AIMO 2021 Primary 5 — Preliminary (Open Trial 1)

What is the value of $x$ if $(x+2):2=(5x-8):4$.

In the figure below, E and F are the midpoints of AD and DC respectively. ABCD is a figure. What is the area of the shaded region?

What is the sum of the first 1952 terms of the series $\frac11,\frac12,\frac22,\frac13,\frac23,\frac33,\frac14,\frac24,\frac34,\frac44,\ldots$?

Original choices: A: 1000; B: 1007,5; C: 1952; D: 1002.

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

A tourist was travelling to a town which was 60 km away. He walked at a speed of 6 km/h at first. Then, he hitched a ride on a scooter travelling at 18 km/h. He arrived at the town 4 hours from the time he set off. How long had he walked?

In the figure below, how many triangles can be formed using any three points as the vertices?

Editorial convention: Interpret the intended dot pattern as a regular 3-by-3 rectangular grid.

Original choices: A: 16; B: 56; C: 64; D: 9.

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

How many times does the digit “0” appear in a 200-page book?

Editorial convention: Count occurrences in page numbers 1 through 200, without leading zeros.

Anna multiples her month of birth by 31. She then multiples her day of birth by 12. The sum of the two products is 213. When is her day of birth?

If 17 is written as the sum of a few whole numbers, what is the product of these numbers when it is maximum?

Here is the net of a cube, and each face is labeled with a letter. When the cube is formed, what letter is on the face opposite to the one labeled with the letter A?

The side of each square grid is 2 cm. Find the area the shaded region.

Between 1 and 2009, how many numbers are multiples of 5 and 7?

Original choices: A: 250; B: 450; C: 630; D: 631.

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

Choose any three letters from a, b, c and d. In how many ways can we arrange the three numbers?

The average age of A, B and C is 19. The average age of B, C and D is 22. The average age of A, C and D is 21. How old is A?

A car travels from Town A to Town B at a speed of 90 km/h. It then returns at a speed of 60 km/h. What is the average speed of the car for the whole trip in km/h?

Find the value of fraction $\displaystyle\frac{1}{1+\frac{1}{2+\frac{1}{3+\frac15}}}$.

What is the sum of all the odd numbers smaller than 100?

Editorial convention: Use positive odd integers.

The sum of two numbers is 88. The product of the two numbers is 1612. What is the larger number?

A car travels from Town A to Town B at a speed of 90 km/h. It then returns at a speed of 60 km/h. What is the average speed of the car for the whole trip?

If $=\frac{1000\times1003}{1001\times1002}$; $B=\frac{1000\times1002}{1001\times1003}$; $C=\frac{1000\times1001}{1002\times1003}$, then which has the greatest value?

A 6-digit number begins with th digit 8. The number is divisible by 9. All digits of the number are different. What is the smallest possible value of this number?