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There are 25 multiple choice questions

You have 2 minutes to finish each question

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A trial question will now follow

Trial Question

(2402 + 2402) x 50 equals

A)120 100 B) 240 000

C) 480 400 D) 240 300

E) 240 200

Get Ready To Start…

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1. Which of the following is an odd number?

A) 14 + 7

B) 34 + 5

C) 54 + 3

D) 74 + 2

E) 114 + 1

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2. Which of the following hexominoes is not a possible net for a cube?

A) B) C)

D) E)

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3. I write out the numbers from 1 up to thirty in words. If N denotes

the number of times I write the letter ‘n’, M denotes the number of times I write the letter ‘m’,

and C denotes the number of times I write the letter ‘c’, then N + M + C equals:

A) 31 B) 30 C) 29 D) 28 E) 27

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4. The value of is:

A) B)

C) D)

E)

1 1 1 11 1 1 1

2 3 4 5

1

120

11

120

14

30

175

60

3

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5. What is the probability that the next person you meet has an

above average (= mean) number of arms?

A) 0 B) Nearly 0

C) 0.5 D) Nearly 1

E) 1

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6. In this addition, different letters stand for

different digits, but each letter represents the same digit each time it appears. If the letter O stands for 7, what digit must U represent?

TWO

+TWO

FOUR

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

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7. A square peg just fits in a round hole. What fraction of the hole is occupied by the peg?

A) B)

C) D)

E) None of these

2

π

π-1

22

π - 22

1-π

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8. The 12 digits in a credit card number are to be written in the boxes below. The sum of any three consecutive digits is 16.

The value of x is:

A) 3 B) 4 C) 5 D) 6 E) 7

9 x 4

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9. In the diagram, the triangle is equilateral.

The ratio of the area of the inscribed circle to the area of the

circumscribed circle is:

A) 1:6 B) 1:4 C) 1:2√3 D) 1:3 E) 1:2

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10. Which of the following integers has the smallest number of factors?

A) 26 B) 35 C) 44

D) 53 E) 62

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11. For the simultaneous equations

2x – 3y = 4 and 6y – 4x = 2:

A) x = 1, y = -2/3 B) x = 0, y = 0 C) x = 2, y = 5/3 D) There are infinitely many

solutions E) There is no solution

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12. The units digit of an exactcube:

A) Is never 0 B) Is never 2

C) Is never 3 D) Is never 9

E) Can be any digit 0 - 9

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13. What is the value of

A) √3 B) 3 C) 27

D) 81 E) 243

20160

7 6 5 4 3 3

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14. If h hens lay e eggs in d days, how many days would it take H hens to lay E eggs?

A) B)

C) D)

E)

Hde

Eh

EHd

he

Ehe

Hd

ehd

EH

Ehd

He

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15. On Saturdays I work in Pizza Shack. Employees get 40% off the price of

any meal. On Monday night, prices are reduced by 30% for all customers. And as a special promotion this

month, all prices have been cut by 25%. What is the most I can save

altogether if I go for a meal at Pizza Shack some time during this month?

A) 95% B) 68.5% C) 55% D) 40% E) 31.5%

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16. A sequence begins 1, 3, 4, 7, 11,…, each term is equal to the sum of the two previous terms. How many of

the following statements are true?

I The 20th term is divisible by 2

II The 30th term is divisible by 3

III The 40th term is divisible by 4

IV The 50th term is divisible by 5

A) 0 B) 1 C) 2 D) 3 E) 4

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17. An n by n by n cube is constructed from n3 unit cubes glued together, and the large cube is suspended in space. If I walk around the cube with one eye closed, what is the largest number of unit cubes I would ever be able to see at one time?

A) 3n2 – 3n + 1 B) 3n2 – 3n C) 3n2 – 1

D) 3n2 E) 3n2 – 9n +1

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18. A metal rod AB hangs vertically from a hinge at A, so that the end B just touches the horizontal ground 2 m from a vertical wall. While A stays fixed, the lower end B is pushed to one side until it touches the wall, 2 cm above the ground. How long is the rod (in m)?

A) 100 B) √3.9204 C) 100.01

D) 2 E) 100.005

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19. An equilateral triangle is initially completely black. First the middle quarter is painted white. Then the middle quarter of each of the three remaining black triangles is painted white and so on. What fraction of the triangle ultimately remains black?

A) 0 B) 1/4 C) 1/3 D) 1/2 E) 9/13

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20. In 1990, the Australian Government decided that Australia would plant one billion

(i.e. one thousand million) trees in the following decade. If one billion trees were planted

during the 10 years, on average, how many were planted per second?

A) 0.03 B) 0.3 C) 3 D) 30 E) 300

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21. Forty years ago Mike McNamara cycled 445.0 km in

12 hours. In the same time trial Beryl Burton completed 446.2 km. How much faster was Beryl’s average speed than Mike’s (in metres per hour)?

A) 1.2 B) 10 C) 11 D) 100 E) 1200

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22. What is the area of the triangle shown here?

A) 20 B) 20 + 3x

C) 80 D) 20x

E) It depends on x

20

x 2x

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23. Rectangle ABCD is made up of 6 squares. The areas of two of the squares are shown. The perimeter of rectangle ABCD in cm is:

A) 44 B) 46 C) 48 D) 50 E) 52

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24. The graph of x2 – y2 = 0 is:

A) a straight line

B) a parabola

C) a circle

D) a single point

E) two straight lines

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25. If and what

is the value of ?

A) 2 B) 4

C) 8 D) 16

E) 32

1x y 3x y 2 2

2x y