AMO 2027 Grade 3 SET 4 - Self-study

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.



Enter one whole number, without units.

A rectangle has perimeter 144 cm. Its length is three times its breadth. What is the difference between its length and breadth, in centimetres?



Choose one option.

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.

Solve: $826-(626-529)+201$.



Choose one option.

Find the sum of $A+B+C$ if different letters stand for different digits.

**Editorial note:** A8 and BCC are ordinary base-ten numbers; A and B are nonzero leading digits. Choose one option.

Harry brought a few marbles to school. He distributed one-third of the marbles among his friends on the bus. He then gave 20 marbles to his classmates. Now he is left with only one-fourth of his marbles. How many marbles did he have at first?

Both fractions refer to his original number of marbles.

Choose one option.

Fill the grid with the numbers 11 to 19, using each once, so that each row and each column sums to 45. What is X + Y?

For this self-study edition, if the stated conditions allow more than one completed grid, enter any one possible value of X + Y. No extra diagonal condition is imposed.



Enter one whole number, without units.

Find $48+498+4998+49998$.



Choose one option.

Jack and his father’s weight add up to 100 kg. If Jack loses 4 kg, he will be exactly half of his father’s weight. What is the difference between their weights, in kg?

**Editorial note:** Find the difference before Jack loses weight; his father’s weight stays unchanged. Choose one option.

If there are 8 roses for every 5 daffodils in the garden bed, how many daffodils are there if there are 96 roses?

Enter one whole number, without units.

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?



Choose one option.

How many consecutive zeros are there at the end of the following product? $25\times25\times6\times6\times36$.

Enter one whole number, without units.

Eight notebooks and 10 pens cost 480 dollars. One pen costs 15 dollars less than one notebook. Find the price of 5 notebooks.



Choose one option.

The lamp is more costly than the watch and the candle stand. The candle stand is less expensive than the watch but more expensive than the basket. Which is the second most expensive item? Use the booklet options below.



Choose one option.

Ten small ropes of equal length are knotted together to form a big rope 81 cm long. The question says the knotted area is 1 cm for every rope. How long is each small rope, in centimetres?

Use the source model: join the ten ropes end to end in one open chain; each join reduces the total length by 1 cm.



Enter one whole number, without units.