Australian Mathematics Competition 2018 - Middle Primary Year 3 and 4 - Problems & Solutions

Problem 1:

What is double 4?

(A) 2
(B) 3
(C) 8
(D) 12
(E) 24

Problem 2:

Which pattern has exactly 10 dots?

Problem 3:

Which of the following is the same as 6 tens and 3 ones?
(A) sixty-three
(B) six and three
(C) thirty-six
(D) six hundred and three
(E) sixty-one

Problem 4:

When I add 11 and another number, I get 19. What is the other number?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Problem 5:

What is the diameter of this coin?

(A) 20 mm
(B) 21 mm
(C) 22 mm
(D) 25 mm
(E) 30 mm

Problem 6:

Which one of these numbers is closest to (208 ?)
(A) 190
(B) 200
(C) 205
(D) 210
(E) 218

Problem 7:

Kate made this necklace from alphabet beads.

She put it on the wrong way around, showing the back of the beads. What does this look like?

Problem 8:

Each day, tours of Parliament House and the National Museum begin at 8.30 am . The tours for Parliament House leave every 15 minutes and the tours for the National Museum leave every 20 minutes.

How often do the tours leave at the same time?
(A) every 5 minutes
(B) every 15 minutes
(C) every 30 minutes
(D) every 45 minutes
(E) every 60 minutes

Problem 9:

The children in class 3 P voted on their favourite pets. Sally recorded the results in a column graph but forgot to draw in the column for cats. There are 29 children in the class and everyone voted once. How many children voted for cats?

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

Problem 10:

Which of the following is a whole?
(A) 1 half plus 2 quarters
(B) 2 quarters plus 2 halves
(C) 3 quarters plus 1 half
(D) 1 half plus 1 quarter
(E) 4 quarters plus 1 half'

Problem 11:

Mrs Chapman put 58 books back on the library shelves. She put 12 books on each shelf except the last shelf. How many books did she put on the last shelf?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

Problem 12:

This solid cube is built from small cubes. How many small cubes cannot be seen from this view?

(A) 6
(B) 8
(C) 9
(D) 10
(E) 11

Problem 13:

Shelley walked into a lift. She went down 5 floors, up 6 floors, then down 7 floors. She was then on the second floor.
On which level did she enter the lift?

(A) 1st floor
(B) 2nd floor
(C) 3rd floor
(D) 6th floor
(E) 8th floor

Problem 14:

Six friends each make a phone call to another city. The cost of each call depends on the time taken for the call as well as the distance.

From this diagram decide whose phone call lasts longer than Pat's, but costs less.
(A) Al
(B) Bill
(C) Jo
(D) Mia
(E) Zac

Problem 15:

One of these shapes made of squares has been flipped and turned to make the following pattern, without any overlaps. Which one?

Problem 16:

Karen, Warren, and Andrew bought plastic letters to spell each of their names on their birthday cakes. Their birthdays are on different dates, so they planned to reuse letters on different cakes. What is the smallest number of letters they needed?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

Problem 17:

At Susie's party, they have four pizzas to share and each person gets $\frac{2}{3}$ of a pizza. How many people are at the party?

(A) 4
(B) 6
(C) 8
(D) 12
(E) 16

Problem 18:

Fred looked at the clock during the Library lesson. Which one of these times could the clock have shown?

Problem 19:

Three standard dice are sitting next to each other as shown in the diagram. There are 7 faces visible. How many dots are hidden on the other 11 sides?

(A) 26
(B) 36
(C) 41
(D) 54
(E) 63

Problem 20:

The numbers from 1 to 3 are entered into the circles in the grid shown. Two circles joined by a line may not contain the same number. There are several ways of doing this. What is the smallest possible total of the eight numbers?

(A) 10
(B) 12
(C) 14
(D) 15
(E) 16

Problem 21:

Six small eggs weigh the same as five medium eggs. Six medium eggs weigh the same as four large eggs. How many small eggs would weigh the same as five large eggs?

(A) 5
(B) 6
(C) 8
(D) 9
(E) 12

Problem 22:

Pictures of fruit have been placed in this grid to represent numbers less than 10 . The totals for each row and column are shown. What is the total value of an apple and an orange?

(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

Problem 23:

Warren drew two large squares that overlap to form the hexagon shown. The area of each small square is 1 square centimetre. In square centimetres, what is the total area of the hexagon that Warren drew?

(A) 12
(B) 36
(C) 48
(D) 60
(E) 72

Problem 24:

Beginning with a row of 20 coins, Anh takes the first coin, then every fourth coin after that. From the remaining coins, Brenda takes the first coin and every third coin after that. From the remaining coins, Chen takes the first coin and every second coin after that. Dimitris takes all the remaining coins. Does anyone get more coins than all the others?

(A) Yes, Anh does
(B) Yes, Brenda does
(C) Yes, Chen does
(D) Yes, Dimitris does
(E) No, they all get the same number of coins

Problem 25:

Yasmin has a \(20 \times 20 \) square of paper that is coloured on one side. She folds over a strip along each edge to make a white square with an \(8 \mathrm{~cm} \times 8 \mathrm{~cm}\) coloured square inside. How far from each edge is each fold?

(A) 8 cm
(B) 6 cm
(C) 4 cm
(D) 3 cm
(E) 1 cm

Problem 26:

Four archers are having some target practice, each with two arrows. Ari hits regions A and C for a total of 15 . Billy hits regions A and B for a total of 18 . Charlie hits regions B and C for a total of 13 . If Davy hits region B twice, what will his score be?

Problem 27:

A teacher wants her students to guess the three-digit number that she is thinking. She gives these clues:

• It is divisible by both 3 and 11 .
• If you subtract one, the result is divisible by both 2 and 7 .

Which number is it?

Problem 28:

These staircases are made from layers of blocks. Each staircase is one block wider, one block longer and one block taller than the previous staircase. How many blocks are needed to build the 12 -step staircase?

Problem 29:

In the algorithm below, the letters (a, b) and (c) represent different digits from 0 to 9 . What is the three-digit number (a b c) ?

Problem 30:

I wrote the counting numbers joined together:

\(1234567891011121314151617 \ldots\)

Which of the counting numbers was I writing when the 100th zero was written?