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The first volume of the sixth grade is an Olympic math problem (the answer is also required)
1999× 1998- 1998× 1997- 1997× 1996+ 1996× 1995

1. Zhang Qiang bought a coat, a hat and a pair of trousers with 270 yuan. Coat is more expensive than trousers 140 yuan, coat and trousers are more expensive than hats 2 10 yuan. How much is the coat, hat and trousers that Zhang Qiang bought?

2. There is a natural number less than 200, and the sum of all digits of each number is odd, and it is the product of two digits (for example, 144= 12× 12). Then the third largest number in this kind of natural number is _ _ _ _ _.

3. There are at most _ _ _ _ _ _ prime numbers in nine consecutive natural numbers.

4. Find all the different prime factors of 1992, and their sum is _ _ _ _ _

5. A fraction is a reduced fraction if the denominator is reduced by 2, and a reduced fraction if the denominator is reduced by 9.

Three. Problem solving: (1 ~ 7 5, 8, 9, 10 10, * * 65)

1. Zhang Qiang bought a coat, a hat and a pair of trousers with 270 yuan. Coat is more expensive than trousers 140 yuan, coat and trousers are more expensive than hats 2 10 yuan. How much is the coat, hat and trousers that Zhang Qiang bought?

2. Students take large and medium-sized cars to go for a spring outing. Each large car can take 65 people and each medium-sized car can take 26 people. At present, there are 338 students and teachers How many large and medium-sized cars are needed in order to make everyone have a seat and there are no extra seats in the car?

Two workers produced a batch of scarves, which was originally planned to be completed in 6 hours. In fact, everyone processed two more pieces per hour than originally planned, and finished the task in five hours. How many scarves are there in this batch?

4. Shorten one side of the square by 20% and increase the other side by 2 meters to get a rectangle, which is equal to the area of the original square. So, how many square meters is the square?

The sum of numerator and denominator is 23. After the denominator is increased by 19, a new score is obtained. If you change this score to the simplest score, what is the original score?

6. The car and the bike run in opposite directions from A and B at the same time. Cars travel 50 kilometers per hour and bicycles travel 10 kilometers per hour. After the two cars met, they still drove in the original direction. When the car arrives at B, go back to the place where the two cars meet, and the bike goes forward 10 km to find the distance between A and B.

7. If the natural numbers p, 2p+ 1 and 4p+ 1 are all prime numbers, then 8 +55=?

8. When a ship found a leak, it had entered some water, and now the water has entered the ship at a constant speed. If 10 people wash water, 12 hours can wash it out; 15 people wash water, which can be finished in 6 hours. If it is completed in 3 hours, how many people will be needed to wash the water?

9. The weights of A, B, C and D are different, and the average weight of two of them is equal to the other two. The average weight of Party A and Party B is 8kg less than that of Party A and Party C, while that of Party B and Ding Pingjun is 49kg. Q: (1) What is the average weight of A, B, C and D? (2) What's the weight of B?

10. Five students from Party A, Party B, Party C, Party D and Party E inquired about the students who won the first prize in the fifth grade communication competition in Central South Primary School from different channels (the specific list is as follows):

A inquire: surnamed Li, female classmate, age 13, from Guangdong.

B: Zhang, male student, age 1 1, from Hunan.

C Inquiry: surnamed Chen, female classmate, age 13, from Guangdong.

D Inquiry: surnamed Huang, male classmate, age 1 1, from Guangxi.

E Inquiry: Zhang, male student, age 12, from Guangdong.

In fact, the surname, gender, age, native place and other real situations of the students who won the first place have been listed in the above table. Only one of the information of the five students is correct.

Please judge this classmate who won the first prize accordingly.

1 1. Party A and Party B process a batch of parts together, and it takes 8 hours to complete the task. If Party A processes it alone, it will take 12 hours to complete it. Now, after two hours of production, Party A will go out to do other work, and Party B will continue to produce 420 parts to complete the task. Q

12. A project can be completed by Party A alone for 63 days and then by Party B alone for 28 days. If both parties cooperate, it will take 48 days to complete. Now Party A does it alone for 42 days, and then Party B does it alone. How many more days will it take? Question 1. The clerk changed a 5 yuan RMB and a 50-cent RMB into 28 yuan RMB with face values of 1 yuan and 1 respectively. How much RMB do you want?

Question 2: There are 50 RMB * * with total face value 1 16 yuan. As we all know, one yuan is more than two yuan. How many RMB are there in three denominations?

Question 3: There are 400 movie tickets from 3 yuan, 5 yuan and 7 yuan, with a value of 1920 yuan, among which 7 yuan and 5 yuan have equal tickets. How many movie tickets are there for each of the three prices?

Question 4: Two kinds of cars are used to transport goods. Each car contains 18 boxes, and each car contains 12 boxes. Now there is a 18 car, worth 3024 yuan. If each case is cheap in 2 yuan, the goods are worth 2520 yuan. Q: How many cars are there?

Question 5. A truck can transport ore 20 times a day in sunny days and 12 times a day in rainy days. Transportation 1 12 times a day, with an average of 14 times a day. How many days are it rainy these days?

Question 6. A batch of watermelons has been delivered and will be sold in two categories, the large one in 0.4 yuan and the small one in 0.3 yuan. In this way, these watermelons are worth 290 yuan. If the price per kilogram of watermelons is reduced by 0.05 yuan, this batch of watermelons can only be sold in 250 yuan. Q: How many kilograms is the watermelon?

Question 7. In the darts competition, it is stipulated that each player gets 65,438+00 points, and each player misses the target and gets 6 points. Each player throws 10 times and scores * * * 152 points, in which player A scores more than player B 16 points. Q: How many times did each player win?

Question 8. There are 20 questions in the math contest. Every time he answers a question correctly, he gets 5 points. If he answers a wrong question, he will not only get no points, but also deduct 2 points backwards. Xiaoming got 86 points in this competition. Q: How many questions did he answer correctly?

9\ For a rope, use half for the first time, use the remaining half for the second time, and so on. After five times, how much of this rope is left?

1. solution: x sheets of 1 element and (28-x) sheets of 1 angle.

x+0. 1(28-x)=5.5

0.9x=2.7

x=3

28-x=25

A: There are three Zhang Yiyuan bills and 25 dimes.

2. Solution: Let 1 element have X, 2 yuan (x-2) and 5 yuan (52-2x).

x+2(x-2)+5(52-2x)= 1 16

x+2x-4+260- 10x = 1 16

7x= 140

x=20

x-2= 18

52-2x= 12

A: There are 20 1 yuan, 8 18 in 2 yuan and 2 12 in 5 yuan.

3. Solution: 7 yuan and 5 yuan have X pieces, and 3 yuan has (400-2x) pieces.

7x+5x+3(400-2x)= 1920

12x+ 1200-6x = 1920

6x=720

x= 120

400-2x= 160

A: 3 yuan has 160 and 7 yuan and 5 yuan have 120.

4. Answer: Total cargo: (3024-2520)÷2=252 (boxes)

There are x buses and (18-x) cars.

18x+ 12( 18-x)= 252

18x+2 16- 12x = 252

6x=36

x=6

18-x= 12

Answer: Bus No.6, 12.

5. Solution: Days = 1 12÷ 14=8 days.

It rained on day X.

20(8-x)+ 12x = 1 12

160-20x+ 12x = 1 12

8x=48

x=6

There are six rainy days.

6. Solution: Watermelon number: (290-250)÷0.05=800 kg.

There is a big watermelon x kg.

0.4x+0.3(800-x)=290

0.4x+240-0.3x=290

0. 1x=50

x=500

There are 500 kilograms of big watermelons.

7. Solution: A: (152+ 16)÷2=84.

B: 152-84=68 points.

Set armor x times

10x-6( 10-x)=84

10x-60+6x=84

16x= 144

x=9

Set b to y times.

10y-6( 10-y)=68

16y= 128

y=8

A: Nine times for A and eight times for B. ..

8. Answer: Suppose he answered question X correctly.

5x-2(20-x)=86

5x-40+2x=86

7x= 126

x= 18

A: He got it right 18.

9\ 1/2* 1/2* 1/2* 1/2* 1/2= 1/32