Tasks for the Mathematics Olympiad for students of 4 classes with the answers …

## Olympiad (autumn session)

1. The mass of the box with lemons 25 kg. After selling half of all the lemons, the box was put on the scales. Scales showed 15 kg. Find the mass of the empty box.

1) 5 2) 10 3) 2.5 4) 12.5

2. The perimeter of the square is 20 cm. How many square centimeters will the square’s area increase if its perimeter is increased by 12 cm?

1) 64 2) 25 3) 39 4) 89

3. A horse eats a haystack in one month, a goat in two months, a sheep in three months. In what time will a horse, a goat and a sheep together eat such a haystack?

1) 11/6 months 2) 6/11 months 3) 0.5 months 4. The perimeter of the rectangle is 48 cm, and its length is 2 cm longer than the width. Find the area of this rectangle.

1) 144 2) 121 3) 143 4) 120

5. Rabbit gives 400 g of fluff per year. To keep it, you need a cage 75 cm long and 60 cm wide. What area should be taken under the cages for rabbits, from which 24 kg of fluff are obtained per year?

27 m 2 2) 25 m 2 3) 24 m 2 4) 26 m 2 6. Vasya has twice as many fives as fours in mathematics. How many fives does he have, if the total is 9?

1) 6 2) 3 3) 4 5) 5

7. The car drove from one locality to another as many kilometers as it traveled minutes. What is the speed of this car per hour?

1) 36 km / h 2) 48 km / h 3) 60 km / h 4) 72 km / h

8. There are several benches in the hall. If 2 students sit on each bench, 7 students will be left without a seat. If 3 pupils sit on each bench, then 5 benches will remain free. What is the number of students in the hall?

1) 21 2) 35 3) 51 4) 56

9. It is necessary to cut 5 logs into 6 parts each. How long does it take if one cut takes 4 minutes?

1) 120 minutes 2) 100 minutes 3) 90 minutes 4) 110 minutes

10. In the country club there are two rooms. The length of the first room is 5 m, and the width is 4 meters. The second room has the same width, but 2 m longer. For whitewashing the ceiling of the second room they paid 800 rubles more. How much did you pay for whitewashing the ceilings of both rooms?

1) 5600 rubles 2) 4000 rubles 3) 3200 rubles 4) 4800 rubles

11. There is five times more water in the bucket than in the kettle, and 8 glasses of water in the kettle less than in the bucket. How many glasses of water do you have in a bucket and kettle?

1) 18 2) 14 3) 16 4) 12 12. Anton wrote out all three-digit numbers, the numbers of which are in descending order. What is the difference between the largest and smallest of these numbers?

1) 899 2) 665 3) 777 4) 800 13. Dima has 7 coins in his pocket, each either 5 rubles or 10 rubles. How much money is in his pocket?

1) 30 2) 45 3) 37 4) 57

14. If we erase the number 3 in the number 20312, we get the number 2012. How many five-digit numbers exist from which the number 2012 can be made by deleting one number?

1) 45 2) 46 3) 48 4) 49

15. In a class of 28 children. Of them – 15 go to the vocals, 12 – go to the dance and 5 people are engaged in both circles. How many children from this class are not involved in any of these circles?

Word Olympiad Download

**Answers grade 4**

**one.** **one** **2** **3** **3** **2** **four.** **3** **five.** **one** **6** **one** **7** **3** **eight.** **3** **9.** **2** **ten.** **four** **eleven.** **four** **12.** **3** **13.** **2** **14.** **one** **15. 6**

## Olympiad (winter session)

a) In two rooms, 50 chairs. When 10 chairs were carried out from one hall, the chairs remained equally in the halls. How many chairs were in each hall originally?

b) Find the sum of 1 + 2 + 3 + 4 + … + 98 + 99 + 100.

c) What is more than half half 20 or quarter quarter 80?

d) The three-digit number on the left is assigned a number 1. How much did the number increase?

d) The mass of the box with lemons 25 kg. After selling half of all the lemons, the box was put on the scales. Scales showed 15 kg. Find the mass of the empty box.

e) 3 hens in 3 days laid down 3 eggs. How many eggs will 6 chickens be laid in 6 days? 9 chickens in 9 days?

g) The length of the fence is 20 meters. How many pillars are in the fence, if a pillar is at a distance of two meters from a pillar?

2. To several monkeys, 50 bananas were distributed so that each received at least 1 banana and no two monkeys had evenly divided bananas. What is the largest number of monkeys that could get bananas?

3. Write the answer in numbers and words:

a) name 2 numbers whose number of digits is equal to the number of letters that make up the name of each of these numbers.

b) give 2 numbers in which the number of letters that make up the name of each of these numbers is equal to the number itself.

4. A rectangular sheet of paper with sides of 8 cm 4 cm was cut into 4 equal parts, and then a square was made of them. How was this done? Complete the picture.

5. 1 microbe got into the jar, and after 10 minutes the jar was filled with microbes, and it is known that the number of microbes doubled every minute. How many minutes the bank was filled with microbes half? Write the answer and your reasoning.

6. Two cyclists ride towards each other, the distance between them is 240 km. At the initial moment of movement, the fly takes off and begins to fly forward and backward between cyclists until they meet. Cyclists drove all this at a speed of 40 km / h, and the fly flew at a speed of 60 km / h. What is the distance flying fly?

7. Imagine traveling with a friend on a super train. You are driving in neighboring cars. A friend goes to the 17th carriage from the beginning of the train, and you are to 134th from the end. How many cars on the train? Write the answer and your reasoning.

8. The old clock is 20 seconds behind. How long will they show a day after the hands have set at 12 o’clock? Write a decision on the actions and their reasoning.

9. A small koala eats leaves from one eucalyptus tree in 10 hours, and each of its parents eats twice as fast. How long does this family consume all the leaves from a single eucalyptus tree? Write down the decision on the actions with explanations and answer.

**Answers:**

a) In Hall 1 – 30 chairs, in Hall 2 – 20 chairs.

f) 1 chicken in 3 days will carry 1 egg, which means in 6 days it will carry 2 eggs, in 9 days – 3 eggs, then 6 chickens in 6 days will lay 12 eggs, and 9 chickens – 27 eggs.

g) if 1 is counted, then 11 pillars, if not counted, then 10 pillars.

3. a) 100 – one hundred, 1000000 – one million; b) three, eleven

5. 1 min – 2, 2 minutes – 4, 3 minutes – 8, 4 minutes – 16, 5 minutes – 32, 6 min. – 64, 7 min. – 128, 8 min. – 256, 9 min. – 512, 10 min. – 1024.

1024: 2 = 512 – 9 min.

6. 40×2 = 80 (km / h) – approach speed

240: 80 = 3 (h) – were on the way

8. 1) 24×20 = 480 (s) – behind

2) 480: 60 = 8 (min) – lagged behind

3) 24×60 = 1440 (min) – in the day.

4) 1440 – 8 = 1432 (min) = 11h 52 min – began to show.

9. Suppose there are 1000 leaves on a tree.

1) 1000: 10 = 100 (l.) – eats a small koala in 1 hour.

2) 100×2 = 200 (l.) – 1 parent eats in 1 hour.

3) 200×2 + 100 = 500 (l.) – the whole family eats in 1 hour.

4) 1000: 500 = 2 (h) – during this time the family will implement all the leaves from 1 tree.

## Olympiad (spring session)

1. Solve the equation: (490 – x) – 250 = 70

2. Solve the equation: (1604 – x) – 108 = 800

3. Find the solution to the equation: (456 + 112) – x = 400

4. Solve the equation: (x + 54) – 28 = 38

5. Solve the equation: 999-x = 223 • 4

6. Solve the equation: x: 7 = 323-299

7. Find the solution to the equation: x-145 = 28 • 9

8. Solve the equation: 2 • (300 + x) = 600

9. Solve the equation: 800: x-300 = 500

10. Solve the equation: (x + 200): 400 = 2

**Problem number 1** Marina’s shoe locker has three pairs of shoes. In the dark, she randomly takes 4 shoes. Will there be an elongated pair of identical shoes?

**Problem number 2** Two cucumbers weigh as much as 4 tomatoes, and one tomato as three turnips. How many tomatoes should be on the left bowl, so that the scales are in balance, if on the right bowl there is 1 cucumber and 3 turnips?

**Problem number 3** 32 boxes of candies, 9 kg each, and 36 boxes of waffles, 8 kg each, were brought to the store. What sweets brought more and how many pounds more?

**Task number 4** On the first day, 900 people arrived at the sanatorium, and on the second, 9 times less than on the first. All holidaymakers settled in the room, 2 people each. How many rooms did all the guests take?

**Problem number 5** From two cities along the river at the same time two motor boats floated towards each other. The speed of the first boat is 15km / h, the second boat is 35km / h. The first boat moved along the river. The flow rate of the river is 5km / h. After how many hours did the boats meet, if the distance between the cities is 250km?

**Problem number 6** There were 128 trees in the garden. 3/8 trees are apple trees, 2/4 pears, and the remaining trees are plums. How many plums were in the garden?

**Task number 7** At one apiary, 56 hives to another 48. From the first apiary, 80 kilograms of more honey were collected than from the second. How much honey was collected from each apiary if there was an equal amount of honey in each piece of evidence?

**Problem number 8** Two workers earned together 900 rubles. One worked 2 weeks and the other 4 weeks. How much money did everyone earn?

**Problem number 9** The hare covers 14 km in 2 hours, and the falcon in 3 hours flies 210 km. How many times does a falcon move faster than a hare? How many kilometers per hour is the hare’s speed less than a falcon’s speed?

**Task number 10** Vasya and Petya fished. Vasya pecked well, Petri got worse. How many fish they caught together, if Petya caught 18 less than they caught together and one of them 14 less than the other.

## Math puzzles

**Riddle №1** These two turkeys weigh 20 pounds together, the butcher said. “However, a pound of turkey meat costs two cents more than a pound of large turkey meat.” Mrs. Smith bought a turkey for 82 cents, and Mrs. Brown paid $ 2, 96 cents for a big turkey. How much did each turkey weigh?

**Riddle №2** It is necessary to cross out six digits so that the remaining numbers are together 20. Can you do this? 111 777 999

**Puzzle number 3** Is it possible to express the number 28 in two twos?

**Puzzle number 4** I went hunting hunter with a dog. They walk in the forest, and suddenly the dog saw a hare. For how many jumps does the dog catch up with the hare, if the distance from the dog to the hare is 40 jumps of the dog and the distance the dog runs for 5 jumps, does the hare run for 6 jumps? The task implies that the races are done at the same time as the hare and the dog.

**Riddle №5** In the pond launched 30 pikes, which gradually eat each other. A pike is considered to be full if it has eaten three pikes (well-fed or hungry). What is the greatest number of pikes that can get enough?