Australian AMC 2024 - Intermediate

Of the following, which is closest to 14?

What is the value of $(57\times346)+(43\times346)$?

What is the value of $x$ in the diagram?

The average of 2024 and an unknown number is $2\frac12$. What is the unknown number?

What is the area of the shape drawn in the grid?

Let $p$ be 12% of 300 and $q$ be 6% of 600. What is the difference between $p$ and $q$?

The largest integer $n$ for which $0.6n$ is less than 17 is

Pat has 12 eggs,2 kg of flour, and 2 L of milk. His pancake recipe calls for 2 eggs,250 g of flour and 400 mL of milk. He makes as many pancakes as he can while using the ingredients in the proportions given in the recipe. How much flour will he have left?

Theo’s collection of toy dinosaurs is stored in two containers. He noticed that one of the containers had 4 times as many dinosaurs in it as the other. He moved 18 to the other container so that the two containers had the same number. How many dinosaurs are in Theo’s collection?

Eiliyah is drawing an isosceles triangle on the number plane. It has an area of 6 square units. She has already plotted two vertices of the triangle, at(1,1) and(3,1). Which of the following could be the coordinates of the third vertex of the triangle?

Yalis has to take a tablet every 9 hours. The course of medication is 15 tablets. He takes his first tablet at 11 am on Tuesday. When will he take his last tablet?

How many digits are in the number $202^4$?

In the diagram, the concentric circles are equally spaced, with radii from 1 to 6, and the lines from the origin are equally spaced 20° apart. Which of these five areas is largest?

Kate and Jim exercise at their local beach, going from one end to the other and back. Starting together, Kate jogs at a steady pace of 10 km per hour, while Jim walks at 6 km per hour. They first meet again after 30 minutes. How long, in kilometres, is the beach?

This star has order-10 rotational symmetry, with 10 internal right angles as shown. What is the size of each of the obtuse angles marked with a dot?

A game uses the two spinners shown. The player who spins the higher number wins. Equal spins are a draw. What is the probability that player one wins?

When the number 9045 is split into two 2-digit numbers, the first number is twice the second number:90=2 × 45. Many other 4-digit numbers can be split into two 2-digit numbers where the first number is twice the second. There is a unique 2-digit number that divides into all such 4-digit numbers. What is this number?

Triangle $ABC$ has a right angle at $A$, and side $AC$ is twice as long as $AB$. Also $MN$ is the perpendicular bisector of $BC$, as shown. In area, what fraction of $\triangle ABC$ is $\triangle CMN$?

A researcher surveys 10 households and creates this scatterplot showing how many people and how many internet-connected devices are in each house. To help categorise her data, she adds a vertical line representing the median number of people and a horizontal line representing the median number of devices. One extra household is surveyed and the results are added to the scatterplot. What will happen to the median lines?

I make up all the 5 digit numbers that use each of the digits from 1 to 5 once. I then arrange these 120 numbers in increasing order from 12 345 to 54 321. Which number is the 42 nd in this order?