Australian Mathematics Competition - 2021 - Upper Primary Division - Grades 5 & 6- Questions and Solutions

Problem 1:

This Nigerian flag is white and green. What fraction of it is green?

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

Problem 2:

Which number makes this number sentence true? $\square$ -5=9

(A) 0 (B) 4 (C) 12 (D) 9 (E) 14

Problem 3:

What is the perimeter of the quadrilateral shown?

(A) 13 cm (B) 15 cm (C) 17 cm (D) 19 cm (E) 21 cm

Problem 4:

Which of the following decimal numbers has the smallest value?

(A) 0.0002 (B) 0.002 (C) 0.02 (D) 0.2 (E) 2.0

Problem 5:

$\frac{1}{2}+\frac{2}{4}-\frac{4}{8}=$

(A) $\frac{1}{2}$ (B) 1 (C) $1 \frac{1}{2}$ (D) 2 (E) 4

Problem 6:

Suri has a number of 20-cent and 50-cent coins. Which of the following amounts of money is it NOT possible for her to make?

(A) 50 cents (B) 60 cents (C) 80 cents (D) 30 cents (E) 70 cents

Problem 7:

A square of paper is rolled up, pressed flat, and then cut as shown.

What could the sheet of paper look like when unrolled and leid flat?

Problem 8:

Leo is waiting in line at school. There are four students ahead of him and twice as many behind him. How many students are in this line?

(A) 4 (B) 8 (C) 9 (D) 12 (E) 13

Problem 9:

Cassandra makes a healing potion from a mixture of herbs. She uses this balance to weigh out the herbs. If she uses 5 grams of fennel, how many grams of mint will she need?

(A) 5 (B) 10 (C) 15 (D) 20 (E) 40

Problem 10:

There are 14 pieces of fruit in a bowl. There are twice as many nectarines as pears, and half as many nectarines as apples. There are no other types of fruit. How many apples are there?

(A) 2 (B) 4 (C) 6 (D) 8 (E) 10

Problem 11:

I am shuffling a deck of cards but I accidentally drop a card on the ground every now and then. After a while, I notice that I have dropped five cards. From above, the five cards look like one of the following pictures. Which picture could it be?

Problem 12:

This rectangle has been made by joining two squares together. Each square has an area of $25 \mathrm{~cm}^2$. What is the perimeter of the rectangle?

(A) 18 cm (B) 20 cm (C) 26 cm (D) 30 cm (E) 50 cm

Problem 13:

A kangaroo is chasing a wallaby that is 42 metres ahead. For every 4 -metre hop the kangaroo makes, the wallaby makes a 1-metre hop. How many hops will the kangaroo have to make to catch up with the wallaby?

(A) 8 (B) 10 (C) 11 (D) 14 (E) 21

Problem 14:

A piece of straight wire is 50 cm long. Six right-angled bends are made in the wire, so that it ends up looking like the diagram shown:

The lengths of two sections are shown. What is the length marked $x$ ?

(A) 28 cm (B) 31 cm (C) 34 cm (D) 36 cm (E) 39 cm

Problem 15:

Margie and Rosie both live near Lawson train station. Each plans to catch the 10 am train. Margie thinks her watch is 10 minutes fast, but in fact it is 10 minutes slow. Rosie thinks her watch is 10 minutes slow, but in fact it is 5 minutes fast. Each of them leaves home to catch the train without having to wait on the platform. Who misses the train, and by how much?

(A) Margie by 10 minutes (B) Margie by 20 minutes (C) Rosie by 5 minutes (D) Rosie by 15 minutes (E) Neither of them

Problem 16:

Sally was playing with block patterns and came up with this one she called Hollow Squares. They all follow the same pattern.

How many blocks would she need to make Hollow Square 7 ?

(A) 28 (B) 30 (C) 32 (D) 34 (E) 53

Problem 17:

I have a jug containing 100 mL of liquid, which is half vinegar and half olive oil. How much vinegar must I add to make a mixture which is one-third olive oil?

(A) 30 mL (B) 40 mL (C) 50 mL (D) 60 mL (E) 100 mL

Problem 18:

It is 10 am now. What time will it be in 2021 hours time?

(A) 11 am (B) 1 pm (C) 3 pm (D) 4 pm (E) 5 pm

Problem 19:

Alexander's pen leaked on his addition homework, covering up three of the digits in the calculation shown. How many different possibilities are there for the correct working?

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

Problem 20:

Our school is organising a quiz night. They are expecting from 25 to 35 people to come. The people will be arranged in teams of 6 to 8 people. What is the range of possible numbers of teams to expect?

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

Problem 21:

In an election for school captain, there were 4 candidates and 453 students each voted for one candidate. The winner's margins over the other candidates were 31,25 and 19. How many votes did the winner receive?

(A) 113 (B) 127 (C) 129 (D) 131 (E) 132

Problem 22:

Three blocks with rectangular faces are placed together to form a larger rectangular prism. All blocks have side lengths which are whole numbers of centimetres. The areas of some of the faces are shown, as is the length of one edge.

In cubic centimetres, what is the volume of the combined prism?

(A) 360 (B) 540 (C) 600 (D) 720 (E) 900

Problem 23:

Three gears are connected as shown. The two larger gears have 20 teeth each and the smaller gear has 10 teeth.
The middle gear is rotated half a turn in the direction of the arrows, turning the M upside down.

What do the three gears look like after this rotation?

Problem 24:

Anna has a large number of tiles of three types:

She wants to build a green rectangle with a white frame similar to those below.

She builds such a rectangle using as many tiles as possible while using exactly 20 completely green tiles. How many tiles will she use altogether?

(A) 80 (B) 66 (C) 48 (D) 42 (E) 39

Problem 25:

In Jeremy's hometown of Windar, people live in either North, East, South, West or Central Windar. Jeremy is putting together a chart showing where the students in his class live, but unfortunately his dog chewed his survey results before he managed to label the five columns.

He only remembers two things about the survey: South Windar is more common than both East and Central Windar, and the number of students in North and Central Windar combined is the same as the total of the other three regions. Using only this information, how many columns can Jeremy correctly label with \(100 \%\) certainty?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 5

Problem 26:

Pip starts with a large square sheet of paper and makes two straight cuts to form four smaller squares. She then takes one of these smaller squares and makes two more straight cuts to make four even smaller ones, as shown.

Continuing in this way, how many cuts does Pip need to make to get a total of 1000 squares of various sizes?

Problem 27:

Seven of the numbers from 1 to 9 are placed in the circles in the diagram in such a way that the products of the numbers in each vertical or horizontal line are the same. What is this product?

Problem 28:

A hare and a tortoise compete in a 10 km race. The hare runs at \(30 \mathrm{~km} / \mathrm{h}\) and the tortoise walks at \(3 \mathrm{~km} / \mathrm{h}\). Unfortunately, at the start, the hare started running in the opposite direction. After some time, it realised its mistake and turned round, catching the tortoise at the halfway mark. For how many minutes did the hare run in the wrong direction?

Problem 29:

I want to place the numbers 1 to 10 in this diagram, with one number in each circle. On each of the three sides, the four numbers add to a side total, and the three side totals are all the same. What is the smallest number that this side total could be?

Problem 30:

The sum of two numbers is 11.63 . When adding the numbers together, Oliver accidentally shifted the decimal point in one of the numbers one position to the left. Oliver got an answer of 5.87 instead. What is one hundred times the difference between the two original numbers?