Reason - practice for 14 year olds - page 24 of 40
Number of problems found: 796
- 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. - Tracksuit 5460
The tracksuit became cheaper by 15% later on sale and later by 10%. How many euros did Janka save if she bought this set after the second discount and paid € 45.9? - Mother and daughter
The mother is four times older than her daughter. Five years ago, her daughter was seven times younger than her mother. How many years do they have now? - Equations 5445
The digit sum of a two-digit number is 8. If we change the order of the digits, we get a number 18 smaller than the original. Identify these numbers. We are using linear equations of two unknowns.
- 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 - Big number
What is the remainder when dividing 10 by 9 to 47 - 111? - Remainder
A is an arbitrary integer that gives remainder 1 in the division with 6. B is a random integer that provides the remainder with division by two. What makes remainder in a division by three products of numbers A x B? - Asymmetric 5407
Find the smallest natural number k for which the number 11 on k is asymmetric. (e.g. 11² = 121) - 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? - Is right triangle
Decide if the triangle XYZ is rectangular: x = 4 m, y = 6 m, z = 4 m - 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 - Three-digit 5312
Find the smallest four-digit number abcd such that the difference (ab)²− (cd)² is a three-digit number written in three identical digits. - Minutes 5310
They had three tower clocks in the city. Some went right, the others were 10 minutes ahead of the day, and the thirds were 12 minutes late each day. One day they struck all the clocks at noon at once. How long will it be like this again?
- Kaufland sales-off
As a rule, the goods to the approaching end consumption in Kaufland three days before the consumption end to 30% off and one day before the consumption end to 50% discounts. Sometimes, however, the seller has been mistaken, and the second discount is alre - Filled 5265
The tank is filled to two-thirds of its volume. It will only be half full if we pump 100l of water from it. What is the volume of this tank? - ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the average train speed for both journeys woul - Six on dice
When throwing two dice, what is the probability they will fall at least one six? - Isosceles triangle
The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at a ratio of 5:6. Find the triangle area.
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