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5. The English Schools Foundation Hong Kong Click when ready...

7. You now have 30 seconds left 10987654321STOP Trial Question How many prime numbers are there between 90 and 110? A) 4B) 5 C) 7D) 23E) 61

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10. You now have 30 seconds left 10987654321STOP 1. A bag contains 20 red sweets, 20 blue sweets, 20 yellow sweets and 20 green sweets. How many sweets would a blindfolded person have to eat to be certain of eating at least one sweet of each colour ? A) 4B) 5C) 7D) 23E) 61

11. You now have 30 seconds left 10987654321STOP 2. A person walks from A to B along the lines shown. How many different paths are there that are exactly 6 units long ? A) 23 B) 39 C) 42 D) 45 E) 46 A B

12. You now have 30 seconds left 10987654321STOP 3. If the distance between consecutive fence posts is 5 metres, how many posts would be needed to build a fence around a triangular region with sides 20m, 20m and 30m ? A) 11 B) 13 C) 14 D) 15 E) 17

13. You now have 30 seconds left 10987654321STOP 4.Thirty two teams enter a competition, the teams are paired randomly with each other in each round, the winning team goes forward to the next round. How many matches must be played before we get a winner ? A 16 B 31 C 32 D 64 E 496

14. You now have 30 seconds left 10987654321STOP 5.A triangle has sides of length 5cm, 5cm, and 6cm. What is its area, in cm 2 ? A 12B 15 C 18D 20E 30

15. You now have 30 seconds left 10987654321STOP 6.If and, then equals A  1B  5C D 1 E 2

16. You now have 30 seconds left 10987654321STOP 7. The number 56665 is a palindrome, it reads the same forwards and backwards. The next palindrome will be 56765. What will the 8 th palindrome be after 56765 ? A 56865B 57065C 57475 D 57575E 58085

17. You now have 30 seconds left 10987654321STOP 8.In the diagram you see a quarter-circle. A semi-circle is drawn with XY as the diameter. What is the ratio ? A B 1 C D E T C S X Y

18. You now have 30 seconds left 10987654321STOP 9. How many blocks are missing in this cube? (Assume that all unseen blocks are present) A 64B 27 C 25D 24E 23

19. You now have 30 seconds left 10987654321STOP 10. The area of the triangle that is bounded by y = 2x, y = 6 and y = 6  x is A 1B 1½ C 2D 2½ E 3

20. You now have 30 seconds left 10987654321STOP 11. It is actually impossible, but assuming that you could tear a playing card in half, put the two pieces together and tear again (getting four), put them together and tear again and so on 52 times and then piled up the pieces, approximately how high would the stack be ? A 5cm B 50cm C 1m D 100m E From the Earth to the Sun

21. You now have 30 seconds left 10987654321STOP 12. How many squares are there in this diagram ? A) 23B) 39C) 42 D) 45E) 46

22. You now have 30 seconds left 10987654321STOP 13.Rearranging the digits of the number 579 produces different numbers. The sum of all such numbers, including 579, is A) 4662B) 4065C) 3705 D) 3687E) 3303

23. You now have 30 seconds left 10987654321STOP 14. The area of a circle is 36  cm 2. The circumference, in cm is A 6  B 18  C 12  D 12  E 18 

24. You now have 30 seconds left 10987654321STOP 15. 5 boys and 5 girls sit around a circular table so that boys and girls alternate. How many different seating arrangements are there? A) 1440 B) 2880 C) 7200 D) 14400E) 28800

25. You now have 30 seconds left 10987654321STOP 16. A square floor is tiled with square tiles and there are 125 tiles on the diagonals. How many tiles are in the room? A) 125 B) 961 C) 2566 D) 3844 E) 15625

26. You now have 30 seconds left 10987654321STOP 17. How many terms of this series are needed to make a sum greater than 2½ ? A) 24 B) 22 C) 20 D) 18 E) 16

27. You now have 30 seconds left 10987654321STOP 18. Tom eats twice as many caterpillars as Jennifer, but Jennifer eats three times as many caterpillars as David. Tom eats 40 caterpillars more than David, how many caterpillars does Jennifer eat? A) 8B) 24C) 36 D) 48 E) 60

28. You now have 30 seconds left 10987654321STOP 19. Give the next number in the sequence 2 17 82 257 626 A) 1027B) 1297C) 1513 D) 2027 E) 2107

29. You now have 30 seconds left 10987654321STOP 20. Three vertices of a triangle are A (  5, 6), B (1, 10) and C (3, 20). M is the midpoint of AB. What is the length of MC ? A 21B 19 C 16D 13 E 10

30. You now have 30 seconds left 10987654321STOP 21. What is the maximum number of 70  angles in a heptagon? A) 2B) 3C) 4 D) 5 E) 6

31. You now have 30 seconds left 10987654321STOP 22. In a game of NIM two people take it in turns to take 1,2,3,4 or 5 matches from the centre pile. The person to take the last match is the winner. In order to win, how many matches should you need to take on your first go ? A 1B 2C 3 D 4 E 5

32. You now have 30 seconds left 10987654321STOP 23. In the diagram, if AD = CD = CB, and  A is 40 , then find  DCB. A) 40  B) 35  C) 25  D) 20  E) 10  B A D C

33. You now have 30 seconds left 10987654321STOP 24. Steve has a set of 100 cards numbered consecutively from 1 to 100. He forms pairs of cards which have a sum of 50, such as 12 and 38. How many such pairs can he form ? A) 20B) 24C) 25 D) 49 E) 50 12 38

34. You now have 30 seconds left 10987654321STOP 25. In an art class students are taught to shape a 1 ounce bag of clay into a small statue. During this process some clay is unused. For every five statues made there is enough clay to make one extra statue. If a student is presented with 25 ounces of clay, what is the maximum number of statues that they can sculpt ? A 25 B 30 C 31 D 50 E 51

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38. You now have 30 seconds left 10987654321STOP 26. Which of the following is midway between and ? A) B) C) D) E)

39. You now have 30 seconds left 10987654321STOP 27. An unusual die has its six faces labelled 1, 2, 3, 5, 7, 9. If two such dice are rolled, and the numbers rolled added together, then how many different sums are possible ? A) 36B) 16C) 15 D) 14 E) 13

40. You now have 30 seconds left 10987654321STOP 28. The sum of the acute angles at A, B, C, D and E is A) 150B) 200C) 240 D) 180 E) 360 A B C D E

41. You now have 30 seconds left 10987654321STOP 29. 4 boys take a French test and get an average of 4 marks. 6 girls take the same test and get an average of 6. What is the average for all 10 children? A) 4.8 B) 5.0 C) 5.2 D) 5.4 E) 5.6

42. You now have 30 seconds left 10987654321STOP 30. A large box measures 1.7 m by 1.2 m by 1.5 m. It is to be packed with smaller boxes each measuring 15 cm by 20 cm by 20 cm. What is the greatest number of small boxes that can be fitted into the larger box? A) 510 B) 480 C) 462 D) 448 E) 424

43. You now have 30 seconds left 10987654321STOP 31. In the diagram, the value of y is A) 85B) 40C) 36 D) 30 E) 20 20  yy 3y 

44. You now have 30 seconds left 10987654321STOP 32. If x is an integer, how many integer values of y will there be for A) 0B) 1C) 2 D) 3 E) More than 3

45. You now have 30 seconds left 10987654321STOP 33. A medium size jet has a wingspan of about 40 metres. An albatross is a bird with a wingspan of about 4 metres. If the jet is flying at 100m on a sunny day, at what height would the albatross have to fly to cast a shadow of about equal size ? A 10m B 100mC 400m D 1000m E None of the these.

46. You now have 30 seconds left 10987654321STOP 34. A five digit number 1**** uses the digits 1, 2, 3, 4, 5 once only and is divisible by 4. How many such numbers are there? A) 0B) 3C) 6 D) 12E) 24

47. You now have 30 seconds left 10987654321STOP 35. Mr Tung owns a piece of land. The exact shape of this land is shown here. The perimeter of the land in kilometres is exactly equal to the area of the land in square kilometres. What is the perimeter of his land in km ? A 25.2B 28 C 31.36D 33.6E 42

48. You now have 30 seconds left 10987654321STOP 36. In a chess league, each of the competitors plays each of the others once. If there are 300 games altogether, how many competitors are there ? A) 24B) 25C) 30 D) 32 E) 40

49. You now have 30 seconds left 10987654321STOP 37. is equal to A) B) C) D) 1 E)

50. You now have 30 seconds left 10987654321STOP 38. Thirty equally spaced points on the circumference of a circle are labelled in order with the integers 1 to 30. What number is diametrically opposite 7 ? A) 7B) 21C) 22 D) 23 E) 24

51. You now have 30 seconds left 10987654321STOP 39. What is the total number of digits needed to number the pages of a book from 1 to 250 inclusive ? A) 637B) 639C) 640 D) 642E) 643

52. You now have 30 seconds left 10987654321STOP 40. Which of these four dice is different from the other three ? A FirstB SecondC Third D FourthE All dice the same

53. You now have 30 seconds left 10987654321STOP 41. When 3 24 is divided by 5 the remainder is A 0B 1C 2D 3E 4

54. You now have 30 seconds left 10987654321STOP 42. What is the difference between one hundred millionths and one hundred millionth ? A) 0 B) C) D) 1000E) 100 000 000

55. You now have 30 seconds left 10987654321STOP 43. The greatest value of is A 5B 3C 1D 0E  1

56. You now have 30 seconds left 10987654321STOP 44. A whole number is called an ascending number if each digit in the number is greater than the digit on its left. 1679 is an example of an ascending number. How many ascending numbers are there between 4000 and 5000 ? A) 7B) 8C) 9 D) 10E) 11

57. You now have 30 seconds left 10987654321STOP 45. The largest divisor of 72 3, other than itself, is A 2 9.3 5 B 2 8.3 6 C 2 8.3 5 D 2 5.3 5 E 2 6.3 6

58. You now have 30 seconds left 10987654321STOP 46. If then equals A) B) C) D) E)

59. You now have 30 seconds left 10987654321STOP 47. What is the next term in this sequence of numbers? 1, 1, 2, 5, 29, ….. A) 866B) 145C) 107 D) 73 E) 53

62. You now have 30 seconds left 10987654321STOP 50. If x and y are integers and x > y, the number of integers between (but not including) x and y is A x  y B x + y C x  y  1 D x + y  1 E x  y + 1