1. Xiaoshengchu Olympic Mathematics Test Questions and Answers Analysis
1, in-class knowledge: A has 5 sweets, and B has 12 sweets. Every operation, people with more sugar give some sugar to people with less sugar, so that the number of sugar in people with less sugar doubles. After such an operation in 2009, what is the sugar number of two people? Answer: (5,12) (10,7) (3, 14) (6,1) (12,5) (7,/. 20098=25 1 1, so finally A has 10 and B has 7.
Extracurricular fun: use the seven numbers 17 to form three two-digit numbers and a one-digit number, so that the sum of these four numbers is equal to 100. What is the possible number of answers that meet the requirements? What's the smallest two digits?
A: The sum of the digits added is 28, and the sum of the resulting digits is 1, 28- 1=27, which means there are three decimal places, so the sum of one digit and ten digits must be 20 and 8 respectively. 8= 1+2+5= 1+3+4, so the number may be 57, and the smallest number may be 12.
2. In-class knowledge: Of the 20 numbers from 1 to 20, there must be two numbers, one of which is a multiple of the other.
Answer: According to the questions required by the topic, consider making drawers according to the principle that any two numbers in the same drawer have multiple relationships. Divide these 20 numbers into the following ten groups according to odd numbers and multiples thereof, and regard them as 10 drawers:
{ 1,2,4,8, 16},{3,6, 12},{5, 10,20},{7, 14},{9, 18},{ 1 1},{ 13},{ 15},{ 17},{ 19}。
Choose any one 1 1 from these 201arrays. According to the pigeon hole principle, at least two numbers are taken out of the same drawer. Because two numbers in the same drawer have a multiple relationship, one of these two numbers must be a multiple of the other.
Extracurricular fun: use eight numbers 1 ~ 8 to form four two-digit numbers, so that the sum of these four numbers is equal to 144. What is the minimum product of four numbers?
Answer: 13+28+47+56= 144, 13×56=728.
2. Xiaoshengchu Olympic Mathematics Test Questions and Answers Analysis
1. It is known that the price of a table is 10 times that of a chair. It is also known that a table is 288 yuan more expensive than a chair. How much is a table and a chair? 2, 3 boxes of apples weigh 45 kilograms. A box of pears is 5 kilograms heavier than a box of apples. How much do three boxes of pears weigh?
3. Party A and Party B walked across two places at the same time. Four hours later, they met four kilometers from the midpoint. A is faster than B. How many kilometers is A faster than B per hour?
Reference answer:
1, it is considered that according to the known conditions, a table is 288 yuan more than a chair, which is exactly (10- 1) times the price of a chair, so the price of a chair can be obtained. According to the price of chairs, we can get the price of a table.
Solution: the price of the chair:
288( 10- 1)= 32 (yuan)
The price of a table:
32× 10=320 (yuan)
A table 320 yuan, a chair 32 yuan.
2. think about it: first, you can find that the weight of 3 boxes of pears is more than that of 3 boxes of apples, and the weight of 3 boxes of apples is the weight of 3 boxes of pears.
Solution: 45+5×3
=45+ 15
=60 kg
Three boxes of pears weigh 60 kilograms.
3. Thinking: According to the meeting 4 kilometers away from the midpoint, and the speed of A is faster than that of B, it is known that A walks 4×2 kilometers more than B, and it takes 4 hours to meet. You can work out how many kilometers A is faster than B per hour.
Solution: 4×2÷4
=8÷4
=2 km
A: A is 2 kilometers faster than B per hour.
3. Xiaoshengchu Olympic Mathematics Test Questions and Answers Analysis
1. Party A and Party B walked across two places at the same time. Four hours later, they met four kilometers from the midpoint. A is faster than B. How many kilometers is A faster than B per hour? Think about it: according to meeting at a distance of 4 kilometers from the midpoint and the speed of A is faster than that of B, it can be known that A walks 4×2 kilometers more than B, and it takes 4 hours to meet. You can work out how many kilometers A is faster than B per hour.
Solution: 4×2÷4=8÷4=2 (km)
A: A is 2 kilometers faster than B per hour.
Li Junhe Zhang Qiang spent the same money on the same pencil. Li Jun asked for 13 pencils, Zhang Qiang asked for 7 pencils, and Li Jun gave Zhang Qiang 0.6 yuan money. How much is each pencil?
Thinking: According to the fact that two people paid the same amount of money for the same kind of pencils, Li Jun asked for 13 pencils and Zhang Qiang asked for 7 pencils, we can know that everyone should get (13+7)÷2 pencils, while Li Jun asked for 13 pencils, three more than he deserved.
Solution: 0.6 ÷ [13-(13+7) ÷ 2] = 0.6 ÷ [13-20 ÷ 2] = 0.6 ÷ 3 = 0.2 (.
A: Every pencil is 0.2 yuan.
3. At 8 o'clock in the morning, two buses, A and B, set off from two stations at the same time and walked in opposite directions. After a while, two buses reached both sides of a river at the same time. Because the bridge over the river is being repaired, vehicles are forbidden to pass. The two cars need to exchange passengers and then return to their respective departure stations by the same route. When they arrived at the station, it was already 2 pm. Car A travels 40 kilometers per hour and car B travels 45 kilometers per hour. How many kilometers are there between these two places? (The exchange time is omitted)
Thinking: According to the known fact that two cars start from two stations at 8 am and return to the original station at 2 pm, the travel time of two cars can be calculated. According to the speed and driving time of the two cars, the total distance traveled by the two cars can be calculated.
4. Xiaoshengchu Olympic Mathematics Test Questions and Answers Analysis
After the math contest, Xiaoming and Obana Xiaoqiang each won a medal. One of them won a gold medal, a silver medal and a bronze medal. Teacher Wang guessed: "Xiaoming won the gold medal;" Xiaohua may not win the gold medal; Xiao Qiang won't get the bronze medal. " As a result, Mr. Wang guessed only one right. Then Xiaoming got the _ _ _ card, Xiaohua got the _ _ _ card and Xiao Qiang got the _ _ _ card. Logical reasoning answer:
Logic problems usually adopt correct reasoning directly, analyze them one by one, discuss all possible situations, abandon unreasonable situations, and finally get the answer to the question. Here is an analysis of the medals won by Xiao Ming.
Solution: ① If "Xiao Ming won the gold medal", Xiaohua must have "failed to win the gold medal", which is inconsistent with "Mr. Wang only guessed one" and irrelevant.
(2) If Xiaoming wins the silver medal, we will discuss with Xiaohua separately. If Xiaohua won the gold medal and Xiao Qiang won the bronze medal, then Mr. Wang didn't guess any of them right, which is irrelevant; If Xiaohua wins the bronze medal and Xiao Qiang wins the gold medal, it doesn't matter if Mr. Wang guessed two correctly.
(3) If Xiaoming wins the bronze medal, we will discuss it separately according to Xiaohua's winning situation. If Xiaohua wins the gold medal and Xiao Qiang wins the silver medal, then Mr. Wang only guesses Xiao Qiang's medal ranking, which is in line with the question; If Xiaohua won the silver medal and Xiao Qiang won the gold medal, then Miss Wang guessed two correctly, which is irrelevant.
To sum up, Xiaoming, Xiaohua and Xiao Qiang won the bronze medal, gold medal and silver medal respectively, which is in line with the meaning of the question.
5. Xiaoshengchu Olympic Mathematical Test Questions and Answers Analysis
The teacher took out nine cards from the 13 card, which read 1 ~ 13, and pasted them on the foreheads of nine students respectively. You can see the numbers of the other eight people, but you can't see your own number. Nine students are honest and smart, and card 6 and card 9 cannot be reversed. ) The teacher asked: Please raise your hand if you know the approximate figure of your number now. Two people raised their hands. After the hands were put down, the three people had the following conversation: A: I know how old I am. B: Although I don't know my number, I already know my parity. C: My number is 2 smaller than B's and 1 larger than A's. So, what is the sum of the four cards that were not drawn? answer
The divisors of all numbers from 1 to 13 are listed first. Everyone can only see the numbers on the heads of eight other people. If you want to see eight numbers, you can determine the divisor of your own number. Only the divisors of 1, 3, 4 and 6 can be seen. So the four cards that are not drawn must be about two, all of which are prime numbers. That is, the numbers on the heads of the two students who raised their hands. A said: I know how much I am. So the number on the head of A is not a prime number. B said: Although I don't know my number, I already know my parity. That is to say, B is not sure what his number is now, so it can only be a divisor two. That is to say, the number on his head is a prime number, and he knows the parity, so he sees that there are two on others' heads, and the number of B is an odd prime number. C said: My number is 2 smaller than B's and 1 larger than A's. B is odd, C is odd, and he knows his own number, so he is sure that he is not a prime number. Then c can only be 1 or 9, and c is greater than a 1, so c can only be 9, a is 8, and b is 1 1. Then, there are 2 and 1 1 in the prime number, and the four cards that are not drawn are naturally 3, 5, 7, 13 and 28.