AMO 2027 Grade 3 SET 1 - Self-study

If the product of two numbers is 154 and their sum is 25, find the smaller of the two numbers.

Choose one option.

If 300 digits were used to print the page numbers of a book, how many pages does the book have? Assume its pages are numbered consecutively from 1, with every page number printed once.

Enter one whole number, without units.

Study the sequence 50, 53, 56, 61, 66, 73, 80, … . Find the sum of its 9th and 10th terms. Use the intended rule: consecutive odd increases, starting at 3, are each used twice.



Enter one whole number, without units.

It takes 10 women to stitch 50 soft toys in 2 hours. How many soft toys will 6 women stitch in 4 hours, assuming all women work at the same pace?



Choose one option.

Frank has more than 20 and fewer than 70 marbles. If he makes piles of 4, one marble is left over. If he makes piles of 7, three marbles are left over. How many marbles does he have?



Enter one whole number, without units.

A 4 cm × 4 cm × 4 cm cube is made of 1 cm × 1 cm × 1 cm cubes. The large cube is painted blue on all six outside faces. How many small cubes have exactly one face painted?



Enter one whole number, without units.

There are three boxes labelled 1, 2 and 3. Each box contains different numbers of different coloured marbles.
- The number of yellow marbles is half the sum of the red and blue marbles.
- There are more blue marbles than red marbles.
- Box 1 has 10 marbles.
- The total number of marbles is 60.
How many blue marbles are there?

**Assumption for this self-study exercise:** Each box contains marbles of just one colour, and the three boxes contain red, yellow and blue marbles, one colour per box. This is the interpretation used by the source solution; the original wording does not state it clearly.

Enter one whole number, without units.

Radha has to cut small strips of ribbon of 5 cm each. But after every 3 strips of 5 cm, she cuts a strip of 4 cm mistakenly. If a total roll of 100 cm was cut into small ribbons, how many 5 cm ribbon strips are there?

Choose one option.

A box of apples can be shared equally between 3, 4, 5 or 6 classes. What is the smallest possible number of apples in the box if it had more than 200 but less than 500 apples?

**Editorial note:** Share whole apples with no remainder. Enter only the number, without units.

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.



Enter one whole number, without units.

Henry drives 2 km in the first 10 minutes. After every 10 minutes he increases his speed and travels 1 km farther in the next 10 minutes than in the preceding 10 minutes. How many kilometres does he travel in one hour?



Choose one option.

Josh thought of a two-digit number and then added a zero at the end of that number to make it a three-digit number. He then added the three-digit number to his original number and the result was 726. What was his two-digit number?

Choose one option.

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?



Enter one whole number, without units.

Find the value of the digit in the ones place of the following expression: $99\times101\times103\times105\times107-100\times102\times104\times106\times108$.

Enter one whole number, without units.

What is the sum of the first 50 numbers of the sequence 7, 13, 27, 33, 7, 13, 27, …? Continue the repeating four-number block shown.



Enter one whole number, without units.