Questions 1 to 10, 3 marks each
1.
8
× 9
3
equals
(A) 27
(B) 11
(C) 24
(D) 20
(E) 17
2.
In the diagram, where P QR is a straight
line, x equals
(A) 60 (B) 70 (C) 80 (D) 90 (E) 100
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x
◦
25
◦
75
◦
P
Q
R
3.
If 110 + x = 97 + y, then
(A) x + 13 = y
(B) x = y + 13
(C) x + y = 13
(D) x + y = 207
(E) x
− y = 207
4.
Andy bought 2 chocolates at $1.35 each. How much change should he get from $5?
(A) $2.70
(B) $2.60
(C) $3.30
(D) $2
(E) $2.30
5.
Of the following, which is the largest fraction?
(A)
7
15
(B)
3
7
(C)
6
11
(D)
4
9
(E)
1
2
6.
The average weight of a group of 4 boys and 6 girls is 64 kg. The average weight
of the boys is 70 kg. What is the average weight of the girls?
I 2
7.
Nicky started a mobile phone call at 10:57 am. The charge for the call was 89 cents
per minute and the total cost for the call was $6.23. Nicky’s call ended at
(A) 11:27 am
(B) 11:14 am
(C) 11:04 am
(D) 11:46 am
(E) 11:05 am
8.
A fish tank in the shape of a rectangular prism is
1 m long and 25 cm wide. If it holds 55 L when full,
its height, in centimetres, is
(A) 11
(B) 22
(C) 44
(D) 110
(E) 220
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9.
The larger of two numbers is 3 more than twice the smaller number. If their sum
is 18, what is the smaller number?
(A) 3
(B) 4
(C) 5
(D) 7
(E) 9
10.
A square with side length 2 units is placed
next to a square with side length 5 units as
shown. The shaded area, in square units, is
(A) 13.5
(B) 14.5
(C) 18.5
(D) 19.5
(E) 26
2
5
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.
Questions 11 to 20, 4 marks each
11.
Successive discounts of 10%, 20% and 50% are equivalent to a single discount of
(A) 64%
(B) 75%
(C) 26
2
3
%
(D) 36%
(E) 70%
12.
The game of Four Tofu is played on a 4
× 4 grid.
When completed, each of the numbers 1, 2, 3 and
4 occurs in each row and column of the 4
× 4 grid
and also in each 2
× 2 corner of the grid.
When the grid shown is completed, the sum of the
four numbers in the corners of the 4
× 4 grid is
2
1
1
3
4
13.
In the diagram, P OX = QOX and QOY = Y OZ = ZOR. If P OY = 33
◦
and XOZ = 45
◦
, the size of P OR is
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Q
R
X
Y Z
O
(A) 60
◦
(B) 65
◦
(C) 69
◦
(D) 71
◦
(E) 78
◦
14.
P QRS is a parallelogram and T lies on
P Q such that P T : T Q = 3 : 2. The
ratio of the area of P T RS to the area
of P QRS is
(A) 1 : 2
(B) 2 : 3
(C) 3 : 4
(D) 4 : 5
(E) 5 : 6
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P
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15.
When 50 is divided by a whole number, the remainder is 5. How many different
values are possible for this whole number?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
16.
What fraction of the regular hexagon in the diagram
is shaded?
(A)
1
4
(B)
1
3
(C)
3
8
(D)
5
12
(E)
1
2
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17.
In a school photo, the 630 pupils are arranged in rows. Each row has 3 more pupils
in it than in the row in front. Of the numbers below, which number of rows is
impossible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
18.
A number of runners competed in a race. When Jack finished, there were half as
many runners who had finished before him compared to the number who finished
behind him. Jill was the 10th runner to finish behind Jack and there were twice as
many runners who had finished before her compared to the number who finished
behind her. How many runners were there in the race?
I 4
19.
P QRS is a square with side
√
3. X is
a point on P Q, Y and Z are points on
P S and QR respectively. XY
QS and
XZ
P R. The sum of the lengths of
XY and XZ is
(A)
√
5
(B)
√
6
(C)
√
7
(D)
√
8
(E) 3
S
Q
P
R
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Y
20.
Each of Andrew, Bill, Clair, Daniel and Eva either always lies or is always truthful,
and they know which each of them is.
Andrew says that Bill is a liar.
Bill says that Clair is a liar.
Clair says that Daniel is a liar.
Daniel says that Eva is a liar.
The largest possible number of liars among them can be
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Questions 21 to 25, 5 marks each
21.
On her birthday in 2007, Rachel’s age is equal to twice the sum of the digits of the
year in which she was born. How many possible years are there in which she could
have been born?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
22.
A border of black counters is placed around a rectangular
array of white counters in a way similar to that shown in
the diagram. If the number of white counters is equal
to the number of black counters, for how many different
numbers of white counters can this be done?
~
~
~
~ ~ ~ ~ ~ ~
~ ~ ~ ~ ~
~
~
n n n n
n n n n
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
23.
P QR is a right-angled triangle with
P R = 3 cm and QR = 4 cm.
The
square ST U V is inscribed in
P QR.
What is the length, in centimetres, of
the side of the square?
(A)
30
17
(B)
12
7
(C)
5
3
(D)
60
37
(E)
60
39
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T
V
U
24.
There are four lifts in a building. Each makes three stops, which do not have to
be on consecutive floors or include the ground floor. For any two floors, there is
at least one lift which stops on both of them. What is the maximum number of
floors that this building can have?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 12
25.
A bee can fly or walk only in a straight line between any two corners on the inside
of a cubic box of edge length 1. The bee managed to move so that it visited every
corner of the box without passing through the same point twice in the air or on
the wall of the box. The largest possible length of such a path is
(A) 2 + 5
√
2
(B) 1 + 6
√
2
(C) 7
√
2
(D)
√
3 + 6
√
2
(E) 4
√
3 + 3
√
2
For questions 26 to 30, shade the answer as an integer from 0 to 999 in
the space provided on the answer sheet.
Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks,
question 29 is 9 marks and question 30 is 10 marks.
26.
What is the smallest number of odd numbers in the range 1, . . . , 2006 such that,
no matter how these numbers are chosen, there will always be two which add to
2008?
27.
Two semicircles of radius 1 are drawn
on the diameter of a semicircle of radius
2. A circle C touches all three
semicir-cles as shown. If the radius of the circle
C is
a
b
, where a are b are integers with
no common factors, then what is the
value of a + b?
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C
