# Reason - high school - examples

- 600 pencils

600 pencils we want to be divided into three groups. The biggest groups have ten pens more than the smallest. How many ways can this be done? - Boys and girls

There are 11 boys and 18 girls in the classroom. Three pupils will answer. What is the probability that two boys will be among them? - Three numbers

We have three different non-zero digits. We will create all 3 digits numbers from them to use all 3 figures in each number. We add all the created numbers, and we get the sum of 1554. What were the numbers? - Find the sum

Find the sum of all natural numbers from 1 and 100, which are divisible by 2 or 5 - Trapezoid MO

The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Pool

If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately? - Bonus

Gross wage was 527 EUR including 16% bonus. How many EUR were bonuses? - Logic

A man drinks a barrel of water for 26 days, woman for 48 days, for how many days they drink barrel together? - River

From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river. - Eiffel Tower

Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made of the same material, if it weigh is 2.4 kg? - Two cars

Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet? - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors? - Seating

How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)? - Ravens

The tale of the Seven Ravens were seven brothers, each of whom was born exactly 2.5 years after the previous one. When the eldest of the brothers was 2-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur - Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Gutter

How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material. - Z9–I–1

In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir - Cyclist

Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane? - Mast

Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 5°. Determine the height of the mast, if the sun above the horizon is at angle 37°12'.

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