Because the number of digits is 9, the added digits do not carry digits.

That is, the sum of single digits Y+W=9 instead of19,29,39. ....

So the sum of ten digits X+Z= 13.

So: x+y+z+w=22.

There is a 500-meter-long circular runway. Both parties start from a certain point on the runway at the same time. If they run in the opposite direction, they will meet in 1 minute. If you run in the same direction, 10 minutes later. To know that A runs faster than him, ask: How many meters does A run per minute?

In the opposite direction, the sum of their velocities is 500/ 1=500.

In the same direction, the speed difference between them is 500/ 10=50.

The speed of A is: (500+50)/2 = 275m/min.

The speed of B is: (500-50)/2 = 225m/min.

On a circular runway, at 1:00 in the afternoon, Xiaoming set off from point A and Xiao Qiang set off from point B at the same time. They met at 1:06 pm, at 1: 18 pm, Xiaoming arrived at point B, at 1: 18pm.

For example, Xiao Qiang walked for 6 minutes before meeting him for the first time, and Xiaoming walked for 4 minutes, so Xiaoming's speed is Xiao Qiang's: 6/4= 1. Five times.

It took 18-6= 12 minutes from the first meeting to the second meeting.

So the speed of Xiao Qiang is: (112)/(1+1. 5)= 1/30

That is, Xiao Ming's speed is: 1/30* 1. 5= 1/20

Then Xiao Ming's travel time is: 1/( 1/20)=20 minutes.

4.A, B and C are natural numbers with two digits, the single digits of A and B are 7 and 5 respectively, and the ten digits of C are 1. If the equation ab+c=2005 is satisfied, then a+b+c=?

First of all, we can judge that the unit of C should be 0 by the unit of B is 5.

In this way, we can know that the unit and ten digits of c are 10.

Then AB should be 2005- 10= 1995,

1995, only the single digits of 57 and 35 are 7 and 5 respectively, so it is determined that.

a+b+c=57+35+ 10= 102

5, 22 ...2 [2000 2] divided by 13, what is the remainder?

6. What is the remainder of1square +2 square +3 square ... +200 1 square +2002 square divided by 4?

7. What is the remainder of the product of the number 1998 * 1998 * ... *1998 [2000 multiplications of1998] divided by 7?

8. The remainder of an integer divided by 84 is 46, so what is the sum of the three remainders obtained by dividing by 3, 4 and 7 respectively?

9. The four tour groups A, B, C and D have 69, 85, 93 and 97 tourists respectively. Now, the four tour groups should be divided into groups, and each group should be tourists, so that we can go to go on road trip. It is known that after the three groups A, B and C are divided into several groups of A people in each group, the remaining number of people is the same. How many people are left after the tour group is divided into several groups of A people in each group?

Four players with numbers 10, 37, 57, 77 and 97 play table tennis. It is stipulated that the number of discs played by every two players is the remainder of the sum of their numbers divided by 3. What is the player who plays the most? How many sets did he play?

Answer:

5.222222 can be divisible by 13, so 2000 twos contain 333 cycles, leaving the last 22, so the remainder is 9.

6. Because every even term is divisible by 4, there are only odd terms left. We can know that the square of 1 +3 +5 +7 can also be divisible by 4, and there is also the square of11+15.

7. The remainder of1998 divided by 7 is 3, so we can divide it by 1998=7*n+3.

A total of 2000 * * 1998 = 7 * n+3, so it was three times that of 2000, that is, 3 2000 = 91000 = (7+2)1000, so it became 2 65438 again. 2 1000 =1024100 = (146 * 7+2)100, which becomes the remainder of 2100 divided by 7. Similarly, it finally became 65438+.

9. If it is set to 84a+46, then 84a can be divisible by 3, 4 and 7, and the answer is the sum of three remainders obtained by dividing 46 by 3, 4 and 7. 1+2+4=7.

10, which means that 69=n 1*A+a, 85=n2*A+a, 93 = n3 * a+a.

16 =(N2-n 1)* A 8 =(n3-N2)* A 24 =(n3-n 1)* A

So we can know that A=8 or 4, or 2. If it is 8, the number of people left is 1. If a is 4, the remainder is 1, so whether A is 8, 4 or 2, the remainder is 1.

1 1, because the sum of digits of No.37 is 10, 57 is 12, 77 is 14, and 97 is 16, so we know10+. The remainder of 10+ 16 is 2, that of 12+ 14 is 2, and that of 12+ 16 is 1,14+.

1 1 a book, two typists need 10 days, they will type together for eight days, and Party B will type the rest alone. If this book is typed by Party A alone, it will take 28 days to finish. How many days have you been asking B?

13. For a batch of goods, cars A and B can transport 5/6 of the goods within 6 days. If shipped separately, shipment A 1/3 and shipment B 1/2. If they are shipped separately, how many days will it take for A and B respectively?

13. There are some machine parts. It takes 17 days for A to complete alone, which is more than that for B 1 day. After 8 days of cooperation, the remaining 420 parts were made by A alone. How many parts is a * * *? A * * * for a few days?

14. There are two water pipes A and B on the pool, and both water pipes are opened at the same time 12 hours to fill the pool with water. If tube A is on for 5 hours and tube B is on for 6 hours, only 9/20 of the pool can be filled. How many hours does it take to fill the first tube and the second tube respectively?

Answer:

1 1. It takes 28 days for Party A to fight alone, so Party A can complete the task every day 1/28, and Party A and Party B can complete it together 10, so Party A and Party B can complete the task every day1/0.

12. It takes 6 days to complete 5/6 of the combined transportation of two vehicles, so 5/36 can be completed in one day. When A eats 1/3, B can eat 1/2, so the speed of B is 1.5 times that of A, so A can eat 2/36 of this batch of goods every day, and B can eat it.

13. Party A can complete117 every day and Party B can complete116 every day. After 8 days * * * to complete 33/34, the remaining 1/34 is 420, so these parts are a * * *. A * * * did14280 * 8/17+420 = 7140, a * * * did 1/34 divided by1/7.

14. Both parties start to fill in 12 hours, so both parties start to fill in112 hours. Let Party A inject at X and Party B inject at Y, 5X+6Y=9/20, and the above formula is combined into 5(x+y)+y=9/20. So x =112-1/30 =1/20, so it takes 20 hours for single filling and 30 hours for single filling.

Puccio is a famous mathematician in the former Soviet Union. 195 1 wrote a book, Math Teaching Methods in Primary Schools. There is an interesting question in this book.

This shop sold 1026 meter cloth in three days. The sales volume of the second day is twice that of the first day; On the third day, it sold three times as much as the next day. How much rice cloth do you want to sell in three days?

The problem can be thought of this way: the number of meters sold on the first day is regarded as 1 serving. You can draw the following line segment diagram:

The first day 1 serving; The second day is twice as much as the first day; The third grade is three times that of the second grade, and the first grade is 2×3 times.

Comprehensive calculation shows the number of meters of cloth sold on the first day:

1026÷(L+2+6)= 1026÷9 = 1 14(m)

And 1 14× 2 = 228 (m).

228× 3 = 684m

So the fabrics sold in three days are: 1 14m, 228m and 684m respectively.

Please do the problem in this way.

Four people donated money for disaster relief. B donated twice as much as A, C donated three times as much as B, D donated four times as much as C, and they donated 132 yuan. How much do you want each of the four people to donate?

Newton problem

Newton, a great British scientist, once wrote a math book. There is a very famous topic in the book about cattle grazing on pasture. Later, people called this kind of topic "Newton problem".

The "Newton problem" is like this: "There is a pasture where 27 cows are known to have been raised and the grass has been eaten up in 6 days; Raise 23 cows and eat all the grass in 9 days. If you have 2 1 cow, how many days can you eat all the grass on the pasture? And the grass on the pasture is growing. "

The general solution to this kind of problem is: regard the grass eaten by A Niu Yiri as 1, then there are:

(1) The forage for 27 cows for 6 days is 27× 6 = 162.

(This 162 includes original grass and 6-day new grass. )

(2) The pasture eaten by 23 cows in 9 days was 23× 9 = 207.

(This 207 includes the original grass in the pasture and the grass that has grown for 9 days. )

(3) 1 day: (207-162) ÷ (9-6) =15.

(4) The grassland is 27× 6- 15× 6 = 72.

(5) Feed new grass to 15 cows every day, subtract 2 1 cow from 15 cows, and the remaining 6 cows eat grass from the original pasture:

72 ÷ (21-15) = 72 ÷ 6 =12 (days)

Therefore, it takes 12 days to feed 2 1 cow and eat all the grass on the pasture.

Please calculate it.

There is a pasture, if you raise 25 sheep, you can eat all the grass in 8 days; Raise 2 1 sheep and eat all the grass in 12 days. If you raise 15 sheep, how many days can you eat up the grass growing on the pasture?

Responder: God of Meteor Shower-Probation Period Level 1 7-29 20:57

1. Write 789 () times in a row, and the number can be divisible by 9, which is the smallest.

2. There are six cases of goods in the store weighing 15, 16, 18, 19, 20, 3 1 kg respectively, and two customers bought five cases. It is known that the weight of goods bought by a customer is twice that of a customer. Q: What is the weight of the remaining box of goods in the shop?

3。 The 100 bit, 10 bit and unit bit of three digits are 5, a and b respectively. Write it 99 times: (5ab5ab...5ab) 99 5ab. If the number is divisible by 9 1, what is this three-digit 5ab?

(1) answer: 3 times, which is smaller than the answer given by that person just now!

(2) Answer: 20 adds up and divides by 2, and the remainder is 2. Then divide these six numbers by 2 one by one, and the remainder is 2, which is the weight of the remaining box!

(3) Answer: 546 Because two 5abs can be divisible by 9 1 (5ab5ab=5ab multiplied by 100 1), only the last 5ab is left after 98. Try again and you'll get the answer!

2000 Primary School Mathematical Olympiad Examination Questions

Preparatory work (a)

1. Calculation:12-22+32-42+52-62+…-1002+1012 = _ _ _ _ _.

2. A two-digit number is equal to the sum of its one-digit number and the square of its ten-digit number. This two-digit number is _ _ _ _ _.

3. Five consecutive natural numbers, each of which is a composite number, and the minimum sum of these five consecutive natural numbers is _ _ _ _ _ _ _.

There are several red and white balls. If you take out a red ball and a white ball at a time, there will be 50 white balls when you can't get the red ball; If you take one at a time,

Red ball and

Three white balls, so when there are no white balls, there are 50 red balls left. Then this pile has _ _ _ _ _ _ _ red balls and white balls.

5. The age of a young man this year (2000) is exactly equal to the sum of the figures of the year of birth, so the age of this young man this year is _ _ _ _ _ _ _.

6. As shown on the right, ABCD is a parallelogram with an area of

72 square centimeters, e and f are AB and BC respectively.

Point, the area of the shaded part in the figure is _ _ _ _ flat.

Square centimeters.

7.a is a 2000-bit integer composed of 2000 9s, and B is a 2000-bit integer composed of 2000 8s, so the sum of the digits of a×b is _ _ _ _ _ _ _.

8. Four consecutive natural numbers, from small to large, are multiples of 3, multiples of 5, multiples of 7 and multiples of 9, with the smallest sum.

It is _ _.

9. The charging standard for electricity consumption in a residential area is: the monthly electricity consumption of each household does not exceed 10 kWh, and the charge per kWh is 0.45 yuan; Exceeding 10 degrees without exceeding.

20 degrees, 0.80 yuan per degree; For the part exceeding 20 degrees, 1.50 yuan will be charged for each degree. Within one month, user A paid 7. 10 yuan more than user B.

If user B pays 3.75 yuan more than user C, then user A, user B and user C will pay _ _ _ _ _ _ _ _ _ _ _ _.

10. A car and a big truck met on a 9-kilometer-long narrow road, and they had to reverse the car to continue. As we all know, cars are very fast.

The speed of the truck is three times, and the speed of reversing the two cars is their own speed; The distance a car needs to reverse is four times that of a big truck. if

The speed of the car is 50 km/h, so it takes at least _ _ _ _ _ hours to cross this narrow road.

1 1. Grade five students in a school 1 10, take part in Chinese, math and English activity groups, and each student should take part in at least one group. Known participating language groups

52 people, only 16 people in the language group participated; 6 1 person participated in the English group, and only 15 people participated in the English group; There are 63 participants in the math group.

There are 2 1 people who only participate in the math group. Then there are _ _ _ _ _ people in all three groups.

12. There are eight steps, and Xiao Ming goes from bottom to top. If he can only take one or two steps at a time, he may go up in _ _ _ _ different ways.

Respondent: Bad Cesium-Scholar Level 2 7-3 1 14:00.

1. Dongsheng Village will build a cuboid reservoir with a planned storage capacity of 720 tons. It is known that the pool is 18 meters long, 8 meters wide and at least how many meters deep? (1 m3 water weight 1 ton. )

A classroom is 8 meters long, 6 meters wide and 4 meters high. Paint the roof and four walls of the classroom. Excluding doors, windows and blackboards, the area is 26 square meters. How many square meters is the painting area?

A clothing factory used to use 3.8m cloth for uniforms. After improving the cutting method, each set saves 0.2 meters of cloth. Originally made 1800 sets of uniform cloth. How many sets can you make now?

4. Two cars, A and B, travel in opposite directions from two places, with a distance of 5 16 km. After driving for six hours, the repair of car B was suspended. At this time, the distance between the two cars is 72 kilometers. Two hours later, car A keeps the original speed and meets car B ... Find the speed of car B..

5. Make an uncovered rectangular water tank with iron sheet, which is 5cm long, 4cm wide and 3cm high. How much tin do you need at least?

6 An aluminum sheet with a length of 1.20 cm and a width of 90 cm can be cut into a disc with a diameter of 30 cm. How many pieces can I cut at most?

Answer: 1 m 20 cm = 120 cm.

120÷30=4 90÷30=3

4×3= 12 (block)