = 18$.

A farmer has 12 sheep, 6 cows, and 4 pigs. How many animals does the farmer have in total?

  1. 18

  2. 20

  3. 22

  4. 24


Correct Option: C
Explanation:

To find the total number of animals, we simply add the number of sheep, cows, and pigs: $12 + 6 + 4 = 22$.

A rectangular garden has a length of 10 meters and a width of 5 meters. What is the area of the garden?

  1. 20 square meters

  2. 25 square meters

  3. 30 square meters

  4. 50 square meters


Correct Option: D
Explanation:

The area of a rectangle is found by multiplying the length and width. Therefore, the area of the garden is $10 imes 5 = 50$ square meters.

A train leaves a station at 10:00 AM and travels at a speed of 60 miles per hour. Another train leaves the same station at 11:00 AM and travels in the same direction at a speed of 70 miles per hour. At what time will the second train overtake the first train?

  1. 12:00 PM

  2. 12:30 PM

  3. 1:00 PM

  4. 1:30 PM


Correct Option: B
Explanation:

To find the time at which the second train will overtake the first train, we need to find the time it takes for the second train to travel the distance between the two trains. This distance is equal to the speed of the first train multiplied by the time difference between the two trains. Therefore, the time it takes for the second train to overtake the first train is $rac{60 imes 1}{70 - 60} = 1.5$ hours. Adding this time to the departure time of the second train, we get $11:00 AM + 1.5$ hours = $12:30 PM$.

A store sells a shirt for $20. If the store offers a 20% discount on the shirt, what is the sale price of the shirt?

  1. $16

  2. $17

  3. $18

  4. $19


Correct Option: A
Explanation:

To find the sale price of the shirt, we need to subtract the discount from the original price. The discount is $20 imes 0.20 = $4$. Therefore, the sale price of the shirt is $20 - $4 = $16$.

A company has 100 employees. If 60% of the employees are women, how many women work for the company?

  1. 40

  2. 50

  3. 60

  4. 70


Correct Option: C
Explanation:

To find the number of women who work for the company, we need to multiply the total number of employees by the percentage of women. Therefore, the number of women who work for the company is $100 imes 0.60 = 60$.

A rectangular room has a length of 12 feet and a width of 8 feet. What is the perimeter of the room?

  1. 20 feet

  2. 28 feet

  3. 36 feet

  4. 40 feet


Correct Option: D
Explanation:

The perimeter of a rectangle is found by adding the lengths of all four sides. Therefore, the perimeter of the room is $2 imes (12 + 8) = 40$ feet.

A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that the ball is blue?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5


Correct Option: B
Explanation:

The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcomes are the number of blue balls, which is 15. The total number of possible outcomes is the total number of balls, which is $10 + 15 + 20 = 45$. Therefore, the probability of selecting a blue ball is $rac{15}{45} = rac{1}{3}$.

A circle has a radius of 5 centimeters. What is the area of the circle?

  1. 25π square centimeters

  2. 50π square centimeters

  3. 75π square centimeters

  4. 100π square centimeters


Correct Option: A
Explanation:

The area of a circle is found by using the formula $A = πr^2$. Therefore, the area of the circle is $π imes 5^2 = 25π$ square centimeters.

A train travels 200 kilometers in 4 hours. What is the average speed of the train in kilometers per hour?

  1. 40

  2. 50

  3. 60

  4. 70


Correct Option: B
Explanation:

To find the average speed of the train, we need to divide the distance traveled by the time taken. Therefore, the average speed of the train is $rac{200}{4} = 50$ kilometers per hour.

A store sells a pair of shoes for $100. If the store offers a 30% discount on the shoes, what is the sale price of the shoes?

  1. $70

  2. $75

  3. $80

  4. $85


Correct Option: A
Explanation:

To find the sale price of the shoes, we need to subtract the discount from the original price. The discount is $100 imes 0.30 = $30$. Therefore, the sale price of the shoes is $100 - $30 = $70$.

A company has 200 employees. If 40% of the employees are men, how many men work for the company?

  1. 60

  2. 80

  3. 100

  4. 120


Correct Option: B
Explanation:

To find the number of men who work for the company, we need to multiply the total number of employees by the percentage of men. Therefore, the number of men who work for the company is $200 imes 0.40 = 80$.

A rectangular room has a length of 15 feet and a width of 10 feet. What is the area of the room?

  1. 150 square feet

  2. 200 square feet

  3. 250 square feet

  4. 300 square feet


Correct Option: A
Explanation:

The area of a rectangle is found by multiplying the length and width. Therefore, the area of the room is $15 imes 10 = 150$ square feet.

A bag contains 12 red balls, 18 blue balls, and 24 green balls. If a ball is randomly selected from the bag, what is the probability that the ball is green?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5


Correct Option: A
Explanation:

The probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcomes are the number of green balls, which is 24. The total number of possible outcomes is the total number of balls, which is $12 + 18 + 24 = 54$. Therefore, the probability of selecting a green ball is $rac{24}{54} = rac{1}{2}$.

A circle has a radius of 8 centimeters. What is the circumference of the circle?

  1. 16π centimeters

  2. 24π centimeters

  3. 32π centimeters

  4. 40π centimeters


Correct Option: A
Explanation:

The circumference of a circle is found by using the formula $C = 2πr$. Therefore, the circumference of the circle is $2π imes 8 = 16π$ centimeters.

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