IMAS 2020 — Upper Primary Grades 5–6 — Round 1

Which one among the choices has a value greater than $\frac13$ ?

Select one number among the choices and fill it into the box such that the value of $\frac{17}{\square}$ is closest to 2.

The figure below on the right shows the three invisible faces of the three-dimensional solid below on the left. How many edges does this three-dimensional solid have? View from the right View from the left

It is known that the product of two positive integers is 120. What is the smallest possible value of the positive difference between these two integers?

Albert drove from Town A to Town B at a constant speed of 80 km per hour. If the street sign shown below was seen during the trip, how many hours does it take Albert to drive from Town A to Town B?

Among the figures below, which has the most number of lines of symmetry?

The graph below shows the five most recent test scores that Danny got in Mathematics. The score of his fifth test was accidentally stained with ink on the graph and could not be seen. If Danny knows that his average score for these five tests is 92.4, What was his score on the fifth test?

Among the shapes listed below, which cannot always be formed by using two identical triangles?

It is known that the sum of a positive integer and 4 is a multiple of 3. If the sum of the same positive integer and 3 is a multiple of 7, what is the smallest possible value of this positive integer?

A computer is copying a file at a constant speed. If 1 minute and 45 seconds passed and 79% of the file is still uncopied, how long does it take to completely copy the file?

A box contains some number of red and blue balls. If the number of red balls is two-fifths of the number of blue balls, which of the following numbers can’t be the total number of coloured balls in the box?

Express 2020 as a sum of 290 prime numbers such that the largest prime number used must be as small as possible. What is the largest prime number among these 290 prime numbers?

John can draw a total of 100 sketches in two days. Today, his boss asks him to draw 100 sketches, the only problem is that he will be attending a wedding banquet tomorrow afternoon, so all sketches must be drawn within a day and a half. If he plans to hire a junior artist to work with him together to finish the project in time, how many days at most should the junior artist take to draw 100 sketches?

In the figure below, ABCD is a square with an area of 2020 cm² . Connect the midpoints of each side to get square EFGH and then connect the midpoints of each side of square EFGH to get square MNPQ. What is the area, in cm² , of the shaded region?

There are three boxes that are painted red, yellow and blue respectively. We are to put 2 identical apples and 2 identical pears into these three boxes such that no two identical fruit can be placed into the same box. If empty boxes are allowed, how many different placement methods can we have?

Two bottles of volume 350mL are filled with a mixture of water and alcohol. It is known that the alcohol in the first bottle is 4 times that of water, while the alcohol in the second bottle is 6 times that of water. Now pour both mixtures into a larger empty container. What is the percentage of alcohol in the new mixed solution? (Round off your final answer to one decimal place).

Some overlapping circles divide the plane into several regions. Numbers are filled in these areas such that for any pair of overlapping circles, say A and B, the number in the intersection area of circle A and B is the average of the two numbers in the areas solely in A or B. For example, the figure on the right shows $\frac{1+5}2=3$ , $\frac{5+11}2=8$ and $\frac{11+13}2=12$ . In the figure below, there are five overlapping circles and ten numbers are filled according to the conditions above. What is the sum of the numbers a and b?

There are 43 pearls with a hole in the center that are to be stringed together using a thread such that the thread will form the letters "I", "M", "A", and "S", as shown in the figure below. If each pearl can only be passed through once by the thread, how many from the four letters cannot be done?









I:

M:

A:

S:

The diagram below shows a bicycle model. Its front gear has 24 teeth while its rear gear has 10 teeth. At least how many revolutions does the front gear need to make such that the front and rear gears go back to their initial positions at the same time?

Andy used some number of regular pentagonal cardboards of the same size to form a solid which is shown on the right diagram. How many edges does this solid have?