Reasoning - math word problems - page 49 of 87
Number of problems found: 1734
- Inequality proof
Let a, b, and c be positive real numbers whose sum is 3, each of which is at most 2. Prove that the inequality holds: a2 + b2 + c2 + 3abc - Missing numerals
John described the example but forgot the numerals. Fill them in so that the result is correct. (2 solutions): 3 3 3 3 = 8 - Hiker Path Lengths
The hiker went from A to B and back in 3 hours and 41 minutes. The road from A to B is first uphill, then flat, and finally downhill. A hiker walked up a hill at a speed of 4 km/h, on a flat surface at a speed of 5 km/h, and down a hill at a speed of 6 km - Letter puzzle In the following additional example, the same letters represent the same digits, and the different letters represent different digits: RATAM RAD -------------- ULOHY Replace the letters with numbers so that the example is correct. Find two different repla
- Odd/even number
Pick any number. If that number is even, divide it by 2. If it's odd, multiply it by three and add one. Now, repeat the process with your new number. If you keep going, you'll eventually end up at one every time. Prove. - Digit puzzle Four cards each showed a different digit, one of which was zero. Victor formed the largest four-digit number from the cards, and Martin formed the smallest four-digit number. Adam wrote the difference between Victor's and Martin's numbers on the board. Th
- Harvesters
The first harvester will harvest the grain from the field in 20 hours, and the second, the more powerful, will harvest it in 10 hours. How long will it take for both harvesters to harvest this field if the second harvester has to be set up first, which ta - Card expression Tomas received nine cards with the following numbers and math symbols for math olympiad results. 18, 19, 20, 20, +, -, x, (,) Note 4 numbers and operators plus, minus, times, left parenthesis, right parenthesis. He stored the cards so that there were neve
- Anti-birthdays
Štefka likes to celebrate, so apart from her birthday she came up with anti-birthdays as well: the date of anti-birthdays arises so that the number of the day and the number of the month in the date of birth are swapped. She herself was born on 8.11., so - Clothing company
A clothing company manufactures three kinds of coats. The weekly production is 400 of the first type, 370 of the second, and 230 of the third type. By long-term observation it was found that among the quality coats there are 2/3 of the first type, 7/9 of - CD compartment distribution
Thomas has two compartments with CD-ROMs. The arithmetic average of the number of CDs in both bins is 30. If he added 10 more CDs to the first bin, there would be 1.5 times more CDs than in the second bin. How many CDs are in each compartment? - Year 2018
The product of the three positive numbers is 2018. What are the numbers? - Testing preparation time
Mike has also been preparing for testing 9 for a long time. He devotes a third of his time to Czech, half of his time to mathematics, and discusses with his father for 10 minutes. How many minutes a day does Mike prepare? - Middle finger
Jana counts on one hand, going finger by finger. She starts counting from her thumb through her index finger, middle finger, and ring finger up to her little finger, reaching the number 5. Then she immediately goes back to her ring finger (6), middle fing - Ladder rung cutting
To make a ladder, the craftsman needs to cut as many rungs of the same length as possible. He is to cut them from two boards, one is 220 cm long, and the other is 308 cm long. How long will the bars be, and how many will there be? - Three-digit number
Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number. - Triangle Geometry Proof
On side AB of triangle ABC, points D and E are given such that |AD| = |DE| = |EB|. Points A and B are the midpoints of segments CF and CG. Line CD intersects line FB at point I, and line CE intersects line AG at point J. Prove that the intersection of lin - Z5 – I – 2 MO 2018
Tereza received four identical right-angled triangles with sides of lengths 3 cm, 4 cm, and 5 cm. From these triangles (not necessarily all four) she tried to put together new shapes. She gradually managed to put together quadrilaterals with perimeters of - Mr. Gazdíček
Mr. Gazdíček has in the garden two identical tanks for rainwater, which he uses for continuous irrigation. At the last check, there were 1 000 litres in the first tank and 1 200 litres of water in the second. From the first tank water flows at a rate of 1 - Quadrilaterals II
In the ABCDEFGHIJKL, the two adjacent sides are perpendicular to each other, and all sides except the AL and GF sides are identical. The AL and GF sides are twice as long as the other sides. The lines BG and EL intersect at point M and divide the dodecago
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