Primary School Mathematical Olympiad questions and answers

Question:
1. There are four boxes of fruits. It is known that there are 42 apples, pears and oranges in each box on average. There are 36 pears, oranges and peaches in each box on average. There are 37 apples and pears in each box on average?
2. In a math test, the average score of the whole class is 91.2. There are 21 girls, 92 points on average, and 90.5 points on average for boys. How many boys are there in this class?
Answer: 1. 37 * 2 = 74 (pieces) 42 * 3-36 * 3 = 18 (pieces) (74-18) / 2 = 28 (pieces) 28 + 18 = 46 (pieces)
A: 46 apples in a box and 28 peaches in a box
2. (92-91.2) * 21 = 16.8 (points) 16.8 / (91.2-90.5) = 24 (persons)
A: there are 24 boys in this class
It's suggested to buy a Mathematical Olympiad book. So I won't talk about it here~

RELATED INFORMATIONS

1. Who can help me to do some math problems? (please use primary school knowledge to solve the problems, and write down the detailed solution ideas and process) 1. Two people report any natural number from 1 to 10 in turn. At the same time, they add up the numbers reported. Whoever makes the cumulative sum reach 500 first will win. Then, if the reporter (fill in "first" or "later") is sure to win, he must report () 2. The donkey and the mule walked side by side, carrying heavy packages on their backs. The donkey complained that his packages were too heavy. "Your burden?" the mule retorted, "if you take a package from your back to me, my burden will be twice as much as yours. If you take a package from my back to you, you will carry as much as mine." the donkey carried () packages, The mule carried () packages 3. A scientific investigation team has to cross a mountain. It goes up the mountain at 8:00 a.m. and travels 3 kilometers per hour. When it reaches the top of the mountain, it takes an hour to rest. When it goes down the mountain, it travels 5 kilometers per hour and reaches the bottom of the mountain at 2:00 p.m
2. There is a three digit number. The number on the ten digit is two-thirds of the number on the one digit. The number on the ten digit plus three is equal to the number on the one digit. The number on the hundred digit is the smallest prime number. What is the three digit number?
3. (have a specific formula) 1. It takes six minutes for Party A, five minutes for Party B and four minutes for Party C to manufacture a part. Now 296 parts are allocated to these three people. If they are to complete the task at the same time, how should they allocate the task? 2. A, B and C each have a certain amount of money. The money ratio of a and B is 5:6. The money of C is two-thirds of that of B. the average of the three people is 50 yuan. How much money do they each have? 3. There are two kinds of candy, a and B, whose unit price (yuan / kg) ratio is 5:4. According to the weight ratio of a and B is 2:3, the two kinds of candy are mixed together, and the unit price is 11 yuan / kg, which is just equal to the original money from separate sales. Then what are the unit prices of the two kinds of candy? 3. Draw a circle with a radius of 3cm on a 1:3000000 map. What is the actual land area of this circle? (PAI = 3.14)
4. The perimeter of a circular flower bed is 50.24m, in which three eighths of the area is reserved to grow Cyclamen. What is the area of Cyclamen? The outer diameter of the train wheel is 0.8m, and it turns 400 circles per minute. The train passes a bridge in 15 minutes. How long is the bridge? With a 15.7m long fence, the largest chicken fence should be enclosed. What figure should it form? What is its area?
5. 1. Cut a cylinder along the radius of the bottom, divide it equally, and then put it together into an approximate cuboid. The cuboid is 12.56 cm long and 10 cm high. The volume of the cylinder is () cubic cm 2. The height of the cylinder is three times that of the cone. The ratio of the bottom radius of the cylinder to the bottom radius of the cone is 1:2. The volume ratio of the cylinder to the cone is () 3. The diameter of the bottom of a cone is 8 cm and the height is 12 cm
6. 1. A car will arrive 39 minutes ahead of schedule if it is 12 kilometers faster than the original time limit. If it is 8 kilometers slower than the original time limit, it will arrive 39 minutes late 2. Party A and Party B set out from a and B at the same time, and walked in opposite directions. After they met 6 kilometers away from B, they continued to move forward in the same direction. When they reached B and a respectively, they immediately returned and met 4 kilometers away from A. how many kilometers are there between a and B? It's better to use arithmetic method, or use X to solve equation (use X! Not XY!)
7. Math problems in grade five of primary school Processing a batch of parts, apprentice alone 9 hours to complete, master alone 6 hours to complete (3) Master and apprentice work together for several hours? (please teach me patiently)
8. The greatest common factor of two numbers is 9 and the least common multiple is 135. One of them is 27 and the other is () The least common multiple of three continuous natural numbers is 60. These three numbers (), (), ()
9. Math problem! I don't quite understand the meaning of the problem~ In order to provide a frame for a photo of 29cm in length and 22cm in width, the width of the four sides of the frame should be equal, and the area occupied by the frame is one fourth of that of the photo. How many centimeters should the width of the frame be? Such as the title.
10. A very meaningful mathematical problem In the plane rectangular coordinate system, the line y = x + 1 and y = - 3 / 4x + 3 intersect at point a, respectively intersect the X axis at point B and point C, and point D is a moving point on the line AC (1) Point m is a moving point on the parabola. When the triangle CBM is an isosceles triangle, the coordinates of point m are obtained (2) Point n is a moving point on the parabola. When the triangle BCN is a right triangle, the coordinates of point n are obtained The analytical formula of parabola passing through ABC three points is y = - 7 / 20x ^ 2 + 21 / 20x + 7 / 5
11. I hope to talk about the solution There are 100g sugar in No.1 cup, water in No.2 cup and 100g salt in No.3 cup. First, half of the liquid in No.1 cup and 1 / 4 of the liquid in No.3 cup are poured into No.2 cup, then they are stirred well, and then 2 / 7 of the liquid in No.2 cup is poured into No.1 cup, Then pour out 1 / 7 to 3 cups of the remaining liquid. Q: what is the ratio of salt content to sugar content in each cup
12. In the 10km race around the city, when the first runner reaches the finish line, the second runner is 2km away from the finish line, and the third runner is 2km away from the second runner. When the second runner reaches the finish line, how many kilometers away is the third runner?
13. Xiao Ming raised both ducks and sheep. He asked Xiao Ming how many ducks and sheep there were. Xiao Ming said: ducks and sheep have 13 heads and 36 legs. How many ducks and sheep do you have?
14. Mathematics problems in grade eight It is known that a + B = 10, ab = 17 Find the value of A-B
15. When a machine tool factory manufactures a certain kind of machine tool, it uses 1.5 tons of steel for each machine tool. In fact, it saves 0.25 tons for each machine tool. As a result, it manufactures 10 more machine tools than originally planned. How many machine tools did it originally plan to build?
16. 1. The foundation of a teaching building in Zhaohui primary school is a rectangle with a length of 3.80 meters and a width of 30 meters. According to the plan, its width is 15 cm, and how long should it be? 2. The water supply company needs to install a 31 meter long water pipe. There are two kinds of water pipes of 3 meters and 5 meters. It is known that each pipe of 3 meters is 32 yuan. How much will it cost to install this pipe? 3. Xiaoming asked Xiaohong, "how many rabbits and chickens do you raise in your family?" Xiaohong answered very interestingly. He said, "I raise more rabbits than chickens. Chickens and rabbits have 24 feet in total. Guess how many rabbits and chickens do you raise in my family?" The multiplication and division signs are written in Chinese characters
17. I'd like to ask you to help me with some math problems 1. Find the sum of the first 100 consecutive integers in the string of - 44, - 43, - 42,..., 2001200220032004 2. (- 4 and 3 / 2) + (- 3 and 1 / 3) + (- 6 and 1 / 2) + (- 2 and 1 / 4) write out the calculation process 3. (- 0.5) + (+ 31 / 4) + (+ 2.75) + (- 5 and 1 / 2) calculate and write out the process 4. Find the sum of the opposite number of 3 and 2 / 3 and the absolute value of - 2 and 1 / 3 5.3.3 + 59.8 + (- 12 and 4 / 5) + (- 59 and 4 / 5) + (- 2.3) calculate and write the process 6. (3 / 4 + 1 / 5) + (4 / 5 + 1 / 6) + (5 / 6 + 1 / 7) +... + (7 / 8 + 1 / 9) + (8 / 9 + 1 / 10) calculate and write the process 7. - 5 and 5 / 6 + (- 9 and 2 / 3) + 17 and 3 / 4 + (- 3 and 1 / 2) calculate and write the process Let's do this. If anyone works out the problem according to my requirements first, I'll add another 25 points,
18. We need to work out the formula A total of 156 yuan will be paid for 3kg pear and 4kg apple. It is known that 5kg pear = 2kg apple, so the price of pear and apple can be calculated
19. A kind of fast growing water plant, the number of which increases twice every day. Put one plant in a pond and the pond will be full in 30 days. If it is required to be full in 26 days, put () plants in the pond
20. 2x4+4x6+6x8+.+98x100