Đề vòng chung kết Quốc gia kỳ thi Olympic toán học Quốc tế TIMO 2020-2021 Lớp 6 (Kèm đáp án)

 THAILAND INTERNATIONAL 
 MATHEMATICAL OLYMPIAD 
 FINAL ROUND 2020 – 2021 
 Primary 6 
 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. 
 Number Theory 
13. How many simplified fraction(s) with denominator 2021 is / are there? 
14. A 4-digit number has a remainder 5 when divided by 6, has a remainder 6 
 when divided by 7 and has a remainder 8 when divided by 9. What is such 
 smallest 4-digit number? 
15. What is the smallest 5-digit number (without repeated digits) that can be 
 divisible by 15 and 27? 
16. Find the unit digit of A if: 
 A 12 12 ... 12 534 534 ... 534 2398 2398 2398 ... 2398 
 2021's 2022' s 2023' s
17. The sum of 13 consecutive odd numbers is 1183. What is the second largest 
 number? 
18. Define the operation symbol: 
 4222 
 42 
 42 
 5322 
 53 
 53 
 9622 
 96 
 96 
 Find the value of (6 3) (8  5). 
 Geometry 
19. A cubic water tank with side length 25 cm has a water level of 9 cm. An iron 
 cuboid with dimensions 5cm 5 cm 33 cmis inserted into the water tank 
 vertically, what is the new water level? (in cm) 
20. How many rectangle(s) is / are there in the figure below? 
 3 
 All answers should be written on the ANSWER SHEET. 
 Combinatorics 
25. A flight of stairs has 13 steps. Andy can go up for 1 step, 2 steps or 3 steps 
 each time. The 8th step cannot be stepped on as it is destroyed. How many 
 way(s) is / are there for Andy to go up the stairs? 
26. Numbers are drawn from 90 integers 38 to 127. At least how many number(s) 
 is / are drawn randomly to ensure that there are two numbers whose sum is 
 149? 
27. 7 identical brown vases, 2 identical white vases and 3 identical purple vases 
 are put from left to right. How many different permutation(s) is / are there? 
28. When do the hour hand and the minute hand overlap between 7 P.M and 
 8 P.M? 
29. Now there are infinitely many rooms. If 7854 students are needed to separate 
 into these rooms evenly, how many way(s) is / are there? 
30. Choose 3 digits, without repetition, from 1, 2, 3, 4, 5, 6 to form 3-digit 
 numbers. How many number(s) can be divisible by 18? 
 ~ End of Paper ~ 
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