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. O L Y M P I A D C H A M P I O N E D U C A T I O N C E N T R E Room 309-310, 8 Jordan Road, Yau Ma Tei, Kowloon, Hong Kong SAR, CHINA Tel (852) 3153 2028 / 9310 1240 Fax (852) 3153 2074 Website: www.olympiadchampion.com Email: olympiadchampion@gmail.com GUANGDONG-HONG KONG-MACAO GREATER BAY AREA MATHEMATICAL OLYMPIAD 2019 (GREATER BAY AREA REGION) Primary 6 Question Paper Time allowed: 75 minutes Instructions to Contestants: 1. Each contestant should have ONE Question Book which CANNOT be taken away. 2. There are 3 sections in this exam. Section A consists of 10 questions. Each carries 4 marks. Section B consists of 10 questions. Each carries 5 marks. Section C consists of 5 questions. Each carries 7 marks. The total number of questions is 25. Total score is 125 marks. No points are deducted for incorrect answers or empty answers. 3. NO calculators can be used during the contest. All figures in the paper are not necessarily drawn to scale. 4. This Question Book will be collected at the end of the contest. THIS Question Book CANNOT BE TAKEN AWAY. DO NOT turn over this Question Book without approval of the examiner. Otherwise, contestant may be DISQUALIFIED. All answers should be written on the ANSWER SHEET. 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. Section A: 1st to 10th Question (Each carries 4 marks) 1) When a four-digit natural number is divided by 7, 11 and 13 respectively, find the minimum value of this number. 2) It requires 10 days for 4 people to finish a mission. How many days are required for 5 people? 3) Use a rope to form an equilateral triangle and a square with lengths of 9.42. Now combine 2 ropes, find the radii of the new circle. (Take   3.14 ) 4) The sum of 3 prime numbers is 20. Find the minimum value of the product among these 3 numbers. 5) Find the value of 9 9 9 9 11 11 11 11 ( ) ( ) 4 8 16 32 2 4 8 16        . 6) There are 512 pages in a book with the page number 1, 2, 3, …, 510, 511, 512. How many times does “1” appear? 7) Find the value of 11 22 33 44 ... 1100 1111       . 8) Find the value of 5678 7890 5677 7891    . 9) Find the value of 1 1 1 1 1 1 ... 3 6 6 9 9 12 75 78 78 81 81 84             . 10) Find the value of 5678 602 22712 8517 2839 717     . Section B: 11th to 20th Question (Each carries 5 marks) 11) Today is 17th February 2018 (Sunday). Which year was satisfied that 17th February was on Thursday for All answers should be written on the ANSWER SHEET. 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. the closest case? 12) Find the value of 2 2 2 2 2 2 2 2 137 132 127 122 ... 37 32 27 22         . 13) Find the value of 1 2 3 8 9 10 2 2 2 ... 2 2 2       . 14) Find the last digit of 2 2 2 2 2 2 (1 3 5 95 97 99 )      . 15) Now there are 300 students in Grade 1. 30% of the students are boys. Now 10 girls are added. The school would like to tune the percentage of boys up to 60%. How many boys need to be added? 16) It requires 6 hours for a ferry goes downstream with the same wind direction in the morning. The wind speed is 3km/h and the water flows is 4km/h. In the afternoon, the wind direction is totally changed but the wind speed remains unchanged. It requires 10 hours for a ferry goes upstream, what is the distance? (Unit in km) 17) Between 1 and 100, how many numbers are needed to make sure the product of any 2 numbers is larger than 3600? 18) Ming, Fanny and other 6 classmates sit at a row. Ming and Fanny cannot sit at 2 ends. How many sitting arrangements are there? 19) At 4:27, what is the angle between the hour hand and the minute hand? 20) Find the value of 4 5 6 5 6 7 6 7 8 13 14 15 14 15 16                . All answers should be written on the ANSWER SHEET. 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. Section C: 21st to 25th Question (Each carries 7 marks) 21) Ming and Fanny are walking towards their home at a constant speed. They meet each other after 3 hours. The speed of Fanny’s is faster than Ming’s by 10 metre per minute. 10 minutes later, Fanny discovered that she forgot to bring something and decided to go back home. Once she reaches her home, Ming reaches her home at the same time. What is the distance between 2 homes? (Unit in metres) 22) How many zeros are there from 2,222,222,222 2,222,222,222  ? 23) There is a strange book. When the unit digit is 0, the completed page number will be appeared. Otherwise, it will not be shown the largest digit. (1-digit numbers are excluded) For example, 80 80 101 1 3221 221 3 3     . Now there are 1111 pages. How many “1” will appear? 24) Find the value of 1 2 3 2 3 4 7 8 9 8 9 10 9 10 11 (((111) ) ) (((222) ) ) ... (((777) ) ) +(((888) ) )    +(((999) ) ) . 25) In a party, there are 40 junior secondary students in a total of 80 chicken wings and 100 sausages. Each Secondary 1 student can get 2 chicken wings and 4 sausages. Each Secondary 2 student can get 4 sausages. Each Secondary 3 student can get 3 chicken wings and 1 sausage. How many Secondary 2 students are there? ~ End of Paper ~