Prime numbers - practice for 14 year olds
Number of problems found: 97
- Eggs in basket
If the eggs in a basket are removed twice at a time, one will remain. Two eggs will remain if the eggs are removed three at a time. If the eggs are removed four, five, or six at a time, the three, four, and five eggs will remain, respectively. However, no - Perfect square or cube
Would you classify 324 as a perfect square, perfect cube, both, or neither? ... - A number 8
A number K is such that when it is divided by 27, 30, or 45, the remainder is 3. Find the smallest possible value of K - Jackie 2
Jackie bought an equal number of tulip bulbs and daffodil bulbs. Along the length of her garden, Jackie planted 6 daffodil bulbs and 3 tulip bulbs per foot. She has 5 daffodil bulbs and 29 tulip bulbs remaining to plant elsewhere. How long is Jackie's gar
- Volunteers 81981
Volunteers planted saplings in the forest nursery; spruces made up 55% of all saplings; one-third were edible, and the rest were young pines. How many saplings did they plant if the number of saplings was greater than 1060 and less than 1090? - Together 81979
Three friends split the reward in the ratio of 3:5:7. One of them received exactly €49. How many euros did they get together? - Calculate 81492
Jirka went on a moped for a three-day trip. He drove 90 km on the first day, 30 km on the second day, and 60 km on the third day. He always drove at the same average speed and always the whole number of hours. Calculate the average speed if Jirka drove at - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Differences 80551
Bolek and Lolek each had their own arithmetic sequence. Both Lolek and Bolek's sequence started with the number 2023 and ended with the number 3023. The two sequences had 26 numbers in common. The ratio of Bolek's and Lolka's difference was 5:2. What is t
- The grocery
Susan has decided to make grocery combos for her shop. The wholesaler she buys from sells sugar in packets of 20 in a carton, flour in packets of 12 a carton, and 15 bags of rice in a carton. How many of each item should she buy so there are an equal numb - Two numbers sum and product
Two numbers have a sum of 12 and a product of 27. What is the larger number? - Owl A,B,C
Owl a gives a hoot every 7 minutes. Owl b gives a hoot every 9 minutes. Owl c gives a hoot every 5 minutes except when he has heard owl a or b give a hoot within the previous 2.5 minutes. If this happens, owl c doesn't give a hoot. If all three owls give - What is 20
What is the least number that should be added to 2497 so that the sum of the digits is divisible by 5, 6, and 10? - Treasury 73334
Peter has only two crowns in the treasury and can divide them both in a ratio of 4:5 and in a ratio of 4:7. How many crowns does Peter have in the money box if the amount saved is less than 300 CZK?
- Percentages 64334
In the first delivery of 120 parts, there was 5% waste. In the second delivery in which, 10% of the 80 were scrapped. How much scrap was brought in with the first and second deliveries combined? What % of scrap was there in both deliveries of parts, out o - Increased 64324
The number of books in the city library increased by 0.2% in 2008 and 0.6% in 2009. At the same time, the total number of books remained less than 300,000. How many books were added to the city library in 2009? - The sum 13
What is the sum of the exponents of the prime factors in the prime factorization of 196? - Two-digit number
In a two-digit number, the number of tens is three greater than the number of units. If we multiply the original number by a number written in the same digits, but in reverse order, we get product 3 478. Find the original number. - Coloured numbers
Mussel wrote four different natural numbers with colored markers: red, blue, green, and yellow. When the red number divides by blue, it gets the green number as an incomplete proportion, and yellow represents the remainder after this division. When it div
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