Mathematical Olympiad - practice for 14 year olds - page 2 of 4
Number of problems found: 65
- Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - Luggage and air travel
Two friends traveling by plane had a total of 35 kg of luggage. They paid one 72 CZK and the second 108 CZK for being overweight. If only one paid for all the bags, it would cost 300 CZK. What weight of baggage did each of them have? How many kilograms of - Self-counting machine
The self-counting machine works exactly like a calculator. The innkeeper wanted to add several three-digit natural numbers on his own. On the first attempt, he got the result in 2224. To check, he added these numbers again, and he got 2198. Therefore, he - Mathematical 7136
Out of 50 pupils, 44 solved at least one of the Olympiads - MO Mathematical Olympiad and BO Biology Olympiad. Twenty pupils still need to solve the MO. Of those who dealt with both Olympiads, 1/3 of those who dealt with just one were. How many pupils solv
- MO Z8-I-1 2018
Fero and David meet daily in the elevator. One morning, they found that if they multiply their current age, they get 238. If they did the same after four years, this product would be 378. Determine the sum of the current ages of Fero and David. - Interested 7090
We call a natural number N bombastic if it contains no zero in its notation and if no smaller natural number has the same product of digits as the number N. Charles first became interested in bombastic prime numbers and claimed that there were not many of - Positive 7040
Find all positive integers x and y for which: 1 / x + 1 / y = 1/4 - Manufacturer 6981
The hotelier wanted to equip the dining room with new chairs. He chose the type of chair in the catalog. Only when placing an order did he learn from the manufacturer that they offered every fourth chair at half price as part of the discount offer and tha - Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl
- Last digit
What is the last number of 2016 power of 2017 - Circumference 6598
Adam had three identical rectangles. He put them together and got a rectangle with a circumference of 50 cm. Then, he placed them differently and got a rectangle with a larger circumference. Calculate its perimeter. - Different 5874
Mišo and Rišo ran back and forth on the running track. They started towards each other, each from a different end of the track. Both were still running at the same speed, each at a different speed. The first time, they met 800 m from one end of the track, - Corresponding 5585
Consider the various points corresponding to the numbers a, 2a, 3a + 1 in all possible orders on the straight line representing the number line. For each option, decide whether such an arrangement is possible. If yes, give a specific example; if not, give - Circumscribed 5465
Inside the rectangle ABCD, the points E and F lie so that the line segments EA, ED, EF, FB, and FC are congruent. Side AB is 22 cm long, and the circle circumscribed by triangle AFD has a radius of 10 cm. Determine the length of side BC.
- Z9–I–4 MO 2017
Numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 were prepared for a train journey with three wagons. They wanted to sit out so that three numbers were seated in each carriage and the largest of the three was equal to the sum of the remaining two. The conductor said - Different 5402
Adélka had two numbers written on the paper. When she added their greatest common divisor and least common multiple, she was given four different numbers less than 100. She was amazed that if she divided the largest of these four numbers by the least, she - Average age
The average age of all people at the celebration was equal to the number of people present. After the departure of one person who was 29 years old, the average age was again equal to the number present. How many people were original to celebrate? - One million
Write the million number (1000000) using only nine numbers and algebraic operations plus, minus, times, divided, powers, and squares. Find at least three different solutions. - Participants 5319
In the mathematical competition, its participants solved two tasks. Everyone solved at least one problem, while 80% of the participants solved the first problem, and 50% solved the second problem. Sixty participants solved both tasks. How many participant
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Mathematical Olympiad - practice problems. Maths practice for 14 year olds.