Reason + prime numbers - practice problems - page 5 of 8
Number of problems found: 151
- Orienteering 6301
Twenty-six girls and 39 boys took part in the orienteering race. Create as many of the same teams as possible so that no competitor is left. How many boys and how many girls are on the team? - Endless lego set
The endless lego set contains only 6, 9, and 20-kilogram blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And, of course, they wrote down how much the building weighed. - University 5680
One company employed a university student on a farm for the entire month of June by paying him €16 and a full board for one day. If he did not work that day, he had to pay €6 for the meal. How many days did the student work if he earned €348 in the month - Grandchildren 5633
Michal's grandfather has 4 grandchildren. During this year's celebrations, he discovered that he is 7 times older than Michal, six times as old as Vašek, four times as old as Emil, and three times as old as Honza. This situation can only happen once in a
- Participate 5543
The dance group is preparing for a performance. The program includes dances in pairs, fours, and fives. How many members does a group have to have to dance all these dances and have all their members participate in each dance? - Remaining 5534
On the table lay eight cards with the numbers 2,3,5,7,11,13,17,19. Fero chose three cards. He added the numbers written on them and found that their sum was 1 more than the sum of the numbers on the remaining cards. Which cards could have been left on the - Three-digit 5524
Six cards with digits 1, 2, 3, 4, 5, and 6 are on the table. Agnes made a six-digit number from these cards, divisible by six. Then she gradually removed the cards from the right. A five-digit number divisible by five remained on the table when she remove - Circumference of the garden
The garden is 90 m long. What is the smallest width if it is possible to walk (circumference) in steps of 80 cm or 50 cm? - 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
- Originally 5427
There were red and green candies in the tin. Čenek ate 2/5 of all the red candies, and Zuzka ate 3/5 of all the green candies. Now, the red candies make up 3/8 of all the candies in the can. How many candies were originally in the can? - 123412341234 5415
There is a thousand one-digit number, which consists of repeating digits 123412341234. What remainder gives this number when dividing by nine? - 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 - One hundred stamps
A hundred letter stamps cost a hundred crowns. Its costs are four levels - twenty tenths, one crown, two-crown and five-crown. How many are each type of stamp? How many does the problem have solutions? - 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?
- Paving - joints
We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and the second row in width etc. How many times will the joints meet at a distance of 10 m? - Garden
The garden has the shape of a rectangle measuring 19m 20cm and 21m 60cm. Mr. Novák will fence it. It wants the distance between adjacent pillars to be at least two meters and a maximum of three meters. He would also like the distances between the adjacent - Competition 5095
Ninety boys and 48 girls signed up for the sports competition. How many members of boys' and girls' teams can we assemble so that they have the largest number of members and the same number of members in the boys' and girls' teams? - Sales of products
For 80 pieces of two quality products, the total sales are 175 Eur. Suppose the first quality product was sold for n EUR per piece (n natural number) and the second quality product after 2 EUR per piece. How many pieces of the first quality were sold? - Individual 4881
There are 32 rooms in the hostel. Some have double beds, others have four beds and the rest have 7 beds. There are a total of 139 beds in the hostel. How many are there if a two-digit number gives the numbers of individual species?
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