AIMO 2021 Primary 6 — Preliminary (Open Trial 1)

The ratio of the father’s age to the daughter’s age is 6: 1. The ratio becomes 2: 1 twenty years later. How old is the father?

Change $\frac37$ into a decimal number. What is 1809th digit after the decimal point?

If a and b are two different integers from 10 to 50 find maximum value of $\frac{4a-b}{a-b}$.

Original choices: A: 50; B: 51; C: 52; D: 53.

Answer-format convention: Give the exact result as a short answer; the source choices are retained above.

Find the value of the following expression $(1+\frac13+\frac15)(\frac13+\frac15+\frac17)-(1+\frac13+\frac15+\frac17)(\frac13+\frac15)$.

How many triangles are there in the 4th figure?

A and B set off a journey at the same time. A ha walked $\frac14$ more distance than B. B has used $\frac1{10}$ more time than A. Find the ratio of the speed of A to B.

A car travels from town A to town B at a speed of 60 km/h and 2 hour later, another car travels in the same direction at 100 km/h. At how many hours will the second car catch up with the first one?

Editorial convention: Measure elapsed time from the second car’s departure, assuming both cars continue at the stated speeds.

The remainder is 7 when a number is divided by 9. The remainder is 5 when it is divided by 7. The remainder is 1 when it is divided by 3. What is the number?

Original choices: A: 23; B: 102; C: 75; D: 100.

Answer-format convention: Give all positive solutions in the form $a+bk$, where $k=0,1,2,\ldots$.

If it is 9 o’ clock now, how long will it take for the minute hand of a clock to lie directly over the hour hand in minute?

The figure below is made up of a square and 3 identical rectangles. Find the area of the shaded rectangle in square meter.

Original choices: A: 98; B: 90; C: 95; D: 50.

Answer-format convention: Give the exact result as a short answer; the source choices are retained above.

A rectangular piece of paper measuring 90 cm by 42 cm is to be cut into squares of equal area without any wastage. What is side of each square in cm?

A dress was priced 20% above its cost price. It was then sold at 80% of the marked price. The loss incurred was \$0.84. What was the cost pric of the dress?

Find the unit digit of $19^{19}+97^{97}+2020^{2020}$.

The graph below shows the number of goats sold by a farmer. Which month saw the greatest decrease in sale?

Initially, school field is 50 meters length with 30 meters width. After expansion, the length increased by 20% and the area become 2340 square meters, how many meters the width has increased?

There is a dart game in an amusement park where the goal is to hit the black portions of the regular hexagon in order to win a prize. From the choices below, which dart board will give the highest chance of winning?

Editorial convention: Assume a dart lands uniformly over the hexagon and use the intended equal subdivisions shown.

Four boys need to cross a dark tunnel but they only have a torch among them. A can cross the tunnel in 1 minute. B can cross the tunnel in 1.5 minutes. C can cross the tunnel in 2 minutes. D can cross the tunnel in 2.5 minutes. Given that they need a torch to cross at all time and that the tunnel can only allow passage of two children, find the least possible time needed for four boys to get across the tunnel.

The two players in a League championship will continue to play until one player wins a total of three games. How many ways are there for any player to win the championship?

Editorial convention: Count ordered, no-draw game-result sequences with either of the two named players as champion.

A $4\times4$ grid is made using 40 matches as shown. How many matches are needed to construct a $10\times10$ grid?

How many factors does the number 450 have?

Editorial convention: Count positive integer factors.