Australian Mathematics Competition - 2013 - Middle Primary - Grade 3 & 4 - Questions and Solutions

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Problem 1:

Ten years after the year 2013 will be
(A) 2003
(B) 2013
(C) 2014
(D) 2023
(E) 2113

Problem 2:

How many edges does a cube have?

(A) 4
(B) 6
(C) 8
(D) 9
(E) 12

Problem 3:

Each lap of Laura's school running track is 400 metres long. She runs 3 laps. How far does she run?
(A) 300 m
(B) 600 m
(C) 800 m
(D) 1200 m
(E) 3000 m

Problem 4:

What fraction of this rectangle is shaded?

(A) one-fifth
(B) two-fifths
(C) two-thirds
(D) one-third
(E) three-fifths

Problem 5:

What is three times the difference between 9 and 3 ?
(A) 6
(B) 9
(C) 18
(D) 36
(E) 81

Problem 6:

Jenny's hat has the words COTTON CLUB written on it. What does she see on her hat when she looks in the mirror?

(A) CLUB N COTTO (B) B COTTON CLU (C) BUL CN COTTO (D) COTTON CLUB (E) UBL CN COTTO

Problem 7:

Sally is playing a board game where you throw a dice numbered from 1 to 6 , move along a numbered board and then follow the instructions on each square you land on. On one turn, she throws a 6 and lands on a square which tells her to go back 4 squares. This puts her on a square which tells her to go forward 3 squares. She finishes up on square 7 . What square did she start that turn on?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Problem 8:

Joel is in the centre of a maze which fills a 10-metre square. He knows he can get out of the maze if he follows the path in the spiral pattern below. The maze has exits on the boundary at \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}\) and E . By which exit will Joel leave the maze?

(A) (A)
(B) (B)
(C) (C)
(D) (D)
(E) (E)

Problem 9:

What is the difference between the largest and smallest 3 -digit numbers which can be made from rearranging the 3 digit cards below?

(A) 198
(B) 200
(C) 202
(D) 298
(E) 302

Problem 10:

Brad thinks of a number, doubles it and adds 2 . His result is 14 . What was the number he thought of at the start?
(A) 6
(B) 7
(C) 8
(D) 12
(E) 30

Problem 11:

Alice has two 50 c coins, three 20 c coins and eight 5 c coins. David has four 20 c coins and six 10 c coins. How much more money does Alice have than David?
(A) 40 c
(B) 60 c
(C) 80 c
(D) \(\$ 1.40\)
(E) \(\$ 2.00\)

Problem 12:

Jim is one year older than his brother and one year younger than his sister. The sum of their three ages is 30 . How old is his sister?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

Problem 13:

Mary counts on in 3 s starting at 30 whilst John counts on in 5 s starting at 20 . If they say each number out loud together, starting at the same time, what same number will they both say together?
(A) 30
(B) 40
(C) 45
(D) 50
(E) 60

Problem 14:

Given a 2 -digit number, a new 3 -digit number is formed by putting the digit 1 after it. The new number is
(A) the original number plus 1
(B) ten times the original number plus 1
(C) one hundred plus the original number
(D) one hundred times the original number
(E) one hundred times the original number plus 1

Problem 15:

How many triangles are in the following picture?

(A) 9
(B) 10
(C) 13
(D) 14
(E) 17

Problem 16:

To mix concrete you need 4 shovelfuls of sand, 2 shovelfuls of gravel and 1 shovelful of cement. If 56 shovelfuls are put into a mixer, how many would be of gravel?
(A) 7
(B) 16
(C) 20
(D) 32
(E) 40

Problem 17:

A train from Brisbane to Cairns leaves at \(1: 25 \mathrm{pm}\) on Tuesday, and arrives at \(7: 35 \mathrm{pm}\) on Wednesday. How long was the trip?
(A) 6 h 10 min
(B) 24 h 50 min
(C) 18 h 10 min
(D) 29 h 10 min
(E) 30 h 10 min

Problem 18:

An online poll asked the question, 'Is Maths your favourite subject?'
The results of the poll are as follows:
6 out of every 10 voted yes.
3 out of every 10 voted no.
1 out of every 10 was undecided.
If 120 people answered yes, how many of those polled were undecided?
(A) 20
(B) 24
(C) 30
(D) 45
(E) 70

Problem 19:

George is planning a garden bed which is to be 1 metre wide and a whole number of metres long. It is to be surrounded by 1 metre \(\times 1\) metre pavers as shown in the diagrams below. As the design for the garden gets longer, the number of pavers needs to increase.

Which of the following best describes the number of pavers required for each garden bed design?
(A) The number of pavers needed is 8 times the length of the garden bed.
(B) The number of pavers needed is 6 times the length of the garden bed plus 2.
(C) The number of pavers needed is 4 times the length of the garden bed.
(D) The number of pavers needed is 4 times the length of the garden bed plus 2 .
(E) The number of pavers needed is 2 times the length of the garden bed plus 6 .

Problem 20:

Each triangle in the diagram is equilateral. What fraction of the largest triangle is shaded?

(A) \(\frac{1}{4}\)
(B) \(\frac{15}{64}\)
(C) \(\frac{1}{3}\)
(D) \(\frac{3}{16}\)
(E) \(\frac{7}{32}\)

Problem 21:

Kathy plays Eddie in a game with 12 rounds. In each round the winner scores 5 points and the loser scores 3 points. When the game ends, Eddie's total score is 46 points. How many rounds did Kathy win?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

Problem 22:

Nine cards numbered 1 to 9 are set out as in the diagram. The sum of the numbers in the vertical column is equal to the sum of the numbers in the horizontal row. How many different numbers could be used in the central square of the diagram?

(A) 1
(B) 3
(C) 5
(D) 7
(E) 9

Problem 23:

There are thirty 20c coins in a row. I replace every second coin with a 50 c coin. Next, I replace every third coin with a \(\$ 1\) coin. Finally, I replace every fourth coin with a \(\$ 2\) coin. The value of the thirty coins is now
(A) \(\$ 18.50\)
(B) \(\$ 22.80\)
(C) \(\$ 25.60\)
(D) \(\$ 26.50\)
(E) \(\$ 27.80\)

Problem 24:

There is a shaded square inside a rectangle as shown. From \(A\) to \(B\) is 6 cm and from \(C\) to \(D\) is 8 cm . What is the perimeter of the large rectangle?

(A) 28 cm
(B) 27 cm
(C) 26 cm
(D) 25 cm
(E) 24 cm

Problem 25:

Jake and Joe wanted to buy the same magazine. Jake needed \(\$ 2.80\) more to buy it, while Joe needed \(\$ 2.60\) more. So they put their money together and bought the magazine. They had \(\$ 2.60\) left. How much was the magazine?
(A) \(\$ 10\)
(B) \(\$ 9\)
(C) \(\$ 8\)
(D) \(\$ 7\)
(E) \(\$ 6\)

Problem 26:

I take 2 vitamin C tablets every day. If I increase my dose to 3 tablets a day, a full bottle would last 8 days less. How many tablets are in a full bottle?

Problem 27:

Each side of this large square is 30 cm . The middle of each side is joined to a corner as shown. What area, in square centimetres, has been shaded?

Problem 28:

Starting at 100 and going through to 999 , how many numbers have two or more digits the same?

Problem 29:

In how many ways can three different numbers be selected from the numbers 1 to 12 , so that their sum can be exactly divided by 3 ?

Problem 30:

Adam, Barney and Joe carry 999 books out of the library. Adam works for 3 hours, Barney works for 4 hours and Joe works for 5 hours. They work at different speeds, with Adam carrying 5 books for every 3 books Barney carries and every 2 books Joe carries. How many books did Adam carry?

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