Algebra + reason - practice problems - page 51 of 53
Number of problems found: 1057
- 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? - 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)
- Variations 3rd class
From how many elements can we create 13,800 variations of the 3rd class without repeating? - Directly 55591
If n is a natural number that gives a division of 2 or 3 when divided by 5, then n gives a residue of 4 when divided by 5. Prove directly - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - 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. - 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"? - Consecutive 29761
Determine three consecutive natural numbers, the sum of which is 66. - ICE train
German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the average train speed for both journeys woul - Contradiction 55571
Use the truth table to evaluate the truth of the compound statement (a) [P ∧ (Q ∨ R)] ⇔ [(P ∧ Q) ∨ (P ∧ R)] (b) ¬(P ⇒ ¬Q) ⇒ (¬P ∧ Q) and decide each time whether it is a tautology or A contradiction.
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