# Top PDF 2018IMAS First Round Upper Primary Division Problems

### 2018IMAS First Round Upper Primary Division Problems

Questions 21-25, 6 marks each 21. Mike constructs a sequence in the following way: the first two terms are 1 and 2. Starting from the third term, each term is the smallest possible integer that is not relatively prime to the previous term and has not yet appeared in any of the previous terms. Find the 20 th term of this sequence.

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### 2017IMAS First Round Upper Primary Division Problems

14. There are two routes starting in a bus stop. A bus departs for the first route every 8 minutes and departs the second route every 10 minutes. At 6:00 in the morning, two buses depart for the two routes at the same time. Among the choices below, when will the buses depart for the two routes simultaneously?

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### 2014IMAS First Round Upper Primary Division Problems

22. The inside lane of a track has length 400 m and the outside lane has length less than 500 m. From the marked line, as shown in the diagram, Max and Lynn start running counterclockwise along the track at the same time. Max runs at constant speed on the inside lane. Lynn, whose constant speed is 3 times that of Max, runs on the outside lane. The first time both are back together at the marked line, Max has completed 3 laps. What is the length, to the nearest m, of the outside lane?

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### 2015IMAS First Round Upper Primary Division Problems

6. From one-third of a positive integer, one-quarter of the next integer is subtracted. If the difference is 2, what is the sum of the two integers? （A）31 （B）45 （C）55 （D）79 （E）103 7. The diagram below is the seating plan of a cinema. How many blocks of three adjacent seats are unshaded, not counting those in the first row?

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### 2018IMAS Second Round Upper Primary Division Problems

Do not open the contest booklet until you are told to do so. Be sure that your name and code are written on the space provided above. Round 2 of IMAS is composed of three parts; the total score is 100 marks. Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.

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### 2018IMAS First Round Middle Primary Division Problems

22. How many ways can we divide 6 students into 3 groups so that each group has exactly 2 students? 23. In the figure below, ABCD, EFGH and AJKL are squares. The area of AJKL is 2018 cm 2 . If rectangles EFCI and JBFK both have an area of 1360 cm 2 , then what is the area, in cm 2 , of CGHI?

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### 2018IMAS First Round Upper Primary Division Full Solutions

Totally there are 20  20 8 4 1 53     isosceles right triangles. Hence (E). Answer： （E） 21. Mike constructs a sequence in the following way: the first two terms are 1 and 2. Starting from the third term, each term is the smallest possible integer that is not relatively prime to the previous term and has not yet appeared in any of the previous terms. Find the 20 th term of this sequence.

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### 2017IMAS Second Round Upper Primary Division Problems

Do not open the contest booklet until you are told to do so. Be sure that your name and code are written on the space provided above. Round 2 of IMAS is composed of three parts; the total score is 100 marks. Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.

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### 2014IMAS Second Round Upper Primary Division Problems

Do not open the contest booklet until you are told to do so. Be sure that your name and code are written on the space provided above. Round 2 of IMAS is composed of three parts; the total score is 100 marks. Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.

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### 2015IMAS Second Round Upper Primary Division Problems

7. The diagram shows a path consisting of four semi-circular arcs. Each arc is of length 100 m and uses a different side of a square as its diameter. Initially, Jane is at A and Yves at B. They start walking counter-clockwise at the same time. Jane’s speed is 120 m per minute and Yves’s is 150 m per minute. Each pauses for 1 second whenever they are at the points A, B, C or D. How many seconds after starting will Yves overtake for the first time with Jane?

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### 2016IMAS Second Round Upper Primary Division Problems

z Do not open the contest booklet until you are told to do so. z Be sure that your name and code are written on the space provided above. z Round 2 of IMAS is composed of three parts; the total score is 100 marks. z Questions 1 to 5 are given as a multiple-choice test. Each question has five possible options marked as A, B, C, D and E. Only one of these options is correct.

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### 2014IMAS First Round Middle Primary Division Problems

22. The area of a triangle is 50 cm 2 . Each side is divided into five equal parts, and some pairs of division points are joined as shown in the diagram. What is the total area, in cm 2 of the shaded regions? 23. Oliver arranges his toy ducks and toy turtles in a row as shown in the diagram.

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### 2015IMAS First Round Middle Primary Division Problems

23. There are two classrooms on each of four floors in the school building, x01 and x02 where x is the floor number. Martial Arts and Drama are on the first floor. Calligraphy and Fine Arts are on the same floor. Music is directly above Fine Arts and Painting is directly above Calligraphy. Modeling is directly above Painting. Neither Martial Arts nor Music is in an odd-numbered room. In which room is Dancing?

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### 2016IMAS First Round Middle Primary Division Problems

18. Hanna makes four straight cuts on a round cake. Into at most how many pieces can she cut it? （A）8 （B）10 （C）11 （D）12 （E）14 19. Eight children are sharing 61 balloons. Each gets at least one, and everyone receives a different number. What is the smallest number of balloons that can go to the child receiving more balloons than the others?

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### 2017IMAS First Round Upper Primary Division Full Solutions

【Solution】 If there is no carry when the number is added by 1, sum of digits increases by 1, contradiction to that both sum of digits are divided by 4. If there is a carry, the last digit is 9. Since the sum of all digits changes by 8 when one carry happens and by 17 when two carries happens. It follows that only one carry should happen and the original number has the sum of all digits divided by 4. In order to take the number to be maximal, the first digit should also be 9. The second digit can be either 2 or 6. The largest one is 969.

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### 2016IMAS First Round Upper Primary Division Full Solutions

non-overlapping parts of the other three circles, we need to make the area of the largest circle equal to the total area of the other three circles and there are no overlapping parts b[r]

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### 2014IMAS First Round Upper Primary Division Full Solutions

Since 2014 = 335 × 6 + 4, it means that in the first 2014 terms in the sequence, there are 335 complete periods with an incomplete period of four remaining terms. Therefore, there are 335 terms in the sequence that are divisible by 4. Answer: 335 22. The inside lane of a track has length 400 m and the outside lane has length less than 500 m. From the marked line, as shown in the diagram, Max and Lynn start running counterclockwise along the track at the same time. Max runs at constant speed on the inside lane. Lynn, whose constant speed is 3 times that of Max, runs on the outside lane. The first time both are back together at the marked line, Max has completed 3 laps. What is the length, to the nearest m, of the outside lane?

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### 2015IMAS First Round Upper Primary Division Full Solutions

Answer：096 25. In an election between three candidates, they are supported respectively by 10, 35 and 15 of the first 60 voters. 40 more votes are to be cast, each for one of the three candidates. In how many ways can the candidate currently with 10 supporters become the uncontested winner?

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