Australian Mathematics Competition - 2023 - Middle Primary - Grade 3 & 4 - Questions and Solutions

Problem 1:

What is the total number of petals on all 5 flowers?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 50

Problem 2:

\[
2+3+7+8=
\]

(A) 10
(B) 20
(C) 30
(D) 40
(E) 50

Problem 3:

Which one of these shapes is a rectangle?

Problem 4:

Which digital clock time matches the time shown on the clock face?

Problem 5:

Emma has a bag containing 5 red, 4 yellow, 1 black and 2 blue buttons. When she chooses 1 button at random, what colour is it most likely to be?
(A) green
(B) blue
(C) black
(D) yellow
(E) red

Problem 6:

What fraction of the circle is part A ?

(A) one-half
(B) one-third
(C) two-thirds
(D) one-quarter
(E) three-quarters

Problem 7:

In a board game, Nik rolls three standard dice, one at a time. He needs his three rolls to add to 12.
His first two dice rolls are 5 and 3 . What does he need his third roll to be?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

Problem 8:

Which shape has only one line of symmetry?

Problem 9:

Anastasia Ant is on a sheet of wire mesh with 10 cm squares. She can only move along the wires. She moves 10 cm east, then 30 cm north and 20 cm west. What is the least possible distance she needs to move to return to her starting point?

(A) 10 cm
(B) 20 cm
(C) 30 cm
(D) 40 cm
(E) 50 cm

Problem 10:

A piece of card is cut out and labelled as shown in the diagram. It is folded along the dotted lines to make a box without a top. Which letter is on the bottom of the box?
(A) A
(B) B
(C) C
(D) D
(E) E

Problem 11:

Jiang is threading beads onto a string to make a necklace. He decides to use a sequence, starting with a red bead, then a yellow bead and a blue bead. He repeats this pattern until he has 20 beads on the necklace.
How many red beads will he use?

(A) 5
(B) 6
(C) 7
(D) 8
(E) 9

Problem 12:

How many people played tennis on the busiest day of the week at the Paradise North Tennis Club?
(A) 45
(B) 50
(C) 55
(D) 60
(E) 65

Problem 13:

When this puzzle is complete, each of the four lines will add up to 14 . What will the four missing numbers add to?
(A) 10
(B) 14
(C) 15
(D) 16
(E) 18

Problem 14:

Which one of the following could give an answer of \(25 ?\)
(A) an odd number plus an odd number
(B) an even number multiplied by an even number
(C) an even number divided by an odd number
(D) an odd number minus an even number
(E) an even number multiplied by an odd number

Problem 15:

This bottle holds 4 glasses of water.

Which one of the following holds the most water?

Problem 16:

Fido needs to be weighed at the vet, but he won't sit still. So the vet weighs himself and then weighs himself holding Fido.

How much does Fido weigh?
(A) 23 kg
(B) 26 kg
(C) 28 kg
(D) 30 kg
(E) 32 kg

Problem 17:

Grandma adds 3 spoons of sugar to the juice of 10 lemons to make lemonade. How many lemons are needed if 15 spoons of sugar are used to make Grandma's recipe?
(A) 20
(B) 22
(C) 25
(D) 30
(E) 50

Problem 18:

Janus is making patterns using square tiles.
Each pattern is made by copying the previous pattern, then adding new tiles around the outside edges.
The new tiles alternate in colours, as shown.

What will be the total number of tiles in Pattern 5?
(A) 25
(B) 33
(C) 37
(D) 40
(E) 41

Problem 19:

My laptop's battery meter tells me what fraction of the battery charge is left. I used the laptop for 4 hours and 20 minutes and it went from

What would the reading be after using the laptop for another 130 minutes?

Problem 20:

Syed's mother had some money to share with her family.
She gave one-quarter of her money to Syed.
Then she gave one-third of what was left to Ahmed.
Then she gave one-half of what was left to Raiyan.
She was left with \(\$ 15\), which she kept for herself.
How much money did Syed's mother have to start with?
(A) \(\$ 30\)
(B) \(\$ 45\)
(C) \(\$ 60\)
(D) \(\$ 90\)
(E) \(\$ 120\)

Problem 21:

In 2023, Janine's birthday is on a Thursday. Ngoc's birthday is one month later, meaning that it is on the same day-number in the next month. Ngoc's birthday is not on a Saturday or a Sunday. Which day of the week is Ngoc's birthday?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday

Problem 22:

Sally empties her piggy bank to see how much she has saved. She has 20 coins altogether and the total value of her coins is (\$ 3.80). She notices that she has twice as many 50 c coins as 20 c coins. The remaining coins are 10c coins. How many 10c coins does she have?
(A) 2
(B) 4
(C) 8
(D) 11
(E) 14

Problem 23:

Three different numbers from 1 to 20 are chosen. They add to 20 . Two of the numbers are 2 apart. How many possibilities are there for the largest number?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

Problem 24:

Estelle is making decorations shaped like the 8-pointed star shown. She folds a square of paper to make a triangle with 8 layers as shown.

How could she cut the triangle so that the unfolded shape is the star?

Problem 25:

Tom is digging holes in his garden for his new plants. As he is working he slows down. Each new hole takes a minute longer to dig than the last hole.
The first 5 holes have taken him 35 minutes in total. How long will it take him to dig the next 2 holes?
(A) 11 minutes
(B) 17 minutes
(C) 21 minutes
(D) 24 minutes
(E) 25 minutes

Problem 26:

To unlock a security door, Daniyal enters a code on the keypad shown. To make it easy to remember:

• the code has 10 digits
• the code uses every digit exactly once
• the code steps from button to button only if the two buttons touch
• the code is as large as possible.

What are the last 3 digits in Daniyal's code?

Problem 27:

In this puzzle, \(\triangle\), \(\square\) and represent different nonzero digits. What is the three-digit number \(\triangle \square \bigcirc\) ?

Problem 28:

Ollie arranges the numbers 1 to 6 to form three 2-digit numbers.
Exactly one of his numbers divides by 3 but not divides by 4 , and exactly one other divides by 4 . None of them divide by 5 .
The three numbers add to 93 .
What is the number which does not divide by either 3 or 4 ?

Problem 29:

A table in the shape of a trapezium can seat 5 people. When two tables are put together in a row, 8 people can be seated. What is the smallest number of trapezium tables required to seat 2023 people if they are all placed in a row?

Problem 30:

Yifan has a construction set consisting of red, blue and yellow rods. All rods of the same colour are the same length, but differently coloured rods are different lengths. She wants to make quadrilaterals using these rods.

• When she uses two red, one blue and one yellow rod, the perimeter of the quadrilateral is 36 cm .
• When she uses two blue, one red and one yellow rod, the perimeter is 35 cm .
• When she uses two yellow, one blue and one red rod, the perimeter is 33 cm .

What number do you get when you multiply the lengths of one red rod, one blue rod and one yellow rod?