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Individual Competition Round 1 Questions 1 - 25
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• There are 25 multiple choice questions
• You have 2 minutes to finish each question
• There is no break in this round
• A trial question will now follow

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Trial Question

• (2402 2402) x 50 equals
• 120 100 B) 240 000
• C) 480 400 D) 240 300
• E) 240 200

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• 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?
• 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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• The value of
  is
• A) B)
• C) D)
• E)

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• 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
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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
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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) 16 B) 14 C) 12v3 D)
13 E) 12
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• 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 exact cube 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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• What is the value of
• A) v3 B) 3 C) 27
• D) 81 E) 243

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• 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)

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• 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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• 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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• 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?
• 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) v3.9204 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?
• 0.03 B) 0.3 C) 3 D) 30 E) 300

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• 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
  Beryls average speed than Mikes (in metres per
  hour)?
• A) 1.2 B) 10 C) 11 D) 100 E) 1200

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• What is the area of the triangle shown here?
• 20 B) 20 3x
• 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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• 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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• If and what
• is the value of ?
• A) 2 B) 4
• C) 8 D) 16
• E) 32

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