Đề vòng chung kết Olympic TIMO 2020-2021 Khối 3 (Kèm đáp án)

 THAILAND INTERNATIONAL 
 MATHEMATICAL OLYMPIAD 
 FINAL ROUND 2020 – 2021 
 Primary 3 
 Time allowed: 120 minutes 
 Question Paper 
 Instructions to Contestants: 
1. Each contestant should have ONE Question-Answer Book which CANNOT be 
 taken away. 
2. There are 5 exam areas and 6 questions in each exam area. There are a total of 30 
 questions in this Question-Answer Book. Each question carries 5 marks. Total 
 score is 150 marks. No points are deducted for incorrect answers. 
3. All answers should be written on ANSWER SHEET. 
4. NO calculators can be used during the contest. 
5. All figures in the paper are not necessarily drawn to scale. 
6. Write down the answer in the simplest form. If the calculation result is a fraction, 
 please write down the answer as a proper or mixed fraction, decimal figure is also 
 accepted. Marks will NOT be given for incorrect unit. 
7. This Question-Answer Book will be collected at the end of the contest. 
 DO NOT turn over this Question-Answer Book without approval of the examiner. 
 Otherwise, contestant may be DISQUALIFIED. 
 1 
 All answers should be written on the ANSWER SHEET. 
 Arithmetic 
7. Find the value of 383 926 300 428 554 127 602. 
8. If A represents the same 1-digit number, what is the value of A if the equation is correct? 
 A 
 2 A 9 
 9 9 6 
 Question 8 
9. Find the value of 18 13 3 104 78 23. 
10. Find the value of 315 3 315  9 315  15 315  45. 
11. Find the value of 444 449 454 459 464 469 474 479 484 489. 
12. What is the number that should be filled in the blank if the equation below is correct? 
 43 ___ 258 
 Number Theory 
13. The numbers below follow the arithmetic sequence, what is the 18th number? 
 327、319、311、303、295、 
14. If A is an odd number, determine whehter the result of AAAA ((3 14) (11 19))  
 is an odd or even number. 
15. If A and B are different digits from 0 to 9, find the value of AB . 
 A B 
 × A A 
 2 0 9 
 Question 15 
16. A 3-digit number is divided by 14 to get a remainder of 13. Find the minimum value of 
 this 3-digit number. 
17. The product of A and B is 612. A is 17 times of B. Find the value of A. 
18. The sum of 5 consecutive even numbers is 40. Find the L.C.M. (Least Common Multiple) 
 of all the numbers. 
 3 
 All answers should be written on the ANSWER SHEET. 
24. According to the pattern shown below, what is the figure in the space provided? 
 ▓★▲▲●▓★▲▲●●▓★▲▲●●●▓__▲▲●  
 Question 24 
 Combinatorics 
25. Find the number of 3-digit even number(s) without repetition of digits. 
26. How many 4-digit even numbers can be formed by using 0, 8, 5, 7, 3 and 2? (Each 
 number can only be used once) 
27. Chris has 26 $1 coins, 9 $2 coins and 9 $5 coins and a book costs $8. If he can only buy 1 
 book each time and no change will be provided for each payment, at most how many 
 book(s) can he buy? 
28. Numbers are drawn from 85 integers 46 to 130. At least how many number(s) is / are 
 drawn at random to ensure that there are two numbers whose difference is 11? 
29. It is known that every digit not smaller than the previous digit in a number is called 
 “special number”. For example, 123 and 366. How many 3-digit “special number” which 
 hundreds digit can only be 2, 3, 4 and 5 is / are there? 
30. Class 3A has 33 students. Each student has to exchange presents with each of their 
 classmates. How many time(s) is / are there to exchange the presents? 
 ~ End of Paper ~ 
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