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Garden International School Welcomes you to the
South East Asia Mathematics Competition 2004
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Individual Competition Part I
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• There are 50 multiple choice questions
• You have 2 minutes to finish each question
• There will be a break after 25 questions
• A trial question will now follow

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Trial Question (2 minutes)
2n1 X 4n1 equals
(a) 2n2 (b) 23n3 (c) 42n2
(d) 42n1 (e) 24n-2
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START
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1. How many squares are there in the following
figure?

1. 187
2. 188
3. 189
4. 190
5. 191

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2. Worker A can paint a building in 7
days while worker B can paint a building
in 3 days. If they both work together, how
long will it take them to paint a
building?
A) 50.2 hours B) 50.4 hours C) 50.6 hours D)
50.8 hours E) 60 hours
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• How many triangles are there in the
• following figure?

• 24
• B) 25
• C) 26
• D) 27
• E) 28

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4. A triangle has sides 9cm, 40cm and 41cm. What
is its area?
A) 820cm2 B) 180cm2 C) 184.5cm2 D) 90cm2 E)
360cm2
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5. Each exterior angle of a regular polygon is
8?. How many sides does the polygon have? A 30
B 90 C 40 D 45 E 50
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6. A 12 sided polygon is shown below
Evaluate angle A angle B angle C
angle D angle E angle F

1. 180º
2. 360º
3. 540º
4. 720º
5. Cannot tell

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7. Two concentric circles are drawn such that a
chord of the larger circle, which is of length 12
cm, is tangent to the smaller circle. What is the
shaded area between the two circles?

1. 6p
2. 12p
3. 24p
4. 36p
5. Cannot tell

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8. What is the sum of the integers which are
divisible by 3 and lie between 1 and 1000? A
166830 B 166833 C 166836 D 166839 E 166842

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9. What is the highest common factor of 648,
744 and 864? A 8 B 12 C 16 D 24 E 48
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10. A school teaches 3 foreign languages French,
German and Spanish. Every student in
class 7A studies at least one foreign
language. If there are 49 students in class 7A
and the following statements all hold
23 students study French 31 students
study German 32 students study Spanish
8 students study French and German 12
students study French and Spanish 19
students study German and Spanish Find
the number of students that study all 3
languages. A) 0 B) 1 C) 2 D) 3 E) 4
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11. How many ways can the letters of the
word SUPERINTELLIGENT be arranged?
A) 16! B) 16!/(2!2!2!2!3!) C)
1!1!1!1!1!2!2!2!2!3! D) 16!/(2x2x2x2x3)
E) 16!/11!
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12. The prime factorization of 1050625 is
abcd. Evaluate abcd. A) 52 B)
53 C) 54 D) 55 E) 56
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13. An analogue clock displays the time
as 743. What is the angle between the
hour hand and minute hand? A) 18º
B) 26.5º C) 27.5º D) 28.5º
E) 48º
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• A square of side length l is inscribed in a
  circle inscribed in a square of side length L.
  Find l/L.
• A) cos 30º
• B) cos 45º
• C) cos 60º
• D) tan 30º
• E) 1/3

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15. A circle with centre O is shown

1. v55 cm
2. v39 cm
3. 5 cm
4. 4v2 cm
5. Cannot tell

If EF8 cm and BE3 cm, how long is OF?
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1. An equilateral triangle is divided by arcs as
   shown

ABBCCDDEEFAF1 cm. What is the area of the
shaded region?

1. v3-p
2. v3-p/2
3. v3-p/3
4. v6-p/3
5. v6-p/2

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17. By 8p.m. all the guests had arrived at the
party. By 9p.m. a third had left. By 10p.m. a
third of those remaining had gone. By 11p.m. a
third of those remaining had again departed and
eight guests were left at the party. How many
guests were there originally at 8p.m.? A) 36
B) 33 C) 30 D) 27 E) 24
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18. A car travels from town A to town B at
an average speed of 20 mph and
returns at an average speed of 30 mph.
What is the average speed for the whole
journey? A) 22 B) 23 C) 24 D) 25
E) 26
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19. A newspaper has four pages missing. One of
them is page 21. If the back page is 28, what are
the numbers of the other three missing pages?
A) 6,7,20 B) 7,8,20 C) 7,8,22) D)
8,9,22 E) 9,10,22
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20. What is the next number in the sequence 47,
86, 149, 242, 371, . A 542 B 544 C 534 D
528 E Cannot tell
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21. A person travels 3 m east, 5 m north, 8 m
west, 13 m south, 21 m east, 34 m north, 55 m
west and 89 m south. How far is he from his
starting point? A) 102 m B) 5v205 m C)
7v130 m D) v1830 m E) 3v610 m
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22. A regular pentagon ABCDE has side length
1. What is the length of AC?

1. sin 36º
2. cos 36º
3. (v51)/2
4. (v51)/4
5. 4sin2 36º3

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23. Which of the following is equal to tan
22.5º? A) 0.5tan 45º B) 2-v2 C) v2-1
D) 2v2 E) v21
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24. All the five digit numbers that can be made
from the digits 1, 6, 7, 8 and 9, without
repetition, are summed. What is the total? A
10399944 B 7539432 C 8295384 D 8266584 E 10666584
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25. Complete the sequence 1, 2, 5, 16, 45, 106,
217, 400, ___ A) 680 B) 681 C) 682 D) 683
E) 684
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BREAK TIME
32
Individual Competition Part 2
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33
26. A certain company offers "750 hours of
free Internet use for new subscribers. On closer
inspection it becomes clear that this time must
be used during the new subscriber's first month
of membership! What is the maximum number
of hours in any one month of the year? A 168 B
692 C 720 D 744 E 750
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27. "20 off everything", screamed the sale
posters. I paid 60. What would I have paid
before the sale? A 60 B 66 C 72 D 75 E
80
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28. Which of the following has the greatest
value? A. 0.3 X 7 B. 0.5 X 5 C. 0.2 X
11 D. 0.09 X 30 E. 0.026
X 100
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29. Alice's room is furnished with three-legged
stools and four-legged chairs. There are 17 legs
in all (excluding Alice's!). How many
three-legged stools are there? A. 1 B.
2 C. 3 D. 4 E. 5
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• Old Martha has 5 children, each of whom has 4
  children, each of whom has 3 children, each of
  whom is childless. How many descendants does Old
  Martha have?
• A 12 B 20 C 25 D 60
• E 85

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31. In the diagram the lines PQ and SR are
parallel, as are the lines PS and QT. What is the
value of x? A 139 B 138 C 124 D 98 E 97
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32. The engineering company, Sparks and Tensor
has a complicated system of conveyor belts in its
factory. Components must travel along these belts
in the directions shown by the arrows.How many
different routes are there from A to F along the
conveyor belts? A 4 B 5 C 6 D 7 E 8
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33. Which is the smallest? A B C D E
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34. In the diagram PQ PR RS. What is the
size of angle x? A 54 B 720 C 90
D 108 E 144
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35. It is evening and Meg. who is 1m tall, casts
a shadow of length 3m. If Meg stands on her
brother's shoulders, which are 1.5m above the
ground, how long a shadow will she and her
brother cast? A 3m B 4.5m C 5.5m D 6.5m E 7.5m
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36. Equal regular pentagons are placed together
to form a ring in the manner shown. The diagram
shows the first three pentagons. How many more
are needed to complete the ring? A 6 B 7 C
8 D 9 E 10
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37. In a fit of madness, the bee Zerk left the
hive and flew 1m due North, then 1m due East,
then 1m vertically up. She then made a beeline
for the hive, flying directly home in a straight
line. How far, in m did she fly altogether? A
4 B 3 C 3 D 5 E6
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38. From the information given in the diagram
shown alongside, what is the value of a b? A
3 B 4 C 5 D 6 E 7  
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39. The diagram shows a semicircle containing a
circle which touches the circumference of the
semicircle and goes through its centre. What
fraction of the semicircle is shaded? A
B C D E
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• The letter-product of a number is obtained by
  Multiplying the number by the number of letters
  in the corresponding word. For example, the
  letter-product of 5 is 20, since there are 4
  letters in the word 'five' and 5 X 4 - 20. Which
  of the following has the largest letter-product?
• A 6 B 7 C 8 D 9 E 10

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41. How many of the numbers are
greater than 1 ? A 1 B 2 C 3 D
4 E 5
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42. Below are three statements. (I) 310
is even (II) 310 is odd (III) 310 is
square Exactly which ones are true? A (i)
only B (ii) only C (iii) only D (i) and
(iii) E (ii) and (iii)
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43. I walk to the bike shop at 3 miles per hour
and cycle back along the same route at 12 miles
per hour. What is my average speed, in miles per
hour, for the time I am actually travelling on
the route? A 3.75 B 4.8 C 6 D 8 E 9
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44. A ream of paper (500 sheets) is 5.4 cm thick.
What is the thickness of a single sheet, correct
to one significant figure? A 1 mm B 0.5 mm C
0.1 mm D 0.05 mm E 0.01 mm
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45. If then what is the value of A
6 B 8 C 10 D 12 E 18
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46. Susan is taller than Sophie, but shorter
than Sandra. Stephanie is taller than Sarah, but
shorter than Susan. Who is the tallest of these
five girls? A Susan B Sophie
C Sandra D Stephanie E Sarah
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47. Anna has 3 brothers and 5 sisters. Her
brother Tom has S sisters and B brothers. What is
the value of S X B ? A 8 B 10 C 12
D 15 E 18
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48 What is the value of (a) -1000 (b)
-80 (c) 0 (d) 924 (e) 1000
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49. Ima Divvy used her calculator and
multiplied a number by 20 instead of by 2. What
could she now do to obtain the correct
answer? A divide by 20 B divide by 40
C multiply by 10 D multiply by 0.5 E
multiply by 0.1
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50. A tourist attraction, which opens every
day, needs 30 000 visitors per day on average to
break even. Last week there were 120 000
visitors. What is the number of visitors needed
this week to break even over the two-week
period? A 43 000 B 90 000 C 180 000
D 210000 E 300 000
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THE END