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AMO 2027 Grades 2-3 SET 29 - Self-study

Question 1

The combined age of David and Harry is 50 years now. Ten years ago David was twice as old as Harry. How old will Harry be five years from now?

Question illustration

Enter one whole number, without units.

Question 2

What is the greatest three-digit number divisible by both 5 and 11?

Question illustration

Choose one option.
  1. 899
  2. 990
  3. 992
  4. 995
  5. 999

Question 3

Given that $k\times726$ equals the square of 66, find $k$. Here the square of 66 means $66\times66$.

Question illustration

Enter one whole number, without units.

Question 4

Sixty potatoes weigh 4 kg. Potatoes cost 30 dollars per kilogram. What is the price, in dollars, of two dozen potatoes? Assume all the potatoes have equal weight.

Question illustration

Enter one whole number, without units.

Question 5

The original picture shows a 4 × 4 square grid. How many squares of any size, formed by the grid lines, contain the entire cell marked X?

Question illustration

Choose one option.
  1. 1
  2. 4
  3. 5
  4. 10
  5. 16

Question 6

What will the time be 5400 seconds after 5 pm?

Question illustration

Choose one option.
  1. 6.00 pm
  2. 6.15 pm
  3. 6.30 pm
  4. 4.30 pm
  5. 3.30 pm

Question 7

The product of all the digits of a three-digit number is 12. How many such three-digit numbers are there?

Question illustration

Choose one option.
  1. 15
  2. 12
  3. 9
  4. 11
  5. 18

Question 8

What is the smallest four-digit number divisible by both 7 and 5?

Question illustration

Choose one option.
  1. 1007
  2. 1010
  3. 1035
  4. 1015
  5. 1050

Question 9

Kevin cycles 10 km in 1 hour and 15 minutes. How many kilometres will he cycle in 5 hours? Assume he maintains the same speed throughout.

Question illustration

Enter one whole number, without units.

Question 10

Two years from now John will be twice as old as he was two years ago. How old will he be ten years from now?

Question illustration

Enter one whole number, without units.

Question 11

On a number table from 1 to 100, we start at a number, add 72 and then subtract 36 to reach 50. What was the original number?

Question illustration

Choose one option.
  1. 86
  2. 14
  3. 48
  4. 50
  5. 84

Question 12

Alphabet blocks are stacked in a tower. Block B is seventeenth from the top and fifth from the bottom. How many blocks are in the tower?

Question illustration

Choose one option.
  1. 22
  2. 20
  3. 21
  4. 12
  5. 18

Question 13

Louis rides his bicycle around a park at a constant speed. He completes five and a half rounds, a distance of 2200 metres, before resting. How many metres does he cover in one round?

Question illustration

Choose one option.
  1. 450
  2. 250
  3. 400
  4. 500
  5. 350

Question 14

Add double of 25 to one-third of 21. Subtract that sum from 100. What is the final number?

Question illustration

Choose one option.
  1. 60
  2. 29
  3. 43
  4. 57
  5. 71

Question 15

Each student eats three-fifths of a pizza. Eighteen pizzas are ordered. How many students are there? Assume all 18 pizzas are eaten by these students, with none left over.

Question illustration

Enter one whole number, without units.