AMO 2027 Grades 2-3 SET 4 - Self-study

The sum of the digits of a 2-digit number is 10. The tens digit is 4 times the ones digit. Find the number.

A person was asked to state his age in years. His reply was, “Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am.” What was the age of the person?

Circle the shape with more faces.

The school nurse is recording the heights of students in a class. When comparing their heights, the students find that: Pi is taller than Ksi but shorter than Charlie. Daniel is taller than Edward but shorter than Pi. Who is the tallest among 5 students?

a) Today is Thursday. The day after 59 days will be which day of the week?

b) December 8th, 2007 was Saturday. What day of the week was it on December 8th, 2006?

c) On February 8th, 2005 it was Tuesday. What was the day of the week on February 8th, 2004?

d) If January 1st, 2006 was a Sunday, What was the day of the week January 1st, 2010?

In one side of the road in front of my school, there are 505 trees. The trees are 10m away from each other. How far is the last tree away from the first one?

Melissa, Frank and Shelly are going to meet for a picnic. Melissa has 5 berries while Frank has 9 berries. How many berries should Shelly bring so that they can share and have 8 berries each?

Josh lives on the 6th floor. He needs to climb 48 steps to move from the 2nd floor to the 4th floor. How many steps does he need to climb from the 1st floor to the 6th floor?

A book has 60 pages, numbered from 1 to 60. How many times will the digit 6 be used in numbering the book?

Four girls each caught a fish while at the beach. Teri’s was double the size of Jane's. Jane's fish was shorter than Lynn’s by nine centimetres. Lynn’s was 18 centimetres longer than Reina’s who caught a fish 30 centimetres long. How long were Teri’s, Jane's and Lynn’s fish?

There are 14 rows of seats in cinema. The first row has 15 seats, the second row has 17 seats, the third row has 19 seats, and so on. How many seats are there in the cinema altogether?

A wire of length 20 m is to be folded in the form of a rectangle. How many rectangles can be formed by folding the wire if the sides are positive integers in metres?

Ksi was 10 minutes early for class. Pi came in four minutes after Alice, who was half as early as Ksi. How many minutes early was Pi?

In the algorithm below, the letters a, b and c represent different digits from 0 to 9. What is the three-digit number abc?

The figure below shows a square ABCD with two shaded triangles inside. Given that the total area of the shaded triangles is 242cm², find the length, in cm, of AB.