Reason + power - practice problems
Number of problems found: 42
- Strawberries 82738
Three classmates worked part-time during the summer vacation harvesting strawberries. Jan collected 145 baskets of strawberries during the entire time of the brigade. Peter collected 185 baskets. How many baskets did their classmate Stan collect, if we kn - Rectangle 82087
A 9cm × 15cm rectangle is divided into unit squares. How many paths are there from one rectangle vertex to the opposite vertex if one can only go to the right and up the sides of the squares? - Smallest z9
Find the smallest positive numbers a and b for which 7a³ = 11b⁵ - Positive integer integral
How many different sets of a positive integer in the form (x, y, z) satisfy the equation xyz=1400? - Smallest 79434
Find the smallest natural x such that 2x is the square and 3x is the third power of a natural number. - 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 - The plot
Mr. Duma recently inherited a rectangular plot, part of the estate left by his late father. The plot with the following dimensions: Length=2x+1; Width=x-1. Determine the formula, in terms of x, that best describes the area of the rectangular plot. He has - Granddaughter
In 2014, the sum of the ages of Meghan's aunt, her daughter, and her granddaughter was equal to 100 years. We know the age of each can be expressed as the power of two. In what year was the granddaughter born? - Quiz or test
I have a quiz with 20 questions. Each question has four multiple-choice answers, A, B, C, D. THERE IS NO WAY TO KNOW THE CORRECT ANSWER OF ANY GIVEN QUESTION, but the answers are static, in that if the "correct" answer to ; 1 = C, then it will always be e - Cardboard box
Peter had square cardboard. The length of the pages was an integer in decimetres. He cut four squares with a side of 3 dm from the corners and made a box out of it, which fit precisely 108 cubes with an edge one dm long. Julia cut four squares with a side - 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. - Friction coefficient
What is the weight of a car when it moves on a horizontal road at a speed of v = 50 km/h at engine power P = 7 kW? The friction coefficient is 0.07 - Four pavers
Four pavers would pave the square in 18 days. How many pavers do you need to add to the done work in 12 days? - Diameter 7648
The mug has the shape of a cylinder with a height of 60.7 mm. There is two dl of water in it. If we dip a ball with a diameter of 40 cm into the water, the water will not overflow. What is the minimum diameter of the cup? - Two pipes
How long will the pool be filled with a double supply pipe if it takes the pool to fill the first pipe by 4 hours long and the second pipe 9 hours longer than both pipes open simultaneously? - Statistician 7500
A statistician monitored the variance of monthly wages and found its value to be 640,000. Determine the standard deviation of salaries if there is a one-off increase: a) about CZK 1,800, b) about 5%. - Three machines
The power of the three machines is 2:3:5. Two most powerful machines produce 400 parts per hour. How many components make all three machines in 3 hours? - Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Last digit
What is the last number of 2016 power of 2017 - No smoke
Tobacco company NO-SMOKE adorned its stand at the cigarette-type trade fair with cigarette-shaped. The dimensions of which were 20 times the size of a regular cigarette. Regular cigarette contains 0.8 mg of nicotine. How much nicotine would a giant cigare
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