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Sixty Fifth-grade Olympic Mathematics Problems
1. Zhao Yun bought a laptop by installment. There are two payment methods. One is to pay 850 yuan a month, and then pay 250 yuan every month. One is to hand it over to 400 yuan in the first half of the year and 200 yuan in the second half. The total amount and time of both payment methods are the same. Ask the price of this computer.

2. Is the product of1000 consecutive natural numbers odd or even? Why?

A shopping mall bought 36 washing machines of the same specification, but the ten thousand digits and single digits of the total invoice price were stained, leaving only the total price? 77 1? Yuan. Since each washing machine costs more than 2000 yuan, can you work out the total price?

4. The table tennis training team bought 423 yellow table tennis balls and 344 white table tennis balls, which one was distributed to 9 players equally, and there was no surplus?

5. Give A, B and 55 apples. A gets twice as many apples as B, and C gets at least 10. How many apples did each of them get?

6. There are 920,000 books in Hall A and Hall B. After borrowing 280,000 books from Hall A, the original books in Hall B are 40,000 less than those in Hall A.. How many thousands of books are there in the two libraries?

7. Kobayashi and Yu Xia each have to process 600 parts. They started processing at the same time, but Kobayashi finished four hours earlier than Yu Xia, and at this time he only produced 400 parts. How many hours did it take Xiao Lin to finish this task?

8. Party A and Party B contract a project with salary of 1 1200 yuan. It is known that A spent 10 days, and B spent 12 days to complete this project. The salary for A 5 days is as much as that for B 4 days. How much do Party A and Party B get?

9. Initially, three mixers can mix 24 tons of concrete in 8 hours. Now, due to the tight schedule, two mixers of the same type have been added. How many tons of concrete can be mixed in 24 hours?

10. To produce a batch of parts, it takes 6 hours for Party A to produce alone and 8 hours for Party B to produce alone. If A produces 10 more parts per hour than B, how many parts are there in this batch?

1 1. If you use 1 cent to buy stamps of 4 cents, 8 cents and 1 cent, how many stamps can you buy at most?

12. A pile of goods weighs 96 tons, and it takes 16 hours for Team A to transport alone, and 24 hours for Team B to transport alone. How many hours does it take to transport together?

13. Five footballs and three basketballs need to pay 259 yuan, and two footballs and three basketballs need to pay 154 yuan. So how much does it cost to buy a football and a basketball?

14.3 baskets of apples and 5 baskets of pears * * * weigh 138 kg, and the same 9 baskets of apples and 4 baskets of pears * * * weigh 2 16 kg. How many kilograms are there in each basket of apples and pears?

15.8 kg of green beans and 9 kg of spinach * * * value 16.8 yuan; 9 kg mung bean, 8 kg pineapple * * * value 17.2 yuan. How much is the unit price of mung bean spinach per kilogram?

16. The sum of three numbers A, B, C is 50, 70 and 60. What are the numbers a, b and c?

17.5 cake with 8 sausages, * * * worth 36 yuan. If 1 cake can be exchanged for two sausages, what is the unit price of cake and sausage?

18. There are 24 turtles and cranes with 68 legs. How many turtles and cranes are there?

19. The unit price of Jinqiao Primary School starts from 34,200 prizes in 5 yuan, and * * * goes to 780 yuan, among which 4 yuan and 5 yuan have the same number of prizes. How many copies did you buy for each of the three prizes?

20. 100 monks eat 100 buns, one big monk eats three, and three little monks eat one. Q * * * How many big monks are there? How many young monks are there?

2 1. A two-digit number is divided by 244 and 34. What is this two-digit number?

22. The science and technology group is divided into groups to do experiments, with 3 people in each group and 2 more people, 4 more people in each group and 5 more people in each group. How many people are there in the science and technology team at least?

23.24× 24× 24×…× 24 (24 in 2004), what is the mantissa of the product?

24. The sum of two prime numbers is 39. What are two prime numbers?

25. Divide the nine numbers 20, 26, 33, 35, 39, 42, 44, 55, 9 1 into three groups, and the products of each group are equal.

26. Judge whether 15 1 and 493 are prime numbers or composite numbers respectively.

27. How many factors were there in 2004?

28. Distribute a batch of books to three classes. The difference in the number of books they get in each class is three in turn, and the product of the number of books in three classes is 58,968. How many books will each of the three classes hand out?

29. It is known that the greatest common divisor of two numbers is 2 1 and the least common multiple is 126. What are these two numbers?

30. The product of two numbers is 1734. The greatest common factor of two numbers is 17. What is the sum of these two numbers?

3 1. There are three steel pipes with lengths of 240 cm, 200 cm and 480 cm respectively. If you cut them into the same pieces, what is the longest length of each piece?

32. For a box of chess pieces, 4 pieces count as more than 3 pieces, 6 pieces count as more than 5 pieces, and 15 pieces count as 14 pieces or more. How many are there in this box?

33. The three brothers work in the field. The eldest brother goes home once every six days, the second brother once every eight days, and the younger brother once every 12 days, 10/0/day. When will the three meet again?

34. Xiao Qiang and Xiaoming practice running. Xiao Ming runs 18 meter first, and Xiao Qiang can catch up with Xiao Ming after running for 9 seconds. If Xiao Ming runs 4 seconds first, it will take Xiao Qiang 12 seconds to catch up with Xiao Ming. Ask Xiao Qiang and Xiaoming about their running speed?

35. dorri and Li Ming started from the same place and ran in the same direction at the same time on the circular track. Dorri runs150m per minute and Li Ming runs120m per minute. If the runway is 900 meters long, how many minutes will it take dorri to catch up with Li Ming?

36. On the 600-meter-long circular runway, Party A and Party B leave for the same place and direction at the same time. After running for 400 seconds, Party A caught up with Party B for the first time. Given that the sum of the speeds of A and B is 6.5 meters per second, what are the speeds of A and B respectively?

37. There are two points A and B on the circular runway with a circumference of 200 meters. The distance between a and b is 100 meter. A starts from point A at a speed of 6 meters per second, and B starts from point B at a speed of 5 meters per second while running along the runway. How many minutes does it take for A to catch up with B five times?

38.a and B run on a 400-meter-long circular track. When A ran from the starting point at a speed of 300 meters per minute 1 minute, B also ran out in the same direction from the starting point. From then on, A caught up with B in 5 minutes. How many meters does Qiu B run every minute?

39. It takes six hours for a ship to travel between Port A and Port B, and eight hours to travel upstream. How many hours does it take for the raft to float between Port A and Port B?

How many minutes does it take for a 40.400-meter-long train to pass through a 2.8-kilometer-long tunnel at 40 kilometers per hour?

Sorry, there are only 40 lanes.