Solution: There are (15+18)-10 = 23 (people) in the two groups.
40-23= 17 (person) did not attend.
A: There are 17 people, and neither group will participate.
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There are forty-five students in a class who took the final exam. After the results were announced, 10 students got full marks in mathematics, 3 students got full marks in mathematics and Chinese, and 29 students got no full marks in both subjects. So how many people got full marks in Chinese?
Solution: 45-29- 10+3=9 (person)
A: Nine people got full marks in Chinese.
3.50 students stand in a row facing the teacher. The teacher asked everyone to press 1, 2,3, ..., 49,50 from left to right. Let the students who are calculated as multiples of 4 back off, and then let the students who are calculated as multiples of 6 back off. Q: How many students are facing the teacher now?
Solution: multiples of 4 have 50/4 quotients 12, multiples of 6 have 8 50/6 quotients, and multiples of 4 and 6 have 4 50/ 12 quotients.
Number of people turning back in multiples of 4 = 12, number of people turning back in multiples of 6 ***8, including 4 people turning back and 4 people turning back from behind.
Number of teachers =50- 12=38 (person)
A: There are still 38 students facing the teacher.
4. At the entertainment party, 100 students won lottery tickets with labels of 1 to 100 respectively. The rules for awarding prizes according to the tag number of lottery tickets are as follows: (1) If the tag number is a multiple of 2, issue 2 pencils; (2) If the tag number is a multiple of 3, 3 pencils will be awarded; (3) The tag number is not only a multiple of 2, but also a multiple of 3 to receive the prize repeatedly; (4) All other labels are awarded to 1 pencil. So how many prize pencils will the Recreation Club prepare for this activity?
Solution: 2+000/2 has 50 quotients, 3+ 100/3 has 33 quotients, and 2 and 3 people have 100/6 quotients.
* * * Preparation for receiving two branches (50- 16) * 2 = 68, * * Preparation for receiving three branches (33- 16) * 3 = 5 1, * * Preparation for repeating branches (2+).
* * * Need 68+5 1+80+33=232 (branch)
A: The club has prepared 232 prize pencils for this activity.
5. There is a rope with a length of 180 cm. Make a mark every 3 cm and 4 cm from one end, and then cut it at the marked place. How many ropes were cut?
Solution: 3 cm marker: 180/3=60, the last marker does not cross, 60- 1=59.
4cm marker: 180/4=45, 45- 1=44, repeated marker: 180/ 12= 15,15-/kloc-.
Cut it 89 times and it becomes 89+ 1=90 segments.
A: The rope was cut into 90 pieces.
6. There are many paintings on display in Donghe Primary School Art Exhibition, among which 16' s paintings are not in the sixth grade, and 15' s paintings are not in the fifth grade. Now we know that there are 25 paintings in Grade 5 and Grade 6, so how many paintings are there in other grades?
Solution: 1, 2,3,4,5 * * has 16, 1, 2,3,4,6 * * has15,5,6 * * has 25.
So * * has (16+ 15+25)/2=28 (frame), 1, 2,3,4 * * has 28-25=3 (frame).
A: There are three paintings in other grades.
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7. There are several cards, each with a number written on it, which is a multiple of 3 or 4. Among them, cards marked with multiples of 3 account for 2/3, cards marked with multiples of 4 account for 3/4 and cards marked with multiples of 12 account for 15. So, how many cards are there?
Solution: The multiple of 12 is 2/3+3/4- 1=5/ 12, 15/(5/ 12)=36 (sheets).
There are 36 cards of this kind.
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8. How many natural numbers from 1 to 1000 are divisible by neither 5 nor 7?
Solution: multiples of 5 have 200 quotients 1000/5, multiples of 7 have quotients 1000/7 142, and multiples of 5 and 7 have 28 quotients 1000/35. The multiple of 5 and 7 * * * has 200+ 142-28=3 14.
1000-3 14=686
A: There are 686 numbers that are neither divisible by 5 nor divisible by 7.
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9. Students in Class 3, Grade 5 participate in extracurricular interest groups, and each student participates in at least one item. Among them, 25 people participated in the nature interest group, 35 people participated in the art interest group, 27 people participated in the language interest group, 12 people participated in the language interest group, 8 people participated in the nature interest group, 9 people participated in the nature interest group, and 4 people participated in the language, art and nature interest groups. Ask how many students there are in this class.
Solution: 25+35+27-(8+ 12+9)+4=62 (person)
The number of students in this class is 62.
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10, as shown in Figure 8- 1, it is known that the areas of three circles A, B and C are all 30, the areas of overlapping parts of A and B, B and C, and A and C are 6, 8 and 5 respectively, and the total area covered by the three circles is 73. Find the area of the shaded part.
Solution: The overlapping area of A, B and C =73+(6+8+5)-3*30=2.
Shadow area =73-(6+8+5)+2*2=58.
A: The shaded part is 58.
Grade four 1 class 1 1 There are 46 students taking part in three extracurricular activities. Among them, 24 students from the math group and 20 students from the Chinese group participated. The number of people who participated in the art group was 3.5 times that of those who participated in both the math group and the art group, and 7 times that of those who participated in all three activities. The number of people who participated in both the literature and art group and the Chinese group was twice that of those who participated in all three activities, and the number of people who participated in both the math group and the Chinese group was 10. The number of people seeking to join the art troupe.
Solution: Let the number of people participating in the art group be x, 24+20+x-(x/305+2/7 * x+10)+x/7 = 46, and the solution is X=2 1.
A: The number of participants in the art group is 2 1.
12. There are 100 books in the library. The borrower needs to sign the book. It is known that 33, 44 and 55 books in 100 have the signatures of A, B and C respectively, among which 29 books have the signatures of A and B, 25 books have the signatures of A and C, and 36 books have the signatures of B and C. How many of these books have not been borrowed by any of A, B and C?
Solution: The number of books read by three people is: A+B+C-(A+B+C+C)+A, B, C =33+44+55-(29+25+36)+ A, B, C =42+ A, B, C, A, C is the most.
Three people will always read 42+25=67 (books) at most, and at least 100-67=33 (books) have never been read.
A: At least 33 of these books have not been borrowed by any of Party A, Party B and Party C..
13, as shown in Figure 8-2, five equal-length line segments form a pentagram. If exactly 1994 points on each line segment are dyed red, how many red dots are there on this five-pointed star?
Solution: There are 5* 1994=9970 red dots on the right side of the five elements. If you put a red dot on all the intersections, then at least there are red dots. These five lines have 10 intersections, so there are at least 9970- 10=9960 red dots.
A: There are at least 9960 red dots on this five-pointed star.
14, A, B and C are watered at the same time 100 potted flowers. It is known that A poured 78 pots, B poured 68 pots and C poured 58 pots. So how many pots were watered by three people?
Solution: A and B must have 78+68- 100=46 pots * *, and C has 100-58=42, so all three people poured at least 46-42=4 pots.
Answer: All three people have watered at least four pots of flowers.
15, A, B and C are all reading the same story book. There are 100 stories in the book. Everyone starts with a story and then reads it in order. It is known that A has read 75 articles, B has read 60 articles and C has read 52 articles. So how many stories have A, B and C read together?
Solution: B and C * * * have read at least 60+52- 100= 12 stories. This 12 story A must be read no matter where it starts.
A: A, B and C have read at least 12 stories.
16, calculation: 0.2008+2.008+20.08+200.8+2008.
Answer: (0.2008+0.008+0.08+0.8)+(2+20+200+2008)
= 1.0888+2230
= 223 1.0888
Five cards 17, They are all written in numbers: 0, 0, 1, 2, 3, which can be used to form many different five-digit numbers. Find the average of these five numbers.
18. The rabbit and the kitten go upstairs together. A kitten is twice as fast as a rabbit. When the rabbit went up to the fourth floor, the kitten went up to the () floor.
19. A weed grows 1 time every day, and 12 days can grow to 48 mm. It takes () days when it grows to 6 mm.
20. Xiao Qiang has two packages of sweets, one with 48 capsules and the other with 12 capsules. He took three capsules out of the extra package at a time and put them in a few packages. After () times, the number of capsules in two packages of candy is equal.
2 1. Write a string of numbers immediately after 4444, and each written number is one digit of the product of the first two numbers. For example: 4×4= 16, write 6,4× 6 = 24 after 4, and write 4 after 6 to get a series of numbers: 4444644644 ... This series of numbers starts from 1 and counts to the right. The 444th digit is ().
22. Mom is frying eggs in the pot. Eggs should be fried on both sides. Fry each side for 30 seconds. This pot can only fry two eggs at the same time. It takes at least () seconds to fry three eggs now.
23. There are two piles of fruit, a pile of apples and a pile of pears. If 1 apple is replaced by 1 pear, there are two more apples. If 1 pear is replaced by two apples, there are 1 pear. Think about it, there are () apples and () pears.
24. After repairing a road, there are still 2.6 kilometers left, and it is known that there are 0.2 kilometers more than those that have not been repaired. The total length of this road is () kilometers.
25. A barrel of oil weighs 5.6 kg, and the barrel weighs 3. 1 g after half of the oil is used. The net weight of this barrel of oil is () kilograms.
26. pesticide plant produces a batch of pesticides with a daily output of 0.24 tons. If the price is 28.5 yuan per 500 grams. The value of pesticides produced by this factory every day is () yuan.
27. Know that the numbers A, B, C and D are not zero, and know that:
Number A ÷ B =0.5 number D ÷ B = 1.0 1 number c ÷ 0.4 = b.
A number ÷ 1.25= C number
Compare the sizes of four numbers, A, B, C and D, in descending order, and the third number is ().
28.3.704 The number100th after the decimal point is ().
29. 1993× 199.2- 1992× 199. 1=( )
30. 15.37×7.88-9.37×7.88- 15.37×2. 12+9.37×2. 12=( )
3 1. There are three people, A, B, C, A walks 50 meters per minute, B walks 40 meters per minute, and C walks 60 meters per minute. A, B set out from East Village, C set out from West Village, and set out at the same time. A meets C 40 minutes after takeoff, and B meets C 40 minutes after takeoff.
Bus length 190 meters, truck length 240 meters. The two cars are traveling at a speed of 20 meters and 23 meters per second respectively. On the double-track railway, how many seconds does it take to meet from the front to the rear?
An: 10 second.
33 Calculation1234+2341+3412+4123 =?
An:1110
The first item in arithmetic progression is 5.6, and the sixth item is 20.6. Find its fourth project.
An: 14.6
35 Sum 0.1+0.3+0.5+0.7+...+0.87+0.89 =?
Ann: 22.5
36 Solve the following congruence equation:
(1)5X≡3 (module 13) (2)30x≡33 (module 39) (3)35x≡ 140 (module 47) (4) 3x+4x ≡.
An: (1) x ≡11(mod13) (2) x ≡ 5 (mod 39) (3) x ≡ 4 (mod 47) (4) x.
Can the number 220652532 1 be divisible by 7113?
Ann: Yes.
There are 1.2.5 cent coins * * 100, with a total value of * * 2 yuan. It is known that the total value of 2-cent coins is more than 1 cent coins 13 cents. How many coins are there in each of the three types?
An: 5 1 `one cent, 32 dimes, 17 dimes.
Find a rule to fill in the numbers:
0, 3, 8, 15, 24, 35, _ _ _, 63 A: 48
40, 100 straight line can divide the plane into several parts at most?
An: 505 1
4 1 A B two people went to the ocean, each with 12 days of food, and they explored for _ _ _ days at most.
Ann: Eight days.
The number of all natural numbers divisible by 2 or 3 or 5 or 7 in 42 100.
An: 78
43 1/2 + 1/2+3 + 1/2+3+4 + ......+ 1/2+3+4+....+ 10=?
An: 343/330
44 Take at most a few numbers from 1, 2, 3, ... 2003, 2004, so that the difference between any two numbers is not equal to 9?
An: 1005
Find all the divisors of 360. Ann: 24
In the parking lot, there are 24 cars, four wheels for cars, three wheels for motorcycles and 86 wheels for tricycles. An: 10 vehicle.
The smallest natural number with 8 divisors * * * is _ _. Ann: 24.
48 Find the sum of all two digits except four and one, an; 12 10
Divide a bonus to Group A and Group B, with an average of 6 yuan per person. If only group A gets 10 yuan, only group B gets _ _ _ yuan.
Ann: 15 yuan.
There is a factory suitable for spring outing. There are several carriages with 65 people each, 15 people can't go. There are five more passengers in each car, leaving one car. There are _ _ _ _ _ _ _ cars and * * _ _ individuals.
An: 17, 1 120
Students from 5 1 AB take a bus to visit C. Each bus can take 36 people. After the students of AB fill several cars, the remaining students of A 1 1 and some others of B fill one car. In C, students from A and B take pictures in pairs, and each film can only take 36 pictures. Then the residual film in the camera can be photographed after all.
An: 13 sheets.
Is 52 36A+4/24A+3 the simplest score?
Ann: Yes.
The volume of a cuboid is 374, its length, width and height are prime numbers, and its surface area is _ _ _.
Find the greatest common divisor of 1246 and 624. Ann: 2
Xiaoxi bought coconuts and mangoes, * * * used 43 yuan, 7 yuan for coconuts and 5 yuan for mangoes. She bought coconuts and mangoes, and the kilograms are all integers. So he bought * * * _ _ kilograms of coconuts and mangoes.
Ann: 7
56 100 chickens peck 100 grains of rice. The big chicken pecked 3 grains of rice, the middle chicken pecked 2 grains of rice, and the chicken pecked rice 1/3 grains, so there were only * * * _ _ _ _ chickens. An: 60 or 63 or 66 or 69 or 72 or 75 (the answer must be complete).