AMO 2027 Grade 4 SET 5 - Self-study

Two regular six-sided dice were rolled on the ground. All numbers on their visible faces add to 31. What is the difference between the two numbers facing the ground? Each die has faces 1 to 6, and “visible” means all five faces other than the bottom face.

Choose one option.

The perimeter of a square is 124 cm. What is its area in $\mathrm{cm}^2$?

Choose one option.

Find the 10th term of $550,490,520,460,490,430,\ldots$. Continue the alternating rule: subtract 60, then add 30, and repeat.

Choose one option.

A garland of 200 flowers follows this repeating pattern: 4 red, 3 orange, 5 yellow, then 4 red, 3 orange, 5 yellow, and so on. What is the difference between the numbers of red and yellow flowers?

Enter one whole number, without units.

Ron and Vanda each thought of a two-digit number. The products of their digits were 24 and 35 respectively. The difference between their numbers was 37. What is the sum of their numbers?

Choose one option.

On a 100-metre running track with two distinct ends, a flag is placed every 4 metres, including both ends. How many flags are required?

Enter one whole number, without units.

Four kids can paint four balls in four minutes. If everyone works at the same speed, how many kids can paint 12 balls in 12 minutes?

Choose one option.

Find $A+B+C$ if different letters stand for different digits in the multiplication below. A and B are leading digits and cannot be zero. The diagram reads: the two-digit number A8 multiplied by 8 equals the three-digit number BCC.



Choose one option.

Ten equal short ropes are knotted end to end in one chain to make a rope 81 cm long. Each knot reduces the combined length by 1 cm. How long was each short rope? This uses the overlap interpretation of the source solution.

Enter one whole number, without units.

If $EAT+EAT+EAT=444$, what is $E\times A\times T$?

$EAT$ denotes the three-digit number with hundreds digit $E$, tens digit $A$ and units digit $T$.

Choose one letter A–E.

Sarah and Rose have some pencils. Two-fifths of Sarah’s pencils and eight-ninths of Rose’s pencils are each 40. Who has more pencils, and by how many?

Choose one option.

A box contains balls and bats. If three-sevenths of the items are balls and there are 32 bats in the box, what is the total number of balls and bats in the box?

Choose one option.

Three fruit vendors make 3 fruit baskets in 3 minutes. How many fruit baskets will be ready if 10 fruit vendors work for 15 minutes?

Assume all vendors work independently at the same constant rate, with enough materials. Choose one option.

What is the largest possible digit $m$ in the five-digit number $653m2$ such that the number is divisible by 3?

Enter one whole number, without units.

A festival requires 3500 chairs. If each batch contains 85 chairs, how many whole batches must be ordered?

Enter one whole number, without units.