Finding Olympiad Math Problems, 5th Grade, 5th Grade Math Olympiad Problems

1) Xiao Fang participated in a mathematics competition with four students, and the scores of the four students were 78 points, 91 points, 82 points, and 79 points, and Xiao Fang's scores were 6 points higher than the average score of the five students. Finding Xiaofang's math score?

2) A and B process parts. A processes 6 more parts per day than B, and after B stops for 15 days without processing for 40 days, the number of parts processed by B is exactly half of A's. How many parts did each of them process at this time?

According to the title, people who participate in one, two, and three subjects in the competition are incompatible with each other, that is, those who have participated in one subject in the competition do not belong to those who have participated in two subjects, and those who have participated in two subjects do not belong to those who have participated in one subject, and so on.

So the answer is simple: 203 + 179 + 165 + 143 + 116 + 97 + 89 = 992 (people).

To make the question a little more difficult as an Olympiad question, the question should be modified to make it clear as follows:

A primary school held a competition in mathematics, Chinese, and general knowledge, and 203 people participated in the mathematics competition, 179 people participated in the language competition, 165 people participated in the general knowledge competition, 143 people participated in the mathematics and Chinese competition, 116 people participated in the mathematics and general knowledge competition, 97 people participated in the Chinese and general knowledge competition, and 89 people participated in the competition in three subjects.

e=143-89=54

f=116-89=27

h=97-89=8

a=203-89-54-24=33

b=179-89-54-8=28

c=165-89-8-27=41

a+b+c+d+e+f+h=33+28+41+89+54+27+8=280 (person).

Reference**, red is the number of people in mathematics, blue is the number of people in general knowledge - the number of people in mathematics (two subjects), yellow is the number of people in general knowledge - mathematics (two subjects) - the number of people in Chinese general knowledge (two subjects) + the number of three subjects. Red + Blue + Yellow = Total number of people.

203 + (165-116) + (179-143-97 + 89) = 280 people.

203 students participated in mathematics, 179 Chinese, and 165 general studies, all of which add up to 203 + 179 + 165 = 547

143 students participated in the two subjects, 143 students participated in mathematics and Chinese, 116 people participated in mathematics and general studies, and 97 people in Chinese and general studies, that is, these people reported twice and were added twice, so 547-143-116-97 = 191 should be subtracted

There are 89 people who participated in the three subjects, that is, this part of the people reported three times, was added three times, and should be reduced twice, but this part of the people was reduced three times in the two reports, and this part was reduced one more time, so 191 + 89 = 280 should be added

There is disagreement on this topic. There are 203 students in mathematics, 179 in Chinese, and 165 in general studies, which means that the total number of students participating in mathematics is 203, and then subtracting the double calculation, or does it mean that the number of people who only participate in a single subject of mathematics, and then add two and three subjects to participate in mathematics, the former is 280, and the latter is 725.

It should be 203 + 179 + 165 + 143 + 116 + 97 + 89 = 992 (people), but in this case, this question is very simple and not an Olympiad question. However, according to the meaning of the title, it should be like this.

203+179+165-143-116-97+89=280

This is the knowledge of the university

Remove the same, add the category.

There is the problem of cattle grazing, such as: there is a patch of grass on the pasture, and these grasses grow evenly every day. This pasture can feed 15 cows for 20 days, 20 cows for 10 days, and how many cows can eat the new grass for a day?

Chickens and rabbits in the same cage, the base orange rebalancing mode is: the total number of chickens and rabbits and the total number of feet are known, how many chickens and rabbits are there?

The page number problem is also the number of pages, which mainly refers to the relationship between the number of pages of a book and the numbers used, such as: an extracurricular reading book, its page count is a three-digit number, the single digit number is 4 larger than the hundred digits, and the ten-digit number is larger than the single digit 4, how many pages is this extracurricular reading material?

The basic method of the Logos Elimination Reasoning Hypothesis Method is: first assume that one of the many conditions given is correct, and then combine other conditions to make reasonable reasoning and judgment, if the reasoning leads to contradictions, it means that the null hypothesis is incorrect, and it is necessary to put forward a new hypothesis and make reasonable reasoning... Until the conclusions reached do not contradict the hypotheses provided and all the conditions. Examples:

In geography class, the teacher hung out a map of China with no provinces indicated, and the five provinces were numbered 1 5, and asked the students to write which province each number was.

A: No. 2 is Shaanxi, No. 5 is Gansu;

B A: No. 2 is Hubei, No. 4 is Shandong;

C answer: No. 1 is Shandong, No. 5 is Jilin;

D A: No. 3 is Hubei, No. 4 is Jilin;

A: No. 2 is Gansu, and No. 3 is Shaanxi.

Each of these 5 students only answered one province correctly, and only one person answered correctly for each number, asking which province is from No. 1 to No. 5?

Hope, thank you for doing it.

Beijing Key Middle School Pit Class 5th Grade Past Papers. FYI.

1. In a final exam, 15 students in a class got full marks in mathematics, 12 people got full marks in Chinese, and 4 people got full marks in language and mathematics, so how many students in this class got full marks in at least one subject? Solution: 15+12-4=23

2. There are 42 people in a class, 30 people in the choir have not drafted, 25 people have participated in the art group, and 5 people have not participated in anything. Solution: 30+25-(42-5)=18

3. Among the 100 students, 10 can neither ride a bicycle nor swim, 65 can ride a bicycle, 73 can swim, how many can ride a bicycle and swim at the same time? Solution: (65+73)- 90=48 (person).

4. The TV station surveyed 100 people about the previous day's TV viewing, and 62 people had watched Channel 2, 34 people had watched Channel 8, and 11 of them had watched both channels. How many people haven't watched either channel? Solution: 100- (62+34-11)=15

5. How many natural numbers from 1 to 1000 are neither squares nor cubes?

Analysis: Among the natural numbers from 1 to 1000, there are 31 squares, 10 cubes, and 3 numbers that are both squares and cubes (i.e., sixth). Solution: 1000-(31+10-3)=962

The youngest of the primary school students in a certain school is 6 years old and the oldest is 13 years old.

Solution: There are 8 different ages from 6 to 13 years old, and according to the drawer principle, any 9 students must be selected to ensure that two of them are the same age.

That's a lot, a lot. You can buy this book and draw inferences, this book is very good, and many Olympiad math tutorial classes use this.

Xizhou Glide Qi makes the potato hope to the book as helpful as you.

12 minutes is equivalent to hours.

That is, the first car drove for an extra hour, and the second car took 30 hours to travel the same distance as the second car.

Total distance: 40 km.

If the first car takes t hours, then the second car takes (T-1 5) hours.

30t=40（t-1/5)

t = hours. 30*km

24 km. The first car from the warehouse to Wangcun takes x hours. The second car takes time (hours.

Here 12 minutes = hours. Column equation 30x=40(, x=hours, i.e., 48 minutes. Then the distance between the warehouse and Wangcun is 30*km.

The first truck took x hours. 12 minutes = hours 40x-30x = 40*

10x=8x=So the distance between the warehouse and Wangcun is 30*km.

Let x be the hour, the first car arrives, 30x=40(,x=, so a total of 30*

@"Science Tutor" answers your questions.

Solution: Adoption"Chinese remainder theorem"：

Common multiples of 3 and 5 Common multiples of 3 and 7 Common multiples of 5 and 7.

Divide by 7 and 5 is 75, divide by 5 and 4 is 84, divide by 3 and 2 is 35

It can be seen that 75 + 84 + 35 = 194 satisfies our condition, but not between 200-500, and the processing method is to add several multiples of the least common multiple of 105 to make the result between 200-500.

194 + 105 * 3 = 509 (more than 500, rounded).

A: This number may be 299 or 404.

If you are not sure, please ask, please adopt it in time! Good luck with your studies!

From being divided by 3 by the remainder 2, and by 7 divided by the remainder 5, it can be seen that after the number sought is added by 2, the sad 3 and 7 are divisible, so the number sought is a multiple of 21, and between 200-500, the multiple of 21 has , and no number is cut off by 2

According to another condition, if you divide 5 by 4, you can see that you are 4 or 9, so the answer is three numbers

From the first two conditions, it can be concluded that this number plus 1 can be divisible by 3 and 5 as a multiple of 15, and divided by 7 to give 6. After enumeration, this number can only be 90, 195, 300, 405, 510 after adding 1....

There are a total of chickens and rabbits: (100+92) (4+2)=32.

Suppose these 32 are all chickens, and there are a total of feet: 32 2 = 64.

Less: 100-64 = 36.

More feet per rabbit: 4-2=2.

Rabbits have: 36 2 = 18.

Chickens have: 32-18=14.

When going, it takes 1 to 15 hours per 1 km trip.

On return, it takes 1 10 hours per line of 1 km.

1 km round trip, a total of 2 km, required:

1 15 + 1 10 = 1 6 hours.

The average speed of the round trip is per hour: 2 1 6 = 12 km/h.

Use a brutal foot chopping method.

Suppose you cut off 6 of all 18 insects, a total of 18 insects are cut off:

18 6 = 108 pcs.

Left: 118-108 = 10.

At this point, the feet of both the dragonfly and the cicada are cut off, leaving each spider with 8-6=2 feet.

Spiders have: 10 2 = 5.

Dragonflies and cicadas in total: 18-5=13.

The number of wings is then used to calculate below.

Let's say all 13 of them are dragonflies.

There are a total of wings: 13 2 = 26 pairs.

More: 26-20 = 6 pairs.

Each cicada has fewer wings: 2-1 = 1 pair.

Cicadas have: 6 1 = 6.

Dragonflies are: 13-6=7.

1. The six-digit number ()2004() is divisible by 99, what is this six-digit number?

The 2nd Grade 5 "Into the Wonderful Garden of Mathematics" Competition).

2. The six-digit number 2003 () (divisible by 99, what are its last two digits?)

The first "Hope Cup" National Invitational Tournament).

3. Multiply a three-digit ABC by his inverse ordinal number CBA, and the product obtained is a multiple of 2002. (Final of the 11th Japan Mathematical Olympiad).

4. ABC represents a decimal three-digit number, if ABC is equal to the sum of all two-digit numbers composed of three numbers a, b, and c, write all three-digit numbers that meet the above conditions.

The final of the 10th "Hua Luogeng Gold Cup" Youth Mathematics Invitational Competition).

5. A three-digit natural number is exactly equal to 18 times the sum of its single digits, what is this three-digit number?

The 10th "Zu Chong Cup" Mathematics Competition).

6. The teacher reports a four-digit number, reverses the order of the four-digit number, gets a new four-digit number, and adds the two four-digit numbers. A's answer is 9898, B's answer is 9998, C's answer is 9988, and D's answer is 9888It is known that one of the four students A, B, C, and D has the correct result, so who is the student who did it right?

The 7th "Zu Chong Cup" Mathematics Invitational Tournament).

7. There is a Grand Prix of Intelligence, and the last level is to break through the door of "winning and losing". There are two, one is the door of life and the other is the door of death. Xiao Qiang has defeated several masters after five levels and six generals, and he is the only one who has won and passed the last level.

As long as he can pass the life gate of the two gates, he will win the grand prize in the end, and if he can't pass the life gate, then his previous efforts will be wasted. The final level is like this: in front of both doors stands a soldier, both of whom know which is the door of life and which is the door of death, yet one of them always tells lies, and the other always tells the truth.

But Xiaoqiang didn't know which of the two soldiers was telling the truth and which was lying. He could only ask one of the two soldiers one question before choosing to pass through the two doors, so that he decided to pass through the one (the two doors were identical without any markings).

8. Five couples, A, B, C, D, and E, gather and shake hands with each other when they meet. Curious, Mr. A privately asked everyone (including his wife) about the number of times he had just shaken hands, and he was surprised by the answer. None of the nine people shook hands the same amount.

How many times Mrs. A shakes hands (no handshakes between a couple).