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Individual Competition Round 1 Questions 1-25

Test your problem-solving skills with 25 multiple-choice questions. Each question must be answered within 2 minutes. No breaks in this round. Can you answer them all correctly?

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Individual Competition Round 1 Questions 1-25

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  1. Click when ready...

  2. Individual Competition Round 1 Questions 1 - 25 Click when ready...

  3. 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

  4. Trial Question (2402 + 2402) x 50 equals • 120 100 B) 240 000 C) 480 400D) 240 300 E) 240 200

  5. Get Ready To Start…

  6. 1. Which of the following is an odd number? A) 14 + 7 B) 34 + 5 C) 54 + 3 D) 74 + 2 E) 114 + 1 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  7. 2. Which of the following hexominoes is not a possible net for a cube? • B) C) • D) E) You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  8. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  9. The value of is: • A) B) • C) D) • E) You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  10. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  11. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  12. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  13. 9 x 4 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  14. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  15. Which of the following integers has the smallest number of factors? • A) 26 B) 35 C) 44 • D) 53 E) 62 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  16. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  17. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  18. What is the value of • A) √3 B) 3 C) 27 • D) 81 E) 243 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  19. 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) You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  20. 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% You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  21. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  22. 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 + 1B) 3n2– 3n C) 3n2– 1 • D) 3n2E) 3n2– 9n +1 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  23. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  24. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  25. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  26. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  27. What is the area of the triangle shown here? • 20 B) 20 + 3x • 80 D) 20x • E) It depends on x 20 x 2x You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  28. 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 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  29. The graph of x2 – y2 = 0is: • A) a straight line • B) a parabola • C) a circle • D) a single point • E) two straight lines You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

  30. If and what • is the value of ? • A) 2 B) 4 • C) 8 D) 16 • E) 32 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

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