AMO 2027 Grades 2-3 SET 6 - Self-study

What is Jack’s present age, if after 9 years his age will be 5 times his age 7 years back?

In the following cryptarithm, all the different letters stand for different digits. Find the product of A, B and C.

There are 21 trees planted along the road divider with trees planted at opposite ends. The trees are planted at regular intervals of 20 m. If some lamp posts are to be placed along the opposite side of the road at regular intervals of 10 m, how many lamp posts are required on the opposite side of the road if lamp posts are placed at opposite ends of the road?

James has two dice: one 6-sided with numbers from 1 to 6, and one 8-sided with numbers from 1 to 8. He rolled these 2 dice. How many ways are there to get a sum of 6?

Jane has 143 marbles. She wants to give all her marbles to her 11 friends so that each friend will get the same number of marbles. How many marbles will she give to each friend?

Look at each pattern of shapes. How many matchsticks are there in the 20th shape?

Students are standing in the queue. There are 9 students between John and Sam. After the first 7 students left the queue, Sam became the 5th from the start, and John became the middle of the queue. How many students were there in the queue at first?

Pi arrived at work at 8:14 A.M. and Ksi arrived at 9:12 A.M. How long had Pi been at work when Ksi got there?

Justine is 13 years younger than her uncle Stewart. Stewart is 18 years older than Justine’s sister, Hana. Hana’s mother is 8 years older than Stewart, and 28 years older than her youngest child, Jared. If Jared is 12 years old, how old is Justine?

Pi has a new bookcase for her bedroom with 6 shelves. Each shelf holds 8 books. If Pi has 60 books, how many books will not fit on the bookcase?

What would be a good estimate of the total amount of money made by the bake sale?

A staircase is made of bricks, with 20 bricks in the first step. If each subsequent step has 3 more bricks, how many bricks are on the 54th step?

When you multiply 3 whole number, the result is 120. When you add them, the result is 19. Find the largest among these 3 numbers.

A safari company offers group tours that cost 100 dollars for two people and 20 dollars more for each additional person. If five people share the cost of the tour equally, how much does each person pay?

There are two ducks in front of a duck, two ducks behind a duck and a duck in the middle. How many ducks are there?