Natural numbers - high school - practice problems
Number of problems found: 322
- Geometric progression
For the following geometric progression, find the seventh (7th) term: 4, 12, 36, 108, . - 52 cards
A hand of five cards is dealt from a pack of 52 playing cards. How many different hands can be dealt that contain three aces? - Fruits
(I) bought three apples, two oranges, four pears, and five bananas, which in total cost £3.73. (i) I bought twenty-one apples, no oranges, eight pears, and fifteen bananas, which in total cost £7.57. (i) I bought one apple, eighteen oranges, fourteen pear - Multiple numerical bases
Find the value of x for which 312four+52x=96ten . Hint: four, x, and ten are the base of the given number. - A fair 2
A fair die is thrown two times. What is the probability that the sum of the score is almost 8? - Fibonacci numbers
If the first three Fibonacci numbers are given as x1 = 1, x2 = 1, and x3 = 2, then what is the least value of n for which x(n) > 500? - Determine 82975
Determine the sum of all positive odd numbers less than 78 - Permutations 82516
From how many elements can we make 5040 permutations without repetition? - Subsequent 82511
The theater has 20 rows of seats on the ground floor. There are 16 seats in the first row, and each subsequent row has two more seats than the previous one. Find the number of seats on the ground floor of the theater. - Spectators 82430
In a circus, in one sector for spectators, the seats are arranged in such a way that in each higher row, there is one more seat than in the previous one. How many seats are there in a sector with 22 rows if there are 8 seats in the first row? - We randomly
We randomly select a three-digit number. What is the probability that the number 8 occurs at most once in its notation? - Department 81818
The department has 90 members. There are 4 more older adults in the section than younger adults. There are 10 more older pupils than all adults. How many older and younger teenagers and how many older pupils are there in the section? - Arithmetic 81811
In which arithmetic sequence is the sum of the first five terms with odd indices equal to 85 and the sum of the first five terms with even indices equal to 100? - Received 81487
Nikola and Agáta received a total of 20 roses from their partners. Nikola received 4 more roses than Agáta. How many roses did each have? - Three-digit 81064
A three-digit number has a digit sum of 16. If we change the digits in the hundreds and tens places in this number, the number is reduced by 360. If we swap the ten's and one's digits in the original number, the number increases by 54. Find this three-dig - Five-minute 80951
Karel has an average grade of exactly 1.12 from five-minute episodes. Prove that at least 22 of them have one. - Aquariums 80526
Mirko has a total of 137 fish in three aquariums. He has 19 more fish in the largest aquarium than in the medium. There are 5 fewer fish in the smallest than in the middle one. How many fish does Mirko have in the smallest aquarium? - Equations: 80499
In the field of real numbers, solve the system of equations: 2x + ⌊y⌋ = 2022, 3y + ⌊2x⌋ = 2023. (⌊a⌋ denotes the (lower) integer part of the real number a, i.e., the largest integer not greater than a., E.g., ⌊1.9⌋ = 1 and ⌊−1.1⌋ = −2.) - Two numbers 13
Two numbers are in the ratio 5:8. When 2 is added to each, the ratio of the resulting numbers is 2:3. Find the numbers. - The sum 24
The sum of the three numbers is 80. The first number is 8 less than the third. The second number is 2 times the third. What are the numbers?
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