Class name score
1. Grandpa Xiaojun was born 29 times his age when he died. Grandpa Xiaojun presided over an academic meeting on 1955 and asked how old Grandpa Xiaojun was at that time.
There are three red hats and two white hats. Now, three people in a row give three to each. Everyone can only see the hat of the person in front of him. Now, let three people answer what color their hats are in turn from back to front. The people behind don't know, and neither do the people in the middle. According to the answers of these two people, can you know what color the hat the man in front is wearing?
3. Football teams A, B and C play round robin. The following table gives some matching results. Please fill in the form according to the available figures and point out the results of each game.
Teachers Zhang, Li and Liu teach different courses in middle schools in Beijing, Shanghai and Guangzhou: math, Chinese and foreign languages. Learn again:
(1) Teacher Zhang doesn't work in Beijing;
(2) Miss Li doesn't work in Shanghai;
(3) Beijing does not teach foreign languages;
(4) Teaching mathematics in Shanghai;
Miss Li doesn't teach Chinese.
Q: Which city are the three teachers in? What courses do you teach?
A school held an essay contest, and five students, A, B, C, D and Shu, won the top five. Before awarding prizes, the teacher asked them to guess their ranking.
A said: B is the third, C is the fifth;
B said: garrison fourth, D fifth;
C said: A is the first and fourth;
Ding said: C first, B second;
The defender said: A is the third and D is the fourth;
The teacher said: everyone guessed right in every ranking.
So how should the ranking be ranked?
6. The four cards are written with the words "female, Li, Xue," respectively (one for each card). Take out three cards and cover them on the table. Party A, Party B and Party C can guess what words are on each card, as shown in the following table:
As a result, at least one person guessed the words on each page. Of the three guesses, one person didn't guess once, and two people guessed twice and three times respectively.
What are the words on these three cards?
7.a, B, C, D, E and F are from China, Japan, the United States, Britain, France and Germany. It is now known that:
(1)A and China people are doctors; (2)E and French are teachers;
(3)C and Japanese are policemen; (4)B and F were soldiers, but the Japanese were not;
(5) The British are older than A and the Germans are older than C;
(6)B and China will travel to China next week, and C and the British will spend their holidays in Switzerland next week.
Q: Who are A, B, C, D, E and F?
8. Zhao, Qian, Sun and Li are four people, one is a teacher, the other is a shop assistant, the other is a worker and the other is a cadre. Please judge what each person's occupation is according to the following situation.
(1) Zhao and Qian are neighbors and ride to work together every day; (2) Qian is older than Sun;
(3) Zhao is teaching Li to beat Tai Ji Chuan; (4) Teachers walk to work every day;
(5) The neighbor of the salesperson is not a cadre; (6) Cadres and workers do not know each other;
(7) Cadres are older than salespeople and workers.
9. A, B, C and D all have language barriers. We only know two of the four languages: Chinese, English, French and Japanese. Unfortunately, there is no language that everyone can speak, only one language that three people can speak.
(1) B can't speak English, but when A and C talk, he must translate.
(2) Party A can speak Japanese, while Party D can't understand Japanese, but they can talk to each other;
(3) B, C and D want to communicate with each other, but they can't find a language that everyone understands;
No one can speak Japanese and French at the same time.
Think about it: which two languages can A, B, C and D speak?
10. Five people, A, B, C, D and Shu, each borrowed a story book from the library and agreed to exchange it with each other after reading it. The thickness of these five books is almost the same as that of five people, so five people always exchange books at the same time. After several exchanges, all five of them have finished reading these five books. It is now known that:
(1) The last book read by A is the second book read by B;
(2) The last book read by C is the fourth book read by B;
(3) The second book A that C read was read at the beginning;
(4) The last book read by Ding is the third book read by C;
(5) The fourth book read by B is the third book read by Shu;
(6) The book that Ding read for the third time is the one that C read at the beginning.
Please judge the order of reading these five books according to the above situation.
Analysis and reasoning training volume b
Class name score
1. it is known that A > B, D < C, E > A, B > F, e < d.
Think about it: What does it matter?
A□D D□B F□E
Chinese □ English □ Chinese
There are six people, A, B, C, D, E and F, sitting around a round table. It is known that E and C sit on the right side of C every other person (as shown in the figure), D is opposite to A, B and F sit on the left side of F every other person, and F is not adjacent to A ... Try to locate A, B, C, D, E and F.
Ming Ming, Dong Dong, Lan Lan, Jing Jing, Si Si and Mao Mao attended the meeting. When meeting, every two people shake hands. Mingming shook hands five times, Dongdong shook hands four times, Light Light Blue shook hands three times, quietly shook hands twice, and Sisi shook hands once. How many times did Mao Mao shake hands?
4. A, B, C and D play table tennis. Every two people must play a game. As a result, Party A defeated Party D, and Party A, Party B and Party C won as many games. How many times have you asked Ding Sheng?
There are three pockets, one for two black balls, one for two white balls, and one for one black ball and one white ball. But the labels on the outside of the bag are all wrong, and the words written on the labels are different from the colors of the balls in the bag. Can you take a ball out of one pocket and tell what color the balls in these three pockets are?
6. A said, "I 10 years old, 2 years younger than B, and older than C 1 year old."
B said, "I'm not the youngest. C is three years behind me, and C 13 years old. " .
C said, "I am younger than A, A 1 1 year, and B is 3 years older than A."
One of the above three sentences is wrong. Please confirm the ages of A, B and C. ..
7. Three people, A, B and C, answer the same seven questions. According to the regulations, if you answer correctly, you should tick "√" and if you answer incorrectly, you should tick "X". It turns out that all three people got five questions right and two wrong. The answers given by A, B and C are as follows:
Excuse me: What are the correct answers to these seven questions?
8. A, B and C shot at the target with air guns, and each shot a bullet. The target position is shown in the figure (black dot on the figure), and only one hit the bull's-eye (25 points). When calculating the scores, I found that the scores of the three people were the same. A said, "I got 18 points for two bullets." B said, "I got three points for a bullet." Please judge who hit the bull's-eye.
9. The eight rooms on the first to fourth floors of the Children's Palace are eight activity rooms for music, dance, art, calligraphy, chess, electrician, model airplane and biology.
Known: (1) The first floor is the dance room and electrician room; (2) The chess room is above the model room and the calligraphy room is below; (3) The art room and the calligraphy room are on the same floor, and the music room is above the art room; (4) Music room and dance room are located in odd rooms. Please point out the numbers of the eight activity rooms.
10. Three teachers, Chen, Li and Wang, teach Chinese, Mathematics, Philosophy, Physical Education, Music and Art in Class 5 (1), and each teacher teaches two courses. Now we know (1) that philosophy and mathematics are neighbors. (2) Miss Li is the youngest; (3) Teacher Chen likes to chat with PE teachers and math teachers; (4) PE teachers are older than Chinese teachers; Music teacher and Chinese teacher Miss Li often go swimming together. Can you analyze which two courses each person teaches?
Application of Fractions and Percentages (2)
Example 1: How many grams of water can be added to the brine with a concentration of 10% and a weight of 80 grams to obtain a brine with a concentration of 8%?
Solution: Assuming that X grams of water can be added, 8% saline water can be obtained.
80×10% = [x+80× (1-10%)] 8% solution: x=24.
Example 2: 300g of 20% sugar water. How many grams of sugar do I need to add to make it 40% sugar water?
Solution: Suppose you need x grams of sugar to get 40% sugar water.
Solution: x= 100
Example 3: 600g of15% brine was prepared by mixing 20% brine with 5% brine. How many grams do 20% saline and 5% saline need?
Solution: Let 20% saline be x grams and 5% saline be (600-x) grams.
20% x+(600-x) × 5% = 600 × 15% solution: x=400 5% physiological saline: (600-x) = 200g.
Example 4: There is 300g of 8% brine in container A and 12.5% brine in container B. The same amount of water is poured into container A and container B respectively, so that the concentration of brine in the two containers is the same. How many grams of water should be poured into each container?
Solution: Suppose x grams of water is needed, and 300× 8%: (300+x) =120×12.5%: (120+x) The solution is: x= 180.
Example 5: Three test tubes A, B and C contain 10g, 20g and 30g of water respectively. Pour 10g saline water with a certain concentration into A, mix, take out 10g and pour into B, then take out 10g from B and pour into C. Now the concentration of saline water in C is 0.5%. What is the earliest concentration of brine poured into A?
Solution: =20%
Exercise:
1, a bottle of brine * * * weighs 200g and contains salt10g. The concentration of this bottle of brine is (× 100%=5%).
2. Prepare a portion of salt water and add 20g of salt to 480g of water. The concentration of the brine is (× 100%=4%).
3. The concentration of a sugar water is 15%, and 300 grams of sugar water contains (45) grams of sugar.
4. The concentration of a sugar water is 10%, and 12 grams of sugar requires (108) grams of water.
5. How many grams of water can be added to sugar water with a concentration of 15% and a weight of 200 grams to obtain sugar water with a concentration of 10%?
Solution:15 %× 200 ÷10%-15 %× 200 = 270 (g)
6. 300g of sugar water with the concentration of 10%. How many grams of sugar do I need to add to make it 25%?
Solution: suppose that x grams of sugar is needed to get a 25% solution: x=60.
7. There are 200 grams of 2.5% salt water. How many grams of water should be evaporated to make 3.5% salt water?
Solution: suppose x grams of water are to be evaporated. =3.5% solution: x=57
8. When the nickel content of two steels is 5% and 40% respectively, a steel containing 30% nickel should be obtained 140 ton. How many tons of steel containing 5% nickel and 40% nickel?
Solution: Let x tons contain 5% nickel and (140-x) contain 40% nickel.
5% x+40% x (140-x) =140 × 30% x = 40% nickel:140-x =140-40 =1000.
9. Mix three kinds of brine with concentrations of 20%, 18% and 16% to obtain 100g 18.8% brine. If 18% brine is 30g more than 16% brine, how many grams are there in each of the three kinds of brine?
Solution: Let 16% saline be x grams, 18% saline be (x+30), and 20% saline be (100-30-2x).
16% x+ 18%(x+30)+20%(70-2x)= 100× 18.8% x = 10
18% normal saline: (x+30) = 40; 20% saline is: (70-2x) = 50.
10. Container A contains 150g of 4% salt water, and container B contains a certain amount of salt water. Take out 450g of brine from container B, put it into container A, and mix it into 8.2% brine. Find the concentration of brine in container B.
Fifth grade Olympic math problem (1)
How many consecutive 0s are there at the end of the product of 1×2×3×49×50?
Note: In the factor clock of the multiplication of 50 natural numbers from 1 to 50, the prime factor 2 is more than the prime factor 5, so as long as there is still the prime factor 5 in the factor, the number of consecutive zeros at the end of the product can be determined.
In 1~50, the numbers containing prime factor 5 are as follows:
5 10 15 20 25
30 35 40 45 50
The first four numbers in each row of five numbers in the table have 1 prime factor 5, the fifth number has two prime factors 5, and a * * * contains 12 prime factors 5, which matches 12 prime factors 2, so that there are 12 consecutive zeros at the end of the product of this formula.