Brainstorm mathematical problems 1
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The correct answer is as follows. Are you right?
Brainstorming math problem 2
1. There are 40 students in a class, of which 15 is in the math group, 18 is in the model airplane group, and 10 is in both groups. So how many people don't participate in both groups?
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.
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 and 50 from left to right to count off in turn; 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.
Ready for 2 * * * 50? 16)*2=68, resulting in 3 * * * establishment (33? 16)*3=5 1, the * * of repeated collar is 16*(2+3)=80, and the rest are100-(50+33-16) *.
* * * 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.
7. There are several cards, each with a number written on it. The number is a multiple of 3 or 4, of which 2/3 is a card marked with a multiple of 3, 3/4 is a card marked with a multiple of 4, and 15 is a card marked with a multiple of 12. 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.
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.
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.
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.
Math problem 3 with brain teasers
1. There are 19 people who subscribe to Juvenile Digest, 24 people subscribe to Learn and Play, and 13 people subscribe to both. How many people subscribe to Youth Digest or Learn and Play?
2. In kindergarten, 58 people learn piano, 43 people learn painting, and 37 people learn both piano and painting. How many people learn piano and painting respectively?
3. Among the natural numbers from 1 to 100:
(1) How many numbers are multiples of 2 and 3?
(2) How many numbers are multiples of 2 or multiples of 3?
(3) How many numbers are multiples of 2 instead of multiples of 3?
4. The mid-term examination results of a class in mathematics and English are as follows: 12 Student English 100, 10 Student Mathematics 100, two subjects.
Three people got 100 in all courses, and 26 people didn't get 100 in all courses. How many students are there in this class?
5. There are 50 people in the class, 32 can ride a bike, 265,438+0 can skate, 8 can both, and how many can't both?
6. There are 42 students in a class, 30 students in sports teams and 25 students in literary and art teams, and each student should participate in at least one team. this
How many people are there in the two teams of the class?
Test answer
1. There are 19 people who subscribe to Juvenile Digest, 24 people subscribe to Learn and Play, and 13 people subscribe to both. Ask for a subscription "
How many people are there in Youth Digest or Learn and Play?
19 + 24? 13 = 30 (person)
A: There are 30 people who subscribe to Youth Digest or Learn and Play.
2. In kindergarten, 58 people learn piano, 43 people learn painting, and 37 people learn both piano and painting. How many people learn piano and painting respectively?
Number of people who only learn piano: 58? 37 = 2 1 (person)
Number of people who only learn painting: 43? 37 = 6 (person)
3. Among the natural numbers from 1 to 100:
(1) How many numbers are multiples of 2 and 3?
It is a multiple of 3 and 2 and must be a multiple of 6.
100? 6 = 164
So both 2 and 3 have multiples of 16.
(2) How many numbers are multiples of 2 or multiples of 3?
100? 2 = 50, 100? 3 = 33 1
50 + 33? 16 = 67 (piece)
Therefore, there are 67 numbers that are multiples of 2 or multiples of 3.
(3) How many numbers are multiples of 2 instead of multiples of 3?
50? 16 = 34 (piece)
A: There are 34 numbers that are multiples of 2, but not multiples of 3.
4. The mid-term examination results of a class in mathematics and English are as follows: 12 Student English 100, 10 Student Mathematics 100, two subjects.
Three people got 100 in all courses, and 26 people didn't get 100 in all courses. How many students are there in this class?
12 + 10? 3+26 = 45 (person)
There are 45 students in this class.
5. There are 50 people in the class, 32 can ride a bike, 265,438+0 can skate, 8 can both, and how many can't both?
50? (30 + 2 1? 8)= 7 (person)
A: There are seven people who can't do either.
6. There are 42 students in a class, 30 students in sports teams and 25 students in literary and art teams, and each student should participate in at least one team. this
How many people are there in the two teams of the class?
30 + 25? 42 = 13 (person)
A: There are 13 students in this class.
The number of people who take the entrance examination in a class is as follows: 20 in math, 20 in Chinese, 20 in English, 8 in math English, 7 in math Chinese, 9 in Chinese English, and none of the three subjects. How many students are there in this class at most? How many people at least?
Analysis and solution as shown in Figure 6, students who get full marks in mathematics, Chinese and English are all in this class. Let's assume that there are y students in this class, which are represented by rectangles. A, B and C respectively represent those who get full marks in mathematics, Chinese and English. C=8，A？ B=7，B？ C=9。 Answer? b？ C=X。
According to the principle of inclusion and exclusion
Y=A+B+c-A？ B-A？ C-B？ C+A？ b？ C+3
That is, y = 20+20+20-7-8-9+x+3 = 39+x.
Let's look at how to find the maximum and minimum value of y.
It can be seen from y=39+x that when x takes the maximum value, y also takes the maximum value; When x takes the minimum value, y also takes the minimum value. X is the number of people who get full marks in mathematics, Chinese and English, so their number must not exceed the number of people who get full marks in two subjects, that is, X? 7，x？ Eight and x? 9, from which we get x? 7. On the other hand, students who get full marks in mathematics may not get full marks in Chinese, which means that there are no students who get full marks in all three subjects, so X? 0, so 0? x？ 7。
When x takes the maximum value of 7, y takes the maximum value of 39+7=46, and when x takes the minimum value of 0, y takes the minimum value of 39+0=39.
A: There are at most 46 students and at least 39 students in this class.