1, the decimal point of a decimal point moves to the right and left respectively, and the difference between the two numbers is 2.2, then the decimal point is expressed as a fraction.
2. Price of a leather coat 1.650 yuan. If you sell it at a 20% discount, you can still make a profit 10% (relative to the purchase price). If it is sold at the price of 1650 yuan, it can make a profit in RMB.
3. Find the number11...1(2000) 222 ... 22 (2000) 333 ... 33 (2000) is represented by the number 333 ... 33 (2000).
4. Calculate (1/(1× 2)+2/(/kloc-0 /× 2× 3)+3/(/kloc-0 /× 2× 3× 4)+...+9/(1)
5. The speed of a ship sailing downstream is 30 km/h, and it is known that the voyage of sailing downstream for 3 hours is equal to the voyage of sailing upstream for 5 hours, so the voyage of this ship drifting downstream 1 hour is () km.
6. A TV factory plans to produce 15 sets 1500 sets. As a result, after five days of production, the TV factory has improved its production efficiency by 25% due to the introduction of a new production line, and will complete the plan () days ahead of schedule.
7. Randomly select three numbers from 1, 2, 3, 4, 5, 6, 7, 8, 9 to make their sum even, then there are () different selection methods.
8. The page numbers of a book are consecutive natural numbers 1, 2, 3, 4, …9, 10… When adding these page numbers, someone mistakenly added one of the page numbers twice, and the result is 200 1, so the book has a total of () pages.
9. There are 2 1 flower distributed to 5 people. If the number of flowers allocated to everyone is different, the person who gets the most flowers will get at least () flowers.
10, three workers' masters Zhang Qiang, AARON Li and Chong Wang respectively processed 200 parts. They started to work at the same time. When the task of processing 200 parts in AARON Li was completed, Zhangjiang had processed 160, and there were still 48 parts unprocessed in Chong Wang. When Zhang Qiang finished the task of processing 200 parts, there were still _ _ parts unprocessed in Chong Wang.
1 1, there is a watch 10: 00 on October 29th, which is 4 minutes and a half slower than the standard time,165438+17: 00 on October 5th, which is 3 minutes faster than the standard time, so this watch points to1.
12. The water in the water tank flows out of the water tank at a constant speed. It is observed that at 9: 00 am, the water in the water tank is 2/3 full, and when 1 1, the water in the water tank is only 1/6. So when will the water in the tank just run out? ( )
13. There are 1800 students in Tsinghua High School. If each student has 8 classes and each teacher has 4 classes every day, there are 45 students in each class, 1 teacher. So please introduce the name of the teacher of Tsinghua High School.
Forty-five students from a class took part in the math contest. Results 35 students answered the first question correctly, 27 students answered the second question correctly, 4/kloc-0 students answered the third question correctly, and 38 students answered the fourth question correctly. So there are at least four students in this class?
15, a number first adds 3, then divides it by 3, then subtracts 5, then multiplies it by 4, and the result is 56. This number is _ _ _ _ _.
16. A bottle with a lid contains some water (as shown below). Please calculate the volume of the bottle _ _ _ _ _ _ _ _ _ cm according to the data shown in the figure. .
In a class of Grade 6 17, some students are 13 years old, some students are 12 years old, and the rest are1/kloc-0 years old. The average age of the students in this class is _ _ _ _ _ _.
18, put 25 grams of sugar into an empty cup, pour 100 grams of boiling water, fully stir, and drink half of the sugar water. Add 36 grams of boiling water. If the sugar water in the cup is as sweet as before, you need to add _ _ _ _ _ grams of sugar.
19 grade 1 class all the students participated in the extracurricular sports group and the singing group respectively, and some students also participated in both groups. If the number of people who participate in the two groups is the number of people who participate in the sports group and the number of people who participate in the singing group, then the ratio of the number of people who only participate in the sports group to the number of people who participate in the singing group in this class is _ _ _ _ _ _ _.
20. His baby panda is 2 years old this year. A few years later, when the panda was the same age as its mother, her mother was 18 years old. Mother panda is _ _ _ _ _ years old this year.
2 1, the orchard buys a batch of apples, which are divided into three grades according to quality, the best apples are first class, and the price per kilogram is 3.6 yuan; Next is your apple. The price per kilogram is 2.8 yuan; Third-class apples are 2. 1 yuan per kilogram. The ratio of these three apples is 2: 3: 1. If these three kinds of apples are sold together, it is more appropriate to price them at _ _ _ _ _ _ _ yuan per kilogram.
22, a class of no more than 60 students, in a math exam, the number of people who scored not less than 90 points, 80-89 points, 70-79 points, then there are _ _ _ people below 70 points.
23. There is a column number, which is arranged according to the following rules: 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 6, 7, ... No.2000 in this column.
24. After tripling a five-digit number with 200,000, the result is exactly the same as the number with 2 at the right end of the five-digit number. This five-digit number is _ _ _ _ _ _ _.
25, from 3, 13, 17, 29, 3 1 these five natural numbers, take two numbers at a time as fractions of the numerator, totaling _ _ the simplest fractions.
26. Due to the continuous improvement of the quality of students in Beijing 10 1 Middle School in recent years, especially the joint efforts of teachers and students, the results of college entrance examination have been improved year by year. 200 1 college entrance examination, 59% of the candidates were admitted to key universities; In the 2002 college entrance examination, 68% of the candidates were admitted to key universities; It is estimated that 74% of the candidates will be admitted to key universities in 2003. 10 1 3 The average annual growth rate of entering key universities in these three years is _ _ _ _ _ _ _ _.
27. Draw a straight line on the right through the point P in the parallelogram ABCD, and divide the parallelogram into two parts with equal area (draw a picture and explain the method).
28. 134 A school student went to the park to rent a boat. Rent a big ship, 60 yuan can take six people. Rent a boat, and 45 yuan can accommodate four people. Please design a lease scheme to minimize the rent.
29. A train passed a 900-meter-long railway bridge, and it took 1 minute and 25 seconds to get on the bridge at the front and leave the bridge at the rear. Then the train passed through a tunnel with a length of 1 0,800 meters, and it took 2 minutes and 40 seconds to get the speed of the train and the length of the car body.
30. There is a six-digit number, which is two, three, four, five, six or six digits. Their numbers are exactly the same as the original six digits, but the order is different. Find this six-digit number.
3 1, 50 pieces in a circle, number 1, 2, 3, 4, ... 50, take out every other piece, and ask that the number of the last piece left is 42, so which piece should we start with?
32. Calculate (1.6-1.125+8 (3/4)) ÷ 37 (1/6)+52.3× (3/41).
33.1February 1999, the balance of savings deposits of urban and rural residents nationwide at the end of the month was 5,676.7 billion yuan, and the balance was 1000 billion yuan; 127; Compared with the balance at the beginning of the month, it increased by 18%, so the balance of savings deposits of urban and rural residents nationwide at the beginning of February was () billion yuan (accurate to 100 million yuan).
34. The circumference of the circular runway is 400 meters. Two athletes, A and B, set off clockwise from the starting point at the same time. The speed of A is 400 meters per minute, and the speed of B is 375 meters per minute. () Minutes later, Party A and Party B meet again.
35. The least common multiple of two integers is 1925. These two integers are divided by their greatest common divisor, and the sum of the two quotients is 16. These two integers are () and () respectively.
36. In the math exam, one question is to calculate the average of four scores (5/3), (3/2), (13/8) and (8/5). Xiaoming was careless and copied the numerator and denominator of 1 fraction upside down. The biggest difference between the wrong average and the correct answer is ().
37. The fruit company bought 52,000 kilograms of apples, with the purchase price of 0.98 yuan per kilogram, and paid the freight and other expenses 1.84 yuan, and the estimated loss 1%. If you want to make a profit after all buying and selling 17%. The retail price of apples per kilogram should be set at () yuan.
38. Calculation:19+199+1999+...+19999 ... 99
└ 1999 9┘
39. Xinxin Business Service Company charges 3% service fee for customers to sell goods and 2% service fee for customers to shop. Today, a customer entrusted the company to sell some self-produced goods and buy new equipment. It is known that the company deducted a total of 264 yuan of customer service fee, and the customer just broke even. How much did the new equipment cost?
40, a column number, the first three are 1, 9, and each after 9 is the remainder obtained by dividing the sum of the first three adjacent numbers by 3. What is the number 1999 in this column number?
4 1, a cuboid wood with a volume of 0.078 cubic meters. It is known that this wood is 1.3m long and 3m wide. How many decimetres should it be? Sun Jian politicians calculated the height error to be 3 meters. In this way, what is the volume of this piece of wood of more than 0.078 cubic meters?
42. There are two squares, one big and one small. They are 20 cm apart in circumference and 55 cm apart in area. How many square centimeters is the area of a small square?
43. There are nine small rectangles whose length and width are equal respectively. The area of the big rectangle composed of these nine small rectangles is 45 square centimeters. Find the circumference of this big rectangle.
44、 77× 13+255×999+5 10
45. A = 8.8+8.98+8.998+8.9998+8.99998, and the integer part of A is _ _ _ _.
46. The divisor of1995 is _ _.
47. The equation "Melissa Zhou × Hao Hao+Math = 1994" means the product of two numbers. When one number is added, the total is 1994. In the formula, the three Chinese characters "Xue, Hao and Shu" each represent three different numbers, among which "Shu" stands for _ _ _ _.
48. As shown in the figure 1, the seven Chinese characters "Hao, Gang, Companion, Help, Hand, Shen and Qiu" represent the seven numbers 1 ~ 7. It is known that the five sums obtained by adding three numbers on three straight lines and three numbers on two circles are all equal. The "good" in the middle of the picture stands for _ _ _.
49. Uncle Agan, a farmer, wants to build a rectangular chicken coop with * walls with 20 pieces of metal nets 2 meters long 1.2 meters wide (as shown in Figure 2). In order to prevent chickens from flying out, the height of the henhouse should not be less than 2 meters. In order to maximize the area of henhouse, the length of BC should be 100 meter.
50. Xiao Hu and Xiao Tu calculate the product of two digits of A and B. Xiao Hu misread the single digit of A, and the calculation result is1274; Xiao Tu misread the ten digits of a number, and the calculation result was 8 19. One number is _ _ _ _.
In the 5 1 and 1994 World Cup, four teams, A, B, C and D, were in the same group. In the group stage, each of the four teams will play a game with the other three teams. According to the regulations: the winning team in each game can get 3 points; The losing team gets 0 points; If the two sides draw, each team will get 1 point. Known:
(1) The total scores of the four teams in three games are divided into four consecutive odd numbers;
(2) Team B ranked first in total score;
(3) Team D only tied with the other team twice, one of which was tied with Team C. ..
According to the above conditions, it can be inferred that the total score of team _ _ _ ranks fourth.
52. There are 2 16 bricks stacked on an open space (as shown in Figure 3). This pile of bricks has two walls. Now the surface of this brick pile is covered with lime, and there are _ _ _ _ bricks covered with lime.
53. In an enterprise in a southern city, 90% employees are shareholders, 80% employees are "10,000 yuan households" and 60% employees are wage earners. Then, at least _ _% of the "ten thousand households" in this enterprise are shareholders; At least _ _ _ _ _ _ (fill in a score) of the wage earners are "ten thousand households".
54. There is a bug on the grid paper (Figure 4), which starts from a point O on the straight line AB and crawls along the horizontal or vertical line on the grid paper. The length of each paragraph on a square paper is 1 cm. After climbing a few short sections, the bug is still on the straight line AB, but it does not necessarily return to the O point. If the bug has climbed over 2 cm in total, there are _ _ _ kinds of crawling routes for the bug; If the bug has climbed over 3 cm, the crawling route of the bug is _ _ _ _.
55. Natural numbers are arranged according to certain rules as follows:
According to the arrangement law, 99 ranks in the _ _ _ row and the _ _ _ column.
56. As shown in Figure 5, AF=2FB, FD=2EF, and the area of right triangle ABC is 36 square centimeters. Find the area of parallelogram EBCD.
57. Limin Store bought a batch of mosquito-repellent incense from a grocery company, and then sold it at a price increase of 40% per bag according to the net profit it hoped to make. However, when 90% of the mosquito-repellent incense was sold at this price, the summer passed quickly. In order to speed up the capital turnover, the store sold all the remaining mosquito-repellent incense at a preferential price of 30% off the price. So the actual net profit is less than the expected net profit 15%. According to the regulations, no matter what the price, after selling this batch of mosquito-repellent incense, business tax 300 yuan should be paid (taxes and money used to buy mosquito-repellent incense as the cost). How much did it cost to buy this batch of mosquito-repellent incense at Limin Store?
58. Three oil drums, A, B and C, each contain several kilograms of oil. For the first time, part of the oil in barrel A was poured into barrel B and barrel C, so that the oil in barrel B and barrel C was doubled respectively. Pour the oil in barrel B into barrel C and barrel A for the second time, so that the oil in barrel C and barrel A is twice as much as that before the second pouring; Pour the oil in barrel C into barrel A and barrel B for the third time, so that the oil in barrel A and barrel B is twice as much as that in the previous barrel for the third time, so that the oil per barrel is 16kg. How many kilograms of oil were originally contained in the three oil drums A, B and C?
59. Gardeners should plant trees equidistantly at the edge of a circular flower bed with a circumference of 300 meters. They first dug a hole every 3 meters along the edge of the flower bed. When they finished digging 30 holes, they were suddenly told that they would plant a tree every 5 meters instead. In this way, how many holes will they have to dig to complete the task?
60. A college student who learns from Lei Feng's group works in a restaurant for half an hour every day, and everyone can earn 3 yuan money. By165438+1October 1 1, they had earned a total of 1764 yuan. The team plans to earn 3000 yuan before February 9, 2008 and donate it to Project Hope. So the team must add one person in a few days. Q: This extra person has to work in the restaurant every day from the date of 165438+ 10, so that he can earn exactly 3000 yuan before the date of 65438+February 9?
6 1, there are male and female athletes practicing long-distance running on the circular track, the running speed is constant, and the male athletes run a little faster than the female athletes. If they start from the same starting point and run in the opposite direction at the same time, they will meet every 25 seconds. Now, they start from the same starting point and run in the same direction at the same time. 13 minutes later, the male athlete caught up with the female athlete. How many laps did the female athlete run when she caught up? (The number of laps is rounded off)
Is the sum of all digits in the multiple of 62.555555 odd? If yes, please give examples; If not, please explain why.
63. The picture on the right is a right-angled trapezoid. Please draw a line segment and divide it into two quadrangles with the same shape and equal area. (Please indicate the data and symbols indicating the position of the line segment or write a diagram).
64. The following five figures have two characteristics: (1) consists of four squares of the same size connected together; (2) Every small square has at least one common edge with another small square. We call the graph with the above two characteristics "Tetris".
If a Tetris rotates on a plane, which is the same as another Tetris (such as B and E in the above picture), then these two Tetris are only one kind.
In addition to the above four kinds, there are several Tetris. Please draw them all.
65. Fill in the appropriate operation symbols in the following "□" to make the equation hold: (1□ 9 □ 2) × (1□ 9 □ 2) × (19 □ 9 □ 2) =1992.
66. The length of an isosceles trapezoid with three sides is 55cm, 25cm and 15cm respectively, and its base is the longest side. Therefore, the circumference of this isosceles trapezoid is _ _ cm.
There are 90 seats on a row of benches, and some seats have been taken. At this moment, another man came and sat on this bench. Interestingly, no matter where he sits, he is adjacent to the person who has already sat. It turns out that at least _ _ people have been seated.
68. 1992 divided by the natural number a, the quotient is 46, the remainder is r, a=__, and r=__.
69. On the Double Ninth Festival, 25 old people came to Yanling Teahouse for tea. Their ages are exactly 25 consecutive natural numbers. Two years later, the sum of the ages of these 25 old people is exactly 2000. The oldest of them is _ _ _ years old this year.
70. The school bought several books on history, literature and art, and popular science, and each student borrowed two at will. Then, at least two of these _ _ _ students must have borrowed similar books.
7 1, in a math contest, five players got 404 points, and their scores were not equal, and the player with the highest score got 90 points. Then the player with the least score will get at least _ _ _ _ points and at most _ _ _ _ points. (Each player's score is an integer)
72. It is necessary to saw the high-quality copper tube with a length of 1 meter into a small copper tube with a length of 38 mm and 90 mm, and it will consume 1 mm copper tube every time. Then, only when the sawed 38 mm copper tube is _ _ _ _ _ section and the sawed 90 mm copper tube is _ _ _ _ _ _ section, the copper tube loss can be minimized.
73. Two engineering teams, Party A and Party B, jointly built a 4200m-long highway, and Team B built100m more than Team A every day. Now it will be repaired by engineering team A for 3 days. The rest of the road sections were jointly repaired by Team A and Team B, and it took only 6 days to complete. Q: How many meters do the A and B engineering teams build roads every day?
74. A person rides a bicycle from the county seat to the township to set up a factory. He started from the county seat by bike and completed half the journey in 30 minutes. At this time, he sped up, driving 50 meters more every minute than before. After riding for another 20 minutes, he knew from the mileage card on the side of the road that it would take another 2 kilometers to set up a factory in the township and seek the total distance from the county to the township.
75. The width and height of a cuboid are equal, both equal to half the length (as shown in figure 12). Cut this cuboid into 12 small cuboids, and the sum of the surface areas of these small cuboids is 600 square decimeters. Find the volume of this big cuboid.
There are 1992 buttons. Two people take turns to take a few buttons from them, but each person takes at least 1 buttons and at most 4 buttons. Whoever takes the last button loses. Q: What are the countermeasures to ensure victory?
77. There is a square piece of thick paper with a side length of 24 cm. If you cut a small square at each of its four corners, you can make a carton without a lid. Now, to maximize the size of the carton, how many centimeters should the side length of the cut cubes be?
78. Jin Shifu, an individual blacksmith shop, needs two shapes of iron blanks (A) and (B) as shown in Figure 13 to process some iron products. At present, there are two pieces of scrap iron A and B (as shown in figure 14 and figure 15). The small squares in figure 13, figure 14 and figure 15 are all equilateral squares. Jin Shifu wants to choose one piece from them, so the selected iron sheet is just suitable for processing the complete set of this iron sheet product ("complete set" means that there are as many iron sheets as (a) and (b)) without wasting any materials. Q: (1) Which scrap iron should Jin Shifu choose from? (2) How to cut the selected scraps? Please draw a cut line mark on the picture or use a shadow to indicate the blank space of a shape. )
79. Just modify one digit of 2 1475, and the modified number can be divisible by 225. How to modify it?
80.( 1) How to divide nine identical chocolates equally among four children (each chocolate can only be cut into two pieces at most)?
(2) If the word "four" in the above (1) is changed to "seven", will it be divided? If so, how to do it? If not, why?
Preliminary examination questions of the 4 th China Jinbei Youth Mathematics Invitational Tournament
Preliminary examination questions of the 4 th China Jinbei Youth Mathematics Invitational Tournament
1. Please write the calculation result of the following formula as a fraction:
2. There are 13 nails on a board (right). A few nails can be covered with rubber bands to form triangles, squares, trapezoids and so on (below). Please answer: How many squares can be formed?
3. Here is a cylinder and a cone (below). Their height and base diameter are marked on the map, and the unit is cm. Please answer: What is the ratio of cone volume to cylinder volume?
There are five scores here:,,,,. In descending order, which number is in the middle?
Nowadays, the popular variable-speed bicycle is equipped with several gears with different numbers of teeth on the drive shaft and the rear shaft respectively. Different gears are connected by chains, and several different speeds are obtained through different transmission ratios. There are three gears on the transmission shaft of "Hope" variable-speed bicycle, with the number of teeth being 48, 36 and 24 respectively. There are four gears on the rear axle, with the number of teeth being 36, 24, 16 and 12 respectively. Q: How many different speeds does this gearbox have?
6. The ABCD area of a large square in the figure is 1, and other points are the midpoint of its sides. Excuse me: What is the area of the shadow triangle? (see the picture below)
7. In the formula on the right, the sum of the addends is three times that of the sum. Q: What is the addend at least?
8. There are 60 apples in the basket. Take them all out and divide them into even piles so that the number of each pile is the same. Q: How many ways are there?
9. Xiaoming plays the game of rings, and he gets 9 points for a chicken, 5 points for a monkey and 2 points for a puppy. Xiao Ming has set 10 times, and every time he is trapped, every small toy is trapped at least once. Xiao Ming 10 times 6 1. Q: How many times has the chicken been caught?
10. Many two-wheeled motorcycles and four-wheeled sleeping cars are parked in the garage, and the ratio of the number of cars to the number of wheels is 2: 5. Q: What is the ratio of the number of motorcycles to the number of sleeping cars?
1 1. There is a clock, which is 25 seconds slow every hour. At noon on March 2 1 Sunday 12 this year, the instructions were correct. Excuse me, when will this clock show the correct time next time?
12. Someone goes from place A to place B. If he rides a motorcycle from the first place 12 hours, and then rides a bike for 9 hours, he just arrives at the second place. If he rides a bike from A for 2 1 hour, and then rides a motorcycle for 8 hours, and just arrives at B. Q: How many hours does it take to ride a motorcycle to B?
13. The two circles in the picture below have only one thing in common, a, with a large circle diameter of 48 cm and a small circle diameter of 30 cm. Two beetles started from point A at the same time and crawled along two circles at the same speed in the direction indicated by the arrow. Q: How many times did the beetle climb on the small circle? Are the two beetles the farthest apart?
14. If you sell a juvenile book at the original price, you will make a profit of 0.24 yuan for each book sold; Now the price has been reduced, as a result, the book sales have doubled and the profit has increased by 0.5 times. Q: How much is the price reduction for each book?
15 There is a four-story building. The four glasses of each window are painted red and white respectively, and each window represents a number (below).
There are three windows on each floor, representing a three-digit number from left to right. The three digits represented by four floors are: 79 1, 275, 362, 6 12. Q: What are the three numbers on the second floor?
Examination questions of the 4th Huajin Cup Junior Mathematics Invitational Tournament.
1. Simplify
The TV station will broadcast a 30-episode TV series. If the number of episodes scheduled to be broadcast every day is not equal to each other, how many days can the TV series be broadcast at most?
Just a cylinder with a volume of 628 cubic centimeters can be put into a square carton. What is the volume of this carton? (Pi =3. 14)
There is a basket of apples. After dividing them into three equal parts, there are still two apples left. Take out two, divide them into three parts, and there are two left; Then take out two, divide them into three parts, and there are two left. Q: How many apples are there in this basket?
calculate
6. The circumference of the rectangular ABCD is16m. Draw a square on each side of it. It is known that the sum of the areas of these four squares is 68 square meters. Find the area of rectangular ABCD.
7. The "Huajin Cup" Youth Mathematics Invitational Tournament was held in 1986, the second in 1988, the third in 199 1 year, and will be held every two years thereafter. The sum of the figures in the year of the first China Cup was A 1. Q: What was the number of the first 50 "China Cup"? A50= =?
8. Arrange natural numbers in the following order:
In this arrangement, the number 3 is in the second row and the first column, and 13 is in the third row and the third column. Q: In which row and column is 1993 ranked?
9. Try to fill in the eight numbers 1, 2, 3, 4, 5, 6, 7, 8 in the small circle shown in the figure, so that the difference between the numbers filled in the two small circles connected by line segments in the figure (big numbers minus numbers) is exactly 1, 2, 3, 4, 5, 6.
10.11+22+33+44+55+66+77+88+99 divided by 3. What is the remainder? Why?
Six players (1 1. A, B, C, D, E, F) Play a single-cycle table tennis match (each player plays one game with other players), and each player plays one game on three tables at the same time every day. It is known that on the first day B plays D, on the second day C plays E, on the third day D plays F, on the fourth day B plays C, Q: fifth. Who is playing with whom on the other two tables?
12. There are several battens, the lengths of which are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and1cm respectively, and the number is sufficient, so three battens can be appropriately selected.
13. Color the circles in the picture red or blue at will, and ask: Is it possible to make the number of red circles on the same line all odd? Please provide a justification for the answer.
14. Party A and Party B do special training on the same oval runway: start from the same place and run in the opposite direction at the same time. After everyone reached the starting point after running the first lap, they immediately turned back and accelerated the second lap. In the first lap, B's speed is the speed of A, in the second lap, A's speed is higher than the first lap, and in the second lap, B's speed is higher. It is known that the second intersection of A and B is 90 meters away from the first intersection/kloc-0. How long is this oval runway?
15. The area of the square ABCD in the figure is 1, and m is the midpoint of the AD side. Find the area of the shaded part in the picture.
16. For a party of four people, each person brought two gifts for two of the other three people. It proved that there were at least two couples, and each pair gave gifts to each other.
The 4th Huajin Cup Junior High School Mathematics Invitational Tournament Finals.
What is the sum of all odd numbers that are coprime with 77 in 1. 100?
2. Figures A and B are two large rectangles with the same shape and size. The four small rectangles shown in Figure C are placed in each large rectangle, and the diagonal area is empty. As we all know, the length of this big rectangle is 6 centimeters more than its width. Q: What is the circumference of the diagonal area in Figures A and B? How much bigger?
This is a road map. There is a large group of children in A. They are going east or north. At every intersection from A, half of it goes north and the other half goes east. If 60 children have been to intersection B, Q: How many children have been to intersection C?
4.ABCD stands for four digits, EFG stands for three digits, and A, B, C, D, E, F and G stand for different numbers in 1=9. Known ABCD +EFG= 1993. What is the difference between the maximum value and the minimum value of ABCD +EFG?
5. A group of different natural numbers, in which the smallest number is 1 and the largest number is 25. Except 1, any number in this group is equal to twice of a number in this group, or equal to the sum of two numbers in this group. Q: What is the maximum sum of this group? When the sum of these numbers has the minimum value, which numbers are there in this group? And explain why sum is the minimum.
6. A big river has two ports, A and B, and the water flows from A to B at a speed of 4 km/h. Two ships, A and B, travel from A to B at the same time, sailing back and forth between A and B. The speed of ship A in still water is 28 km/h, and the speed of ship B in still water is 20 km/h. It is known that where the two ships meet head-on for the second time, ship A catches up with ship B for the second time.
The 4th Huajin Cup Junior Middle School Mathematics Invitational Tournament Final Question 2
1. The product of the reverse order of two natural numbers is 92565. Find these two natural numbers in reverse order. (For example, 102 and 20 1, 35 and 53, 1 1 and1,... are called inverse numbers, but 120 and 2/kloc-0. )
2. In the production team of a factory, each worker can complete a production task in 9 hours by working in the original post. If the jobs of workers A and B are exchanged, the production task can be completed 1 hour in advance under the condition that the productivity of other workers remains unchanged; If the jobs of workers C and D are exchanged, the production task can be completed 1 hour ahead of schedule while the productivity of other workers remains unchanged. Q: If the jobs of A and B, C and D are exchanged at the same time, the production task can be completed a few minutes ahead of schedule while the productivity of other workers remains unchanged.
3. None of the students in a school have read all the books in the school library. They know that any two books in the library have been read by at least one classmate. Q: Can you find two students, A and B, and three books, A, B and C? A read A and B, but didn't read C, B read B and C, and didn't read A? Explain the judgment process.
4. There are six cuboids with the same side length, the side lengths are 3 cm, 4 cm and 5 cm respectively, and some faces are dyed red, so some cuboids have only one face, some cuboids have only two faces, some cuboids have only three faces, some cuboids have only four faces, some cuboids have only five faces, and one cuboid has six faces. After dyeing, all cuboids are divided into edges.
5. Xiaohua can play a game several times at will, and the score of each game is one of the three numbers of 8, a (natural number) and 0. The sum of the scores of each game is called the total score of this game. Xiaohua once got such a total score: 103, 104,105,65438.
6. Mark 1, 2, 3, 4, 5, 6, 7, 8 on the eight vertices of the cube, and then write the sum of the two numbers marked at both ends of each side at the midpoint of this side. Q: Is it possible that the number written at the midpoint of each side has only five different values? Is it possible that the number written at the midpoint of each side has exactly four different values? If possible, fill in the correct figures in the table in Figure B according to Figure A; If not, explain why.