Inclusion and exclusion
1. There are 4 students in a class, among whom 15 participate in the math group, 18 participate in the model airplane group, and 1 participate in both groups. So how many people don't participate in both groups?
solution: there are (15+18)-1=23 (people) in the two groups, and
there are 4-23=17 (people) who don't participate in either group.
A: There are 17 people who don't participate in either group.
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2. Forty-five students in a class took the final exam. After the results were announced, 1 students got full marks in mathematics, 3 students got full marks in mathematics and Chinese, and 29 students didn't get full marks in both subjects. So how many people got full marks in Chinese?
Solution: 45-29-1+3=9 (person)
Answer: Nine people got full marks in Chinese.
3. Fifty students stand in a line facing the teacher. The teacher asked everyone to press 1, 2, 3, ..., 49, 5 from left to right to count off in turn. Let the students who count as multiples of 4 turn back, and then let the students who count as multiples of 6 turn back. Q: How many students are facing teachers now?
solution: multiples of 4 have 12 5/4 quotients, multiples of 6 have 8 5/6 quotients, and multiples of both 4 and 6 have 4 5/12 quotients.
the number of people who turn backwards in multiples of 4 =12, and the number of people who turn backwards in multiples of 6 ***8, including 4 people who turn backwards and 4 people who turn backwards.
Number of teachers =5-12=38 (people)
A: There are still 38 students facing teachers.
4. At the entertainment party, 1 students won lottery tickets with labels of 1 to 1 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, two pencils will be awarded; (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) Other label numbers are awarded a pencil. So how many prize pencils will the recreation club prepare for this activity?
solution: there are 5 1/2 quotients in multiples of 2, 33 1/3 quotients in multiples of 3, and 16 1/6 quotients in multiples of 2 and 3.
the * * * preparation for the second collar is (5-16) * 2 = 68, the * * * preparation for the third collar is (33-16) * 3 = 51, the * * * preparation for the repeat collar is 16*(2+3)=8, and the rest is 1-(5+.
5. There is a rope with a length of 18 cm. Mark it every 3 cm and every 4 cm from one end, and then cut off the marked place. How many pieces of rope was cut?
solution: 3cm marks: 18/3=6, and the last mark is not crossed, 6-1=59 4cm marks: 18/4=45, 45-1=44, and repeated marks: 18/12=15, 15-1 =
cut it 89 times and it becomes 89+1=9 segments
Answer: the rope * * * was cut into 9 segments.
6. There are many paintings on display at Donghe Primary School Art Exhibition, among which 16 are not from Grade 6 and 15 are not from Grade 5. Now we know that there are 25 paintings in Grade 5 and Grade 6, so how many paintings are there in other grades?
Solution: Grade 1, 2, 3, 4 and 5 * * has 16, 1, 2, 3, 4 and 6 * * has 15, 5 and 6 * * has 25
, so the total * * * has (16+15+25)/2.
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7. There are several cards, and each card has a number written on it, which is a multiple of 3 or 4, of which 2/3 are cards marked with a multiple of 3, 3/4 are cards marked with a multiple of 4 and 15 are cards marked with a multiple of 12. So, how many of these cards are there?
solution: multiples of 12 are 2/3+3/4-1=5/12, 15/(5/12)=36 (pieces)
A: There are 36 cards in one * * *.
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8. How many natural numbers from 1 to 1 are neither divisible by 5 nor divisible by 7?
solution: there are 2 1/5 quotients in multiples of 5, 142 1/7 quotients in multiples of 7, and 28 1/35 quotients in multiples of both 5 and 7. Multiples of 5 and 7 * * * have 2+142-28=314.
1-314=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 should participate in at least one item. Among them, 25 people participated in nature interest groups, 35 people participated in art interest groups, 27 people participated in Chinese interest groups, 12 people participated in Chinese and art interest groups, 8 people participated in nature and art interest groups, 9 people participated in nature and language interest groups, and 4 people participated in Chinese, art and nature interest groups. Ask the number of students in this class.
solution: 25+35+27-(8+12+9)+4=62 (people)
A: The number of students in this class is 62.
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1. As shown in Figure 8-1, it is known that the areas of three circles A, B and C are all 3, and the overlapping areas of A and B, B and C, and A and C are 6, 8 and 5 respectively, while the total area covered by the three circles is 73. Find the area of the shaded part.
solution: the overlapping area of Party A, Party B and Party C =73+(6+8+5)-3*3=2
the shadow area =73-(6+8+5)+2*2=58
Answer: the shadow area is 58.
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-Author: ABC
-Release date: December 24. Among them, 24 people participated in the math group and 2 people participated in the language group. The number of people who participated in the literature and art group was 3.5 times that of those who participated in both the math group and the literature and 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 language group was twice that of those who participated in all three activities, and there were 1 people who participated in both the math group and the language group. Ask for the number of people to join the art group.
solution: suppose the number of people participating in the art group is x, 24+2+x-(x/35+2/7 * x+1)+x/7 = 46, and the solution is X=21
answer: the number of people participating in the art group is 21.
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-Author: ABC
-Release date: December 24. There are 33, 44 and 55 books with signatures of A, B and C in 1 books, among which 29 books have signatures of A and B, 25 books have signatures of A and C, and 36 books have signatures of B and C.. How many of these books have not been borrowed by any one of A, B and C?
Solution: The number of books read by three people is: A+B+C-(A+C+C)+A, B and C =33+44+55-(29+25+36)+ A, B and C =42+ A, B and C. When A, C is the largest, three people have read it.
three people have read at most 42+25=67 (books), and at least 1-67=33 (books) have not been read.
A: At least 33 books in this batch have not been borrowed by any one of A, B and C.
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-Author: ABC
-Release date: December 24. If exactly 1994 points on each line segment are dyed red, how many red points are there on this five-pointed star?
solution: there are 5*1994=997 red dots on the right side of five lines. If a red dot is placed at all intersections, there are at least red dots. These five lines have 1 intersections, so there are at least 997-1=996 red dots.
A: There are at least 96 red dots on this pentagram.
The pictures related to this topic are as follows:
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-Author: ABC
- It is known that A has watered 78 pots, B has watered 68 pots and C has watered 58 pots. So how many pots have all three people watered?
Solution: A and B must have watered 78+68-1=46 pots * *, and C has not watered 1-58=42, so all three people have watered at least 46-42=4 pots
Answer: all three people have watered at least 4 pots of flowers.
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-Author: ABC
-Release date: December 24. Everyone starts with a story and reads it later in order. It is known that A has read 75 stories, B has read 6 stories and C has read 52 stories. So how many stories have A, B and C read together?
Solution: There are at least 6+52-1=12 stories read by B and C * *, and A must read these 12 stories no matter where he starts.
A: A, B and C have read at least 12 stories together.
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-Author: ABC
-Release date: December 24. Everyone starts with a story and reads it later in order. It is known that A has read 75 stories, B has read 6 stories and C has read 52 stories. So how many stories have A, B and C read together?
Solution: There are at least 6+52-1=12 stories read by B and C * *, and A must read these 12 stories no matter where he starts.
A: A, B and C have read at least 12 stories together.
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-Author: cxcbz
-Release date: 24-
solution: there are 2 1/5 quotients in multiples of 5, 142 1/7 quotients in multiples of 7, and 28 1/35 quotients in multiples of both 5 and 7. Multiples of 5 and 7 * * * have 2+142-28=314.
1-314=686
A: There are 686 numbers that are neither divisible by 5 nor divisible by 7.
the division in the question should be divisible.
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-Author: cxcbz
Among them, 24 people participated in the math group and 2 people participated in the language group. The number of people who participated in the literature and art group was 3.5 times that of those who participated in both the math group and the literature and 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 language group was twice that of those who participated in all three activities, and there were 1 people who participated in both the math group and the language group. Ask for the number of people to join the art group.
solution: suppose the number of people participating in the art group is x, 24+2+x-(x/35+2/7 * x+1)+x/7 = 46, and the solution is X=21
answer: the number of people participating in the art group is 21.
1. There are 19 students who subscribe to Junior Digest, 24 students subscribe to Learning and Playing, and 13 students subscribe to both. How many people subscribe to
Youth Digest or Learn and Play?
2. There are 58 piano learners, 43 painting learners and 37 painting learners in kindergarten. How many piano learners and painting learners are there respectively?
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among natural numbers from 3. 1 to 1:
(1) How many numbers are multiples of 2 and multiples of 3?
(2) How many numbers are multiples of 2 or multiples of 3?
(3) How many numbers are multiples of 2 but not multiples of 3?
4. The results of a class's mid-term exams in mathematics and English are as follows: 12 students got 1 points in English, 1 students got 1 points in mathematics, 3 students got 1 points in both subjects
, and 26 students didn't get 1 points in both subjects.