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Individual
Competition
Part II
Questions 26 - 50
Click when ready...
•
There are 25 multiple choice
questions
•
You have 2 minutes to finish each
question
•
There will be no break in this round
•
A trial question will now follow
Click when ready...
Trial Question
(2 minutes)
n+
1
2 X
(a)
n+2
2
n+
1
4
(b)
equals
3n+3
2
(c)
2n+2
4
(d) 42n+1 (e) 24n-2
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26.Writing in 1864, Professor de
Morgan said he was x years old
in the year x2 AD. When was he
born?
A. 1804
B. 1849
C. 1801
D. 1808
E. 1806
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27. Write 1000000000 as the
product of two numbers, neither
of which contains any zeros.
A. 27 x 511
B. 28 x 510
C. 29 x 59
D. 210 x 58
E. 211 x 57
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28. An express train takes 3 seconds to
enter a tunnel, which is 1 km long.
If is is travelling at 120 km/h, how
long does it take to pass completely
through the tunnel?
A. 33 seconds
B. 30 seconds
C. 36 seconds
D. 2 minutes
E. 2 minutes 6 secs
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29. The value of (1)10 +(-1)7 + (-1)4 + (1)9
is:
A. 0
B. 1
C. 2
D. –1
E. -2
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30. A man bought 50 metres of rope
in a shop. He did not know it, but
the metre-rule used to measure
the rope was 1cm short. What
length of rope did he actually get?
A. 49.99 m
B. 49.5 m
C. 49.95 m
D. 49.05 m
E. 45 m
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31. The sum of 7 consecutive
integers is 84. The smallest of
these integers is:
A. 8
B. 9
C. 10
D. 11
E. 12
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1
2
32. If x= , find the largest value in the
list below.
A. x
B. x2
C.
x
D. 80% of x
E.
x
2
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33.If 24 + 23 + 22 + 22 = 2x, then
the value of x is:
A. 6
B. 4
C. 8
D. 5
E. 11
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34.In the sequence, each figure is
made up of small squares of side length
1. What is the outer perimeter of the
fifth figure in the sequence?
A. 9
B. 18
C. 20
D. 24
You now have 30 seconds left
E. 36
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35.Which of the following statements is
not true?
A. There is only one even prime number
B. 61 is a prime number
C. 196 is a perfect square number
D. 23 is the product of two different integers
E. 127 is a perfect cube
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36. In the multiplication example
shown A and B are two different
integers.
A8
x
3B
2730
Find the value of A.
A. 5
B. 6
C. 7
D. 8
You now have 30 seconds left
E. 9
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37.Which of the following is 25% less
than x.
A. 0.75x
B. 25x
C. 0.25x
D. 75x
E. x - 25
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38.Charlie spent of his money on a
book and then gave his brother 2 of
3
what was left. He then had $9.
How much money did Charlie start
with?
A. $27
B. $36
C. $48
D. $44
E. $40
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39.How many ten-thousandths are
required to make one-tenth?
A. 10
B. 100
C. 1000
D. 10000
E. 100000
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40. How many times does the second
hand of a clock revolve in one full
day of 24 hours?
A. 24
B. 60
C. 360 D. 1440 E.86400
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41. When my age is divided by 2, 3, 4
or 6 there is always a remainder of
1, but when divided by 7 there is no
remainder.
How old am I?
A. 14
B. 21
C. 35
D. 49
You now have 30 seconds left
E. 63
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42. A driver stops for a 20 minute break
every 2 hours (i.e. he drives for 2
hours and then stops for 20 minutes
before continuing). At what average
speed must he actually drive at if he
is to complete a 600 kilometre
journey in 6 hours.
A. 100 km/h
B. 112.5 km/h
C. 125 km/h
D. 132.5 km/h
E. 135 km/h
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43. Find the ratio of the area of a
regular hexagon to the area of an
equilateral triangle if their
perimeters are equal.
A. 3:2
B. 1:1
C. 1:3
D. 2:3
You now have 30 seconds left
E. 1:4
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44. Pierre celebrated his birthday on
February 2, 2001. On that day, his
age equalled the sum of the digits in
the year in which he was born. In
what year was Pierre born?
A. 1987
B. 1980
C. 1977
D. 1979
You now have 30 seconds left
E. 1971
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45. In the four digit number 4k32, k can
take the value of any digit from 0 to
9 inclusive.
How many solutions for k are there
to the calculation 4k32  12, so that
the answer is an integer?
A. 0
B. 1
C. 2
D. 3
You now have 30 seconds left
E. 4
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46. In a student council election InWook received 70% of the vote and
Jee-Hae received the remainder. InWook won the election by 112
votes.
How many students voted in the
election?
A. 240
B. 280
C. 320
D. 360
You now have 30 seconds left
E. 400
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47. A dice is biased such that
the probability of landing on
a 6 is ¼ and there exists and
equally likely probability of
landing on the numbers 1, 2,
3, 4, and 5.
Find the probability of rolling
the dice twice and obtaining
a five and a six in any order.
3
A.
40
3
B.
80
3
C.
20
1
D.
20
You now have 30 seconds left
1
E.
18
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48. I recently bought a 10-volume set of
encyclopaedias.
At present I have only arranged the first 9
volumes in order on my shelf, as shown
below. Where should I place the next
volume?
A. 6
and 3
B. 8
and 5
C. 1
and 7
D. 7
and 6
You now have 30 seconds left
E. None
of these
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49.What is the units’ digit of 8100?
A. 0
B. 8
C. 2
D. 4
E. 6
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50.Given that xy = 5, simplify
2
( x y )
2
A. 1
B. 220
C. 25
2
( x  y )2
D. 210
E. 240
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