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7. You now have 30 seconds left 10987654321STOP Trial Question There are 2 painters. David can paint a wall in 6 minutes, and Joanne can paint a wall in 3 minutes. How long would it take to paint the wall if they worked together ?

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10. You now have 30 seconds left 10987654321STOP 1. Twelve is the first abundant number. A number is abundant if the total of all the numbers that divide into the number is bigger than the number. 1, 2, 3, 4, 6 all divide into 12. 1 + 2 + 3 + 4 + 6 = 16. There are 5 other abundant numbers less than 40, find them.

11. You now have 30 seconds left 10987654321STOP 2.A certain substance doubles in volume every 5 minutes. At 9.00am, a small amount, x, is placed in a container and at 10.00am, the container just fills. When was it one quarter full?

12. You now have 30 seconds left 10987654321STOP 3. How many triangles are there in the diagram ?

13. You now have 30 seconds left 10987654321STOP 4. To 1 significant figure, how many hours have you been alive ?

14. You now have 30 seconds left 10987654321STOP 5. Alan and May’s ages add up to 25. May and John’s ages add up to 29. Caroline is 14. Her age is exactly halfway between Alan and John’s ages. How old is May ?

15. You now have 30 seconds left 10987654321STOP 6. What fraction of this rectangle is blue ?

16. You now have 30 seconds left 10987654321STOP 7. We are two numbers less than 100. When we are divided by 2, 4, or 5 we leave a remainder of 1. If you divide us by 3 there is no remainder. Who are we ?

17. You now have 30 seconds left 10987654321STOP 8. Place the numbers 1 to 9 in each of the small triangles so that the sum of the numbers in each of the four larger triangles is 25. 10

18. You now have 30 seconds left 10987654321STOP 9.64 is both a square number and a cube number since 8 2 = 64 and 4 3 = 64. What is the next number after 64 which has this property?

19. You now have 30 seconds left 10987654321STOP 10. A Fibonacci sequence starts with two terms which you add together to find the next term, for instance 10, 12, 22, 34, 56, 90 Can you find two starting numbers which would give 100 as the sixth term ?

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23. You now have 30 seconds left 10987654321STOP 11. In a 4-digit number (  0000 ) the sum of the first two digits is equal to that of the last two digits the sum of the first and last digit is equal to the third digit the sum of the second and fourth digit is twice the sum of the other two digits What is this 4-digit number ?

24. You now have 30 seconds left 10987654321STOP 12. In a 24 hour day, from midnight to midnight, how many times are the hands of a clock at right angles to each other?

25. You now have 30 seconds left 10987654321STOP 13. As part of his classes, Harry has to learn about Anti-Magic Squares. These are squares whose rows, columns and diagonals all add to different numbers. Using the numbers 1 to 9, help Harry find an Anti-Magic Square. ??? ??? ???

26. You now have 30 seconds left 10987654321STOP 14. Find all four possible answers to this equation.

27. You now have 30 seconds left 10987654321STOP 15.Using N for North, S for South, W for West and E for East, describe how to get from the entrance to the exit. Each letter means move one square in that direction. The start is E N N E … N W E S Exit Entrance

28. You now have 30 seconds left 10987654321STOP 16. Both the sails of my model boat are in the shape of a right-angled triangle. They are of different areas, each being an exact number of square centimetres. All their edge lengths are different as well, but each is an exact number of centimetres. However, the area of each is numerically equal to its perimeter. What is the area of each of the two sails ?

29. You now have 30 seconds left 10987654321STOP 17. Can you find the integer x such that 2x is a square and 3x is a cube?

30. You now have 30 seconds left 10987654321STOP 18. A deltahedron is a 3-dimensional shape all of whose faces are equilateral triangles. The simplest of these is a regular tetrahedron, which is made of 4 equilateral triangles. The deltahedron I have has 9 vertices. How many faces does my deltahedron have ?

31. You now have 30 seconds left 10987654321STOP 19. The two points (3, 2) and (15,  3) are the vertices which define the minor diagonal of a rhombus. If the major diagonal is twice the length of the minor diagonal, what are the coordinates of the other two vertices ?

32. You now have 30 seconds left 10987654321STOP 20. Four non-zero digits placed in these four squares will make two numbers across and two numbers down. If the sum of the four numbers is 67, fill in the square. ?? ??