For a weight with two weights with a fruit weight is 200g. There 3,6 kg how road with only 2 times for 3 bags sugar balance weighing 2kg respectively; 1kg ; 0,6kg?
Siku has husky dogs in many different colors. He has 12dogs in total. A third of them are cinnamon and white . A quarterof them are red and white. The rest of them are gray and white. How many of huskies are gray and white
Combinatorics
21. 15 students join a competition. Only top 5 students can be promoted to next round. How many different way(s) of promotion advance is / are there?
Different way: Cách khác nhau.
22. It is known that there are 8 classes of grade 5 in a primary school. At least how many students are there in grade 5 to ensure there exist 41 students in the same class?
At least: Ít nhất; Ensure: Chắc chắn; Exist: Tồn tại.
23. Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
Digit: Chữ số; 3-digit number: Số có 3 chữ số; Even number: Số chẵn; Greater than: Lớn hơn; Repetition of digits is not allowed: Các chữ số không được lặp lại.
24. A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time. How many way(s) is / are there for Peter to go up the stairs?
Step: Bước; Way: Cách.
25. Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are drawn at random to ensure that there are two numbers whose sum is 85?
Integer: Số nguyên; At least: Ít nhất; Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng.
~ End of Paper ~
Combinatorics
21. 15 students join a competition. Only top 5 students can be promoted to next round. How many different way(s) of promotion advance is / are there?
Different way: Cách khác nhau.
22. It is known that there are 8 classes of grade 5 in a primary school. At least how many students are there in grade 5 to ensure there exist 41 students in the same class?
At least: Ít nhất; Ensure: Chắc chắn; Exist: Tồn tại.
23. Choose 3 digits from 1, 2, 3, 4, 6, 8 and 0 to form 3-digit numbers. How many even number(s) greater than 300 is / are there? (The repetition of digits is not allowed)
Digit: Chữ số; 3-digit number: Số có 3 chữ số; Even number: Số chẵn; Greater than: Lớn hơn; Repetition of digits is not allowed: Các chữ số không được lặp lại.
24. A flight of stairs has 10 steps. Peter can go up for 1 step, 2 steps or 3 steps each time. How many way(s) is / are there for Peter to go up the stairs?
Step: Bước; Way: Cách.
25. Numbers are drawn from 80 integers 20 to 99. At least how many number(s) is / are drawn at random to ensure that there are two numbers whose sum is 85?
Integer: Số nguyên; At least: Ít nhất; Random: Ngẫu nhiên; Ensure: Chắc chắn; Sum: Tổng.
~ End of Paper ~
There are 4n pebbles of weights 1, 2, 3, . . . , 4n. Each pebble is coloured in one of n colours and there are four pebbles of each colour. Show that we can arrange the pebbles into two piles so that the following two conditions are both satisfied:
• The total weights of both piles are the same.
• Each pile contains two pebbles of each colour.
A ray consist of a point on a line and all the point on that line on one side of that point. How many rays can we draw through a point on a plane?
Câu 6:
4.8l of oil weigh 3.648kg. How many liters of oil are there if they weigh 4.864kg?
Answer: There are liters
(Write your answer as a decimal in the simplest form)
Câu 7:
Inspecting products of a factory, we find that there are 97 qualified products out of every 100 products on average. What percent of the total products is qualified products?
Answer: %
Câu 8:
A rectangular field has a width of 24.5m and its area equals the area of a square with the sides of 35m. Find the perimeter of that rectangular field.
Answer: m
Câu 9:
The area of a triangle ABC is , take the point M on BC such that BM=MC and the point N on AC such that AN=NC. Find the area of the triangle AMN.
Answer:
Câu 10:
A store sold 902kg of rice which is 10.25% of the total amount of rice. How many kilograms of rice were there in that store at first?
Answer: There were kilograms
Question 1: What is 1/6 of 744? Answer: 124
Question 2: Express seventy thousand, four hundred and nine in numerals. Answer: 70409
Question 3: Study the pattern. 88:8=11 880:8=110 8800:8= ? The missing number is 1100
Question 4: Subtract 346 from 752. Answer: 406
Question 5: The ratio of boys to girls at a school is 5:4. If there are 255 boys at the school then how many students are there at the school? Answer: 459 students.
Question 6: The product of 2 different natural numbers is 9. Their sum is 10
Question 7: Jack, Mary and Jacob buy ice creams. Jack buys twice as many as Mary. Jacob buys three times as many as Jack. If Jacob buys 12 ice creams then Mary buys 2 ice creams.
Question 8: My giant flower doubles its size every day. On Friday, it is 5 ( hay 10 gì đó ) times as big as its was on the preceding Sunday.
Question 9: If we write all of the whole numbers from 10 through 99 and cross out any number in which the first or second digit is divisible by 2 (for example, 41 is crossed out as 4 is divisible by 2 and 36 is crossed out as 6 is divisible by 2), how many numbers are crossed out? Answer: 65 numbers.
Question 10: It takes Bella three hours to clean a house. It takes Anna two hours to clean the house. How long would it take for them to clean it together? Answer: 72 minutes.
There are 35 men and some of women in a meeting room. The ratio of the number of women to the number of men is 7:5 . How many women are there in the meeting room ?