Reason + prime numbers - practice problems - page 3 of 8
Number of problems found: 151
- The tickets
The tickets to the show cost some integer number greater than 1. Also, the sum of the price of the children's and adult tickets and their products was the power of the prime number. Find all possible ticket prices. - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - Matemakak 9432
The cookbook by Matěj Matemakak says: The greatest common divisor of flour weight and sugar weight is 15, the greatest common divisor of sugar weight and lemon peel weight is 6, the product of sugar weight and lemon peel weight is 1800, and the smallest c - Sufficient 9391
In Kocourkov, they use coins with only two values expressed in Kocourkov crowns by positive integers. With a sufficient number of such coins, it is possible to pay any integer amount greater than 53 cats’ crowns accurately and without return. However, we
- Divisible 9331
The number X is the smallest natural number whose half is divisible by three, a third is divisible by four, a quarter is divisible by eleven, and its half gives a remainder of 5 when divided by seven. Find this number. - Significant 9321
Only herbs with 5 and 7 leaves grow in the Old Forest. When the boar Vavřínec collects raw materials for herbal liquor, it always tears off the whole herb and puts it in a basket. What is the most significant number of letters he will ever manage to have - Notebooks 8651
I need to buy exercise books and covers. One notebook costs CZK 12, and one cover costs CZK 3. I have one fifty crown and one twenty crown. How many notebooks and covers can I buy for it? Come up with more options. - Determine 8611
Determine all natural numbers A and B pairs for which the sum of twice the least common multiple and three times the greatest common divisor of natural numbers A and B is equal to their product. - Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
- Several 8130
The hotel has 27 beds in several rooms. There are single, double and triple rooms. How many single, double and triple rooms can there be in the hotel? Give at least three options. - The King
The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them? - Three-digit 8002
Find the largest three-digit number that gives the remainder 1 when divided by three, gives the remainder 2 when divided by four, gives the remainder 3 when divided by five, and gives the remainder 4 when divided by six. - Regularly 7749
Three steamers leave the port. The first regularly returns after three months, the second after four, and the third after six months. How long before they meet again in the port? - Reminder and quotient
There are given the number C = 281, D = 201. Find the highest natural number S so that the C:S and D:S are with the remainder of 1.
- There
There are two numbers on the screen - one in the blue and the other in the red box. In the beginning, both numbers are the same. With each beep, both numbers increase - by 1 in the blue field and by 3 in the red field. At one point, the number 49 appears - The Hotel
The Holiday Hotel has the same number of rooms on each floor. Rooms are numbered with natural numerals sequentially from the first floor, no number is omitted, and each room has a different number. Three tourists arrived at the hotel. The first one was in - Six-digit primes
Find all six-digit prime numbers that contain each one of digits 1,2,4,5,7 and 8 just once. How many are they? - The florist
The florist had 200 roses in the morning. During the day, more than half sold it. The remaining roses will tie to the bouquet. One always remains if a bouquet of 3, 4, 5, or 6 roses is bound. How many roses from the morning shipment were sold? - Chocolate
I have a box of chocolate - white, milk, and dark. The ratio of white to milk with dark is 3:4. The ratio of white and milk to dark is 17:4. Calculate the ratio between white, milk, and dark chocolate.
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