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2. Individual Competition Round 2 Questions 26 - 50 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

4. Get Ready To Start…

5. How many three-digit positive integers are perfect squares? • A) 23 • B) 22 • C) 21 • D) 20 • E) 19 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

6. Paul gives half of his marbles to his best friend and then a third of those remaining to his sister. If his sister receives 9 marbles then the number Paul keeps is: • A) 9 B) 18 C) 27 D) 36 E) 54 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

7. 28. Rectangle ABCD is divided into 5 congruent rectangles as shown. The ratio AB:BC is: A B D C A) 2:1 B) 3:2 C) 4:3 D) 5:2 E) 5:3 You now have 30 seconds left STOP 1 4 6 2 7 8 9 10 5 3

8. James wrote four tests with a maximum score of 100 in each one. The average mark (mean) he obtained on these tests was 88. What is the lowest score he could have achieved on one of these tests? • A) 0 B) 22 C) 50 D) 52 E) 88 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

9. The number of solutions (x, y) of the equation 3x + y = 100, where x and y are positive integers, is • A) 33 B) 34 C) 97 D) 100 E) 101 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

10. 31. On a circle, ten points A1, A2,…, A10are equally spaced. If C is the centre of the circle, what is the size, in degrees, of the angle A1A5C? A) 10 B) 18 C) 36 D) 72 E) 144 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

11. 32. How many square numbers between 1 and 1001 are divisible by 2? A) 15 B) 16 C) 30 D) 32 E) 500 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

12. 33. In the diagram, AC = AB and CX = XY = YB. Which of the following statements is true? C X Y B A A) None of the statements B, C, D, E is correct B) C) D) E) You now have 30 seconds left STOP 1 3 5 6 7 8 9 10 4 2

13. Which of the following five numbers shares a common factor (>1) with exactly one of the other four numbers? • A) 91 B) 52 C) 39 D) 35 E) 24 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

14. I have 64 candle stubs. I can make one full new candle using the wax from 4 stubs. A full candle burns for one hour and then goes out, leaving a stub. If I only light full candles, what is the maximum number of hours I can have candlelight? • A) 16 B) 20 C) 21 D) 64 E) 80 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

15. 36. How many different triangles can be made from five rods of length 2, 3, 4, 5 and 6 cm if they are taken three at a time? • A) 6 B) 7 C) 10 D) 20 E) 60 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

16. Three days ago, yesterday was the day before Sunday. What day will it be tomorrow? • A) Monday B) Tuesday C) Wednesday D) Thursday E) Friday You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

17. ABCD is a square, and P is a point inside the square such that triangle ADP is equilateral. How big is angle PBC? • A) 15o B) 20o C) 25o D) 30o E) 75o You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

18. I have an unlimited number of $1, $2, $3, $4 and $5 stamps. How many different combinations of stamps are there which total $6? • A) 12 B) 10 C) 9 D) 8 E) 6 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

19. 40.434 is a palindromic number, reading the same from right to left as fromleft to right. The number of palindromic numbers between 100 and 1000 is: A) 64 B) 81 C) 90 D) 100 E) None of these You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

20. Huggy the slug crawls d centimetres in t minutes. How many hours would it take her to cover a distance of d metres? • A) B) C) • D) E) You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

21. How many real numbers have the property that the sum of x and the reciprocal of x2is equal to the sum of x2and the reciprocal of x? • 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. How many different order arrangements can be made using all seven letters of the word “ORDERED” each time? • A) 24 B) 56 C) 315 D) 630 E) 5040 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

23. √8 + √18 equals: • A) √19 • B) √20 • C) √26 • D) √28 • E) √50 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

24. I have ten cards numbered 0, 1, 2,…, 9. How many different ways are there to select three different cards whose numbers total 18? • A) 6 B) 7 C) 8 D) 9 E) 10 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

25. 46. The area of the small square is one-third of the area of the large square. What is the value of ? y x A) B) C) D) √3 E) √3 – 1 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

26. Which gives the biggest answer? • A) 16 x 24 • B) 17 x 23 • C) 18 x 22 • D) 19 x 21 • E) 20 x 20 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

27. A cube has surface area 216 cm2. What is its volume (in cm3)? • A) 6 B) 36 C) 125 D) 162√6 E) 216 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

28. How many prime numbers between 10 and 99 remain prime when their digits are reversed? • A) 9 B) 10 C) 11 D) 12 E) 13 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2

29. 50. A drawer contains seven red socks, seven blue socks and seven white socks. Socks are selected one at a time at random. How many socks must be selected to be sure of getting at least two pairs of the same colour? A) 4 B) 7 C) 9 D) 10 E) 12 You now have 30 seconds left STOP 1 10 9 8 7 6 5 4 3 2