Australian AMC 2010 - Junior

The value of $27+48-37$ is

The value of $2^2+3^3$ is

In the diagram, the value of $x$ is

A 55-minute school assembly ends at 10:05 am. At what time did it start?

The value of $2010-20.10$ is

Which of the following is equal to $4+\frac16-\frac23$?

The grey shaded tiles represent $\frac15$ of the large rectangle. How many white tiles must be removed so that the grey tiles represent $\frac13$ of the remaining shape?

A bus is timetabled to stop outside my house at equal intervals throughout the day. It is now 3:25 pm and the last bus arrived 6 minutes ago, but it was 2 minutes late. The next bus is due at 3:52 pm. When is the bus after that due?

A shape is formed when a regular hexagon of side 9 cm has six regular hexagons of side 3 cm added to the outside of it with one at the centre of each side (two of the sides are shown).



What is the perimeter, in centimetres, of the shape?

Follow the instructions in the flow chart.



What number is printed?

On my side of the street the houses are numbered 2, 4, 6, 8, 10, 12, 14 and 16. My house is positioned so that the sum of all the house numbers to the left of me is the same as the sum of all those to the right of me. What is my house number?

The point $X$ (not shown) is the midpoint of $QS$ and the point $Y$ (not shown) is the midpoint of $PT$.



The length of $XY$ is

The manager of an electrical store bought a brand of TV for \$900. He marked up the price by 50%. However, the TV did not sell so the manager decided to reduce the marked price by 20%. At the new price the TV sold and the result for the store was

Place the numbers 1, 2, 3, 4 and 5, one in each circle in the diagram so that no number is joined by a line to a consecutive number.



The sum of the numbers $X$ and $Y$ could be

Three rectangles are lined up horizontally as shown. The lengths of the rectangles are 2 cm, 4 cm and 8 cm respectively. The heights are 1 cm, 2 cm and 4 cm respectively. A straight line is drawn from the top right-hand corner of the largest rectangle to the bottom left-hand corner of the smallest rectangle.



What is the area, in square centimetres, of the shaded region?

Anne says ‘Bob did it’. Bob says ‘Anne is lying’. Chris says ‘I did not do it’. Derek says ‘Anne did it’. Only one statement is false. The one who did it is

An L-shaped path is 5 m wide and has an area of $125\text{ m}^2$.



The perimeter, in metres, of the figure is

The cells of a $20\times20$ grid are labelled with the numbers $1,2,3,\ldots,20$ in the first row, $21,22,23,\ldots,40$ in the next row and so on. Which of the numbers below is in one of the four cells touching the centre of the grid at one of its corners?

How many four-digit numbers



are divisible by 36?

A number is square-free if the only square number dividing it is 1. For example, 6 is square-free but 12 is not.

How many square-free numbers are there between 90 and 100 inclusive?