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E A

The English Schools

Foundation

Hong Kong

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Trial Question

How many prime numbers are there between 90 and 110?

A) 4 B) 5 C) 7 D) 23 E) 61

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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) 4 B) 5 C) 7 D) 23 E) 61


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


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


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


5. A triangle has sides of length 5cm, 5cm, and 6cm.

What is its area, in cm2 ?

A 12 B 15

C 18 D 20 E 30


6. If and , then

equals

A 1 B 5 C D 1 E 2

2

1a

3

1b

ab

ba

36

1


7. The number 56665 is a palindrome, it reads the same forwards and backwards.

The next palindrome will be 56765. What will the 8th palindrome be after 56765 ?

A 56865 B 57065 C 57475D 57575 E 58085


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

CArea

TArea

3

4

132

7

4

15

X

Y


9. How many blocks are missing in this cube?

(Assume that all unseen blocks are present)

A 64 B 27

C 25 D 24 E 23


10. The area of the triangle that is bounded by y = 2x, y = 6 and y = 6 x is

A 1 B 1½ C 2 D 2½ E 3


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


12. How many squares are there in this diagram ?

A) 23 B) 39 C) 42

D) 45 E) 46


13. Rearranging the digits of the number 579 produces different numbers.

The sum of all such numbers, including 579, is

A) 4662 B) 4065 C) 3705D) 3687 E) 3303


14. The area of a circle is 36cm2. The circumference, in cm is

A 6 B 18 C 12

D 12 E 18


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) 14400 E) 28800


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


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

......6

1

5

1

4

1

3

1

2

1


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) 8 B) 24 C) 36 D) 48 E) 60


19. Give the next number in the sequence

2 17 82 257 626

A) 1027 B) 1297 C) 1513 D) 2027 E) 2107


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 21 B 19C 16 D 13

E 10


21. What is the maximum number of 70 angles in a heptagon?

A) 2 B) 3 C) 4 D) 5 E) 6


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 1 B 2 C 3 D 4 E 5


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


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) 20 B) 24 C) 25 D) 49 E) 50

1238


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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26. Which of the following is midway

between and ?

A) B) C)

D) E)

5

1

25

13

25

17

15

7

5

3

25

9

25

8


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) 36 B) 16 C) 15 D) 14 E) 13


28. The sum of the acute angles at A, B, C, D and E is

A) 150 B) 200 C) 240 D) 180 E) 360

A

B

CD

E


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) 5.0C) 5.2 D) 5.4 E) 5.6


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


31. In the diagram, the value of y is

A) 85 B) 40 C) 36 D) 30 E) 20

20

y

3y


32. If x is an integer, how many integer values of y will there be for

A) 0 B) 1 C) 2

D) 3 E) More than 3

2)1(2( xy


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 100m C 400m D 1000m E None of the these.


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) 0 B) 3 C) 6D) 12 E) 24


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 25.2 B 28C 31.36 D 33.6 E 42


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) 24 B) 25 C) 30

D) 32 E) 40


37. is equal to

A) B)

C)

D) 1 E)

mn

n

nm

m

22 mn mn2

22

222

nm

mnmmn

nm


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) 7 B) 21 C) 22

D) 23 E) 24


39. What is the total number of digits needed to number the pages of a book from 1 to 250 inclusive ?

A) 637 B) 639 C) 640D) 642 E) 643


40. Which of these four dice is different from the other three ?

A First B Second C Third

D Fourth E All dice the same


41. When 324 is divided by 5 the remainder is

A 0 B 1 C 2 D 3 E 4


42. What is the difference between one hundred millionths and one hundred millionth ?

A) 0 B) C)

D) 1000 E) 100 000 000

000000100

1

000000100

9999


43. The greatest value of

is

A 5 B 3 C 1 D 0 E 1

Acos21


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) 7 B) 8 C) 9D) 10 E) 11


45. The largest divisor of 723 , other than itself, is

A 29.35 B 28.36 C 28.35

D 25.35 E 26.36


46. If then equals

A) B) C) D) E)

4

7

ba

ba2

2

b

a

3

11

16

49

9

49

16

121

9

121


47. What is the next term in this sequence of numbers?

1, 1, 2, 5, 29, …..

A) 866 B) 145 C) 107 D) 73 E) 53


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

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M C S E A The English Schools Foundation Hong Kong Click when ready