Arithmetic + reason - practice problems - page 21 of 22
Number of problems found: 422
- MO Z6-6-1
Write integers greater than 1 to the blanks in the following figure so that each darker box is a product of the numbers in the neighboring lighter boxes. What number is in the middlebox? - Three dices
What is the probability that the sum of points 14 will be a roll of three dice (B, M, Z)? - Twenty-five
How many are three-digit natural numbers divisible by 25? - Positive integers
Several positive integers are written on the paper. Michaella only remembered that each number was half the sum of all the other numbers. How many numbers could be written on paper?
- House numbering
The residential house has three entrances numbered even numbers, successive immediately behind. The sum of the two numbers on the outside entrances is 68. Calculate the middle of these three numbers. - Report card
Ivor hit 4× grade 5 at the beginning of the school year. How many times must you now catch grade 1 to get grade 2 on the report card? - Budapest 82510
In Trnava, it was -6 degrees Celsius; how much was it in Budapest, which was twice as hot.? - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Star equation
Write digits instead of stars so that the sum of the written digits is odd and is true equality: 42 · ∗8 = 2 ∗∗∗
- Yesterday 13711
If the day before yesterday was the day of the week, what day of the week would it be from today in 50 days? (0 = Monday, 6 = Sunday) - Arithmetic 40671
The number 20 is the arithmetic mean of the eight numbers. Determine their sum. - Solutions 8481
For which integers x is the ratio (x + 11) / (x + 7) an integer? Find all solutions. - Z7-I-4 stars 4949
Write instead of stars digits, so the next write of the product of the two numbers is valid: ∗ ∗ ∗ · ∗ ∗ ∗ ∗ ∗ ∗ ∗ 4 9 4 9 ∗ ∗ ∗ ∗ ∗ ∗ 4 ∗ ∗ - AM of three numbers
The number 2010 can be written as the sum of 3 consecutive natural numbers. Determine the arithmetic mean of these numbers.
- Consecutive 29761
Determine three consecutive natural numbers, the sum of which is 66. - Different 29943
Vojta added five different prime numbers to the top row of the census pyramid. Their sum was 50. What was the biggest number he could get "down"? - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - Three drivers
Three drivers driving in the same direction found that they have the same amount of gasoline. The first is enough to go 6 km, 4 km, second and third 3km. Gasoline they divided, so all three just drove to the nearest petrol station. How many km away was a
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