1. Olympic mathematics problems of fifth-grade pupils
1, a, b and c run from a to b at the same time. When a runs to the finish line, b is 30 meters away from b and c is 70 meters away from b; When B ran to the finish line, C was still 45 meters away from B. Q: How many meters is there between A and B? Answer:
B runs the last 30m, and C runs (70-45) = 25m, so the speed ratio between B and C is 30: 25 = 6: 5. Because B ran 45 meters more than C at the finish line, A and B separated.
45( 1-5/6)= 270 meters.
The shop bought a batch of pens. The retail price120 in 0 yuan is the same as that in 0 yuan 1 15. So what's the purchase price of each pen?
Answer:10× 20-1×15 = 35 (yuan), which is exactly the purchase price of 20- 15 = 5, so the purchase price of each pen is 35÷5=7.
3. In the fifth grade, 47 students took part in a math contest, and their scores were all integers, with full marks of 100. It is known that three students scored below 60, while others scored between 75 and 95. Q: How many students have the same grades at least?
Answer and analysis:
120 ÷ 2 = 60,90 ÷ 2 = 45, and the distance between every two trees is their common divisor. (120,60,90,45) =15, a * * key: (120+90)×2÷ 15=28 (tree).
4. Least common multiple
Grandpa said to Xiaoming, "I am seven times your age now, six times your age in a few years, five times, four times, three times and two times your age in a few years." Do you know the age of Grandpa and Xiaoming now?
Answer: Grandpa is 70 years old and Xiaoming 10 years old. Tip: The age difference between Grandpa and Xiaoming is the common multiple of 6, 5, 4, 3 and 2. Considering the actual situation of age, the least common multiple is 60, so the age difference is 60 years old.
5. Composite number of prime numbers
In August of the summer vacation, Xiaoming stayed at his grandmother's house for five days. The dates of these five days are prime numbers, and only one day is a composite number. These four prime numbers are composite number minus 1, composite number plus 1, composite number multiplied by 2 minus 1, and composite number multiplied by 2 plus 1. Q: When was Xiaoming with his grandmother?
A: Let this composite number be a, then these four prime numbers are (A- 1), (A+ 1), (2A- 1) and (2A+ 1) respectively. Because (A- 1) and (A+ 1) are prime numbers with a difference of 2, there are five groups of1~ 31:3,5; 5,7; 1 1, 13; 17, 19; 2 1,3 1。 After trial calculation, the meaning of the question can only be satisfied when a = 6, so these five days are August 5, 6, 7, 1 1, 13.
2. Fifth-grade primary school students' olympiad math problems
Four players with numbers 1 and 10 1, 126, 173 and 193 play table tennis, and it is stipulated that the number of matches for every two players is the remainder of their numbers divided by 3. So how many sets did the player who played the most games play? 2. What is the remainder of1990 …1990 divided by 9?
3. Arrange 1, 2, 3, …, 30 from left to right into a number 5 1. What is the remainder of this number divided by 1 1?
4. 1994-bit integer, all numbers are 3. Divided by 13, what is the 200th place of the quotient (counting from left to right)? What is the unit number of quotient? What is the remainder?
5, there is a number, divided by 3, the remainder is 2, divided by 4, the remainder is 1. What is the remainder of this number divided by 12?
6. Natural number divided by 247, 63 divided by 248. So what is the remainder of this natural number divided by 26?
7. A natural number is divided by 19 and 9, and then divided by 23 and 7. So what is the minimum value of this natural number?
8. There are 12 households in a residential area, and the house numbers are 1, 2, 3, …, 12 respectively. Their telephone number is 12 continuous six-digit natural number, and each family's telephone number can be divisible by the house number. It is known that the first few digits of these phones are less than 6, and the phone number of this family with the house number of 9 can also be divisible by 13. What's the phone number of this family?
9. There are more than 5,000 toothpicks, which can be divided into small packages according to six specifications. If 10 pieces are packed, there are 9 pieces left in the end. If there are nine in a pack, there are eight left. The specifications of the third, fourth, fifth and sixth categories are 8, 7, 6 and 5 respectively, so they are finally 7, 6, 5 and 4 respectively. How many toothpicks does a * * * have?
10 has a natural number. If you divide it by 63,90, 130, there is a remainder, and the sum of the three remainders is 25. What is one of these three remainders?
3. Fifth-grade primary school students' olympiad math problems
1. Today is Saturday. /kloc-What day is 0/000 day? 2. Two natural numbers A and B (A > B) are known, and the remainder of a and B divided by 13 is 5 and 9 respectively. Find the remainder of a+b, a-b, A× b(a>b a2-b2 divided by 13 respectively.
3.2 100 is divided by a two-digit number and the remainder is 56. Find this two-digit number.
4. The sum of dividend, divisor, quotient and remainder is 903, the known divisor is 35 and the remainder is 2. Ask for a dividend.
5.345 and 543 are divided by an integer to get the same remainder, and the quotient differs by 9. Find this number.
6. There is an integer. Divided by 3 12, 23 1 and 123, the sum of the three remainders is 4 1. Find this number.
7. There are 1 15 candy, 148 cookies and 74 oranges in the kindergarten, which are distributed to the children in the big class on average. As a result, there are 7 sweets, 4 biscuits and 2 oranges. How many children are there in this big class at most?
8. How many cuboid blocks does it take to stack a cube 9 cm long, 6 cm wide and 7 cm high?
9. It is known that the common divisor of a number and 24 is 4 and the least common multiple is 168. Find this number.
10. It is known that the common divisor of two natural numbers is 4 and the minimum common multiple is 120. Find these two numbers.
4. Fifth-grade primary school students' olympiad math problems
1, the express train and the local train leave from two cities at the same time and meet in 2.5 hours. The express train runs 42 kilometers per hour and the local train runs 35 kilometers per hour. How many kilometers are the two cities apart? Two students, A and B, typed a document together. A type 18 words per minute, and B type 22 words per minute. It took them 30 minutes to type this document. How many words are there in this document?
3.A car and B car leave from two places at the same time. Relatively speaking, car A travels 40 kilometers per hour and car B travels 50 kilometers per hour. Three hours later, the two cars are still 25 kilometers apart. How many kilometers are the two places apart?
The distance between the two places is 628 kilometers. Car A travels 60 kilometers per hour and car B travels 80 kilometers per hour. Two cars leave from two places at the same time. Did the two cars meet after four hours? How many kilometers are the two cars apart?
5. Party A and Party B jointly manufacture a batch of parts. Party A makes 124 pieces per hour, and Party B makes 136 pieces per hour. They worked together for 8 hours and overfulfilled 120. How many parts are they going to make together?
6. A cargo ship sailed from port A to port B at 10 in the morning, and a passenger ship sailed from port B to port A at 1 0 in the afternoon. The passenger ship left for four hours to pick up the cargo ship. Cargo ship speed 18 km, passenger ship speed 27 km. How far apart are these two ports?
Reference answer
1, (42+35) × 2.5 = 192.5 (km)
2、( 18+22)×30= 1200
3. (50+40) × 3+25 = 295km
4. I didn't meet it. (60+80) × 4 = 560km 628-560 = 68km
5. (124+136) × 8-120 =1960 (unit)
6.18× 3+(18+27 )× 4 = 234 (km)
5. Fifth-grade primary school students' olympiad math problems
1. A factory has a batch of coal. It was originally planned to burn 5 tons a day, which can last for 45 days. In fact, it burns 0.5 tons less every day. How many days can this batch of coal burn? 2. The school bought150m long plastic rope, cut off 7.5m first, and made three skipping ropes with the same length. According to this calculation, how many plastic ropes are left?
3. To build the canal, it was originally planned to build 0.48km every day and complete it in 30 days. Actually, it's repairing 0.02 kilometers every day. How many days was it actually repaired?
4. Miss Wang reads a book. If he reads 32 pages every day, 15 days will be enough. Now I read 40 pages a day. I can finish reading them a few days in advance.
A car traveled 260 kilometers in four hours. At this speed, it traveled for another 2.4 hours. How many kilometers have you traveled before and after? (Answer in two ways)
Reference answer:
1, 5× 45 ÷ (5-0.5) = 50 (days)
2.( 150-7.5) ÷ (7.5 ÷ 3) = 57 (root)
3.0.48× 30 ÷ (0.48+0.02) = 28.8 (days)
4. 15-32× 15 ÷ 40 = 3 (days)
5, 260 ÷ 4× 2.4+260 = 4 16 (km) 260 ÷ 4× (4+2.4) = 4 16 (km)