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 Junior Division

Questions 1 to 10, 3 marks each

1. The value of 2008 + 8002 is

(A) 1010 (B) 4004 (C) 10 008 (D) 8910 (E) 10 010

2. Which of the following numbers has the largest value?

(A) 2.15 (B) 2.2 (C) 2.08 (D) 2.1 (E) 2.185

2 cm .
.. ..
.... ......

3. The perimeter of the figure, in centimetres, is 2 cm

4 cm .......
(A) 8 (B) 10 (C) 12
(D) 16 (E) 20
...... ......
.. ...

4 cm

1
4. One half of 199 is
2
1 3 1 1 3
(A) 95 (B) 95 (C) 99 (D) 99 (E) 99
2 4 4 2 4

5. The value of x is
. .
... ...
(A) 135 (B) 95 (C) 35 ....
...
...
...
...
...
.
........ .
........
.. . .. .
(D) 55 (E) 45 ... .
...
...
...
...
... .

135◦ .
...
...
...
.

...
...
...
..
x◦

200 × 8
6. The value of is
200 ÷ 8
(A) 1 (B) 8 (C) 16 (D) 64 (E) 200

2 2

1
7. How many squares of any size are there
in the diagram? 1
(A) 9 (B) 11 (C) 12
(D) 14 (E) 16 1
1 1
1
1 1

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8. A train left Fassifern at 8:58 am and arrived at Broadmeadow at 9:34 am on the

same day. The time taken, in minutes, was

(A) 82 (B) 22 (C) 36 (D) 38 (E) 78

9. The digits 5, 6, 7, 8 and 9 can be arranged to form even five-digit numbers. The
tens digit in the largest of these numbers is

(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

10. P QRS is a square and points E and F are outside the square so that P QE and
QRF are equilateral triangles. The size of  EQF , in degrees, is

(A) 60 (B) 90 (C) 120 (D) 150 (E) 180

Questions 11 to 20, 4 marks each

11. A rectangle has an area of 72 square centimetres and the length is twice the width.
The perimeter, in centimetres, of the rectangle is

(A) 34 (B) 36 (C) 42 (D) 48 (E) 54

2 1
12. Marbles of three different colours are in a tin and of the marbles are red, are
5 3
green and the remaining 12 are yellow. The number of marbles in the tin is

(A) 30 (B) 45 (C) 54 (D) 60 (E) 90

L ...........
.. ....
.. ....
S Q
13. In the diagram, triangles P QR and LMN are
..
.. .... ..............
.... ............
.. .. ................ ..

both equilateral and  QSM = 20◦ . What is the ...........

............. ....
..
. .. . .
. .
. .
. ....
20◦
................
.... .
..
..
.

P ..
....
....
...
... .. .... ..
. .... ..
...
value of x?
... .....
... .. ..
... . .. ....
... ... .. .......
.... ..
M
.....
... . ....
..... . ..
.. ......
(A) 70 (B) 80 (C) 90 .. ...
.... .....
.. ..
..
..
. ...........
..........
... .
.. ...........
(D) 100 (E) 110 ..
..
..
x◦ ...
...
.. .......
.. ........... ..
... .
....
..
... ..... .
..... ..... ...
.. ............
N ...
... ..
....
R

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14. At half-time in a soccer match between Newcastle and Melbourne, the score was
Newcastle 1, Melbourne 0. Three goals were scored in the second half. Which of
the following could not be the result of the match?
(A) The match was drawn (B) Newcastle won by 2 goals
(C) Melbourne won by 2 goals (D) Newcastle won by 1 goal
(E) Newcastle won by 4 goals

15. In how many ways can 12 be written as the sum of two or more different positive
whole numbers? (Changing the order of addition does not count as a different
way.)

(A) 12 (B) 13 (C) 14 (D) 15 (E) 16

16. How many different positive numbers are equal to the product of two odd one-digit
numbers?

(A) 25 (B) 15 (C) 14 (D) 13 (E) 11

17. The perimeter of this rectangular paddock is 700 m. It is subdivided into six
identical paddocks as shown.

The perimeter, in metres, of each of the six smaller paddocks is

1
(A) 116 (B) 300 (C) 200 (D) 150 (E) 600
3

18. The student lockers at Euler High School are to be numbered consecutively from 1
to 500 using plastic digits which cost 5 cents each. The total cost of all the digits
will be

(A) $25 (B) $63.65 (C) $69.50 (D) $69.60 (E) $85

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19. In the grid below, the squares are to be filled with the numbers 1, 2, 3 and 4 so
that they appear once only in each row, each column and each diagonal.

1
2
3 X
Y
The largest possible value of X + Y is
(A) 4 (B) 5 (C) 6 (D) 7 (E) 8

20. The average of one group of numbers is 4. A second group contains twice as
many numbers and has an average of 10. The average of both groups of numbers
combined is
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

Questions 21 to 25, 5 marks each

21. A cube with edge length 2 metres is cut up into cubes each with edge length 5
centimetres. If all these cubes were stacked one on top of the other to form a tower,
the height of the tower would be
(A) 32 km (B) 160 m (C) 1600 m (D) 3.2 km (E) 320 m

22. A number is less than 2008. It is odd, it leaves a remainder of 2 when divided by
3 and a remainder of 4 when divided by 5. What is the sum of the digits of the
largest such number?
(A) 26 (B) 25 (C) 24 (D) 23 (E) 22

23. Farmer Taylor of Burra has two tanks. Water from the roof of his farmhouse is
collected in a 100 kL tank and water from the roof of his barn is collected in a
25 kL tank. The collecting area of his farmhouse roof is 200 square metres while
that of his barn is 80 square metres. Currently, there are 35 kL in the farmhouse
tank and 13 kL in the barn tank.
Rain is forecast and he wants to collect as much water as possible. He should:
(A) empty the barn tank into the farmhouse tank
(B) fill the barn tank from the farmhouse tank
(C) pump 10 kL from the farmhouse tank into the barn tank
(D) pump 10 kL from the barn tank into the farmhouse tank
(E) do nothing

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24. A fishtank with base 100 cm by 200 cm and depth 100 cm contains water to a depth
of 50 cm. A solid metal rectangular prism with dimensions 80 cm by 100 cm by
60 cm is then submerged in the tank with an 80 cm by 100 cm face on the bottom.
... ..
... ...
6 ....
...
....
...
...
...
.... ...
.... ...
.... ...
.... ...
.. ...
.

..................... .......................... . . . . . . . . . . ...

............................... ..................................................................... .......
100 . . ... . . . . . . . . . . . ............ .
............................... ............................................................................. .............
..................... .............................................. ...........
..
...
...
...
...
...
...
...
..................... ................. . . . . .................... ............. ... ...
. . . . . . ... . . ..................... . .
................................. ............................................................................. .........................
..................... ................................................... ...................
.................................................................. ...................
.......... ....................
............................ .................................................................................. ............................
? .......... ....................
.................... ......................................... .. .. .. .. .. .. .. .. .. ...............................
.................. ...................................................................
................ ................. . . . . ..........................................
.............. ........................................................................
............ ...................................................................
50 ...
60
.......... ................... . . . ......................................... ....
........ ........................................................................
100 ...... ...................................................................
.... ....................................................................
... . . . . . . . . . . . . . ....................................... 80
...
...
....

200 100
The depth of water, in centimetres, above the prism is then
(A) 12 (B) 14 (C) 16 (D) 18 (E) 20

25. A strip of paper is folded in a line at an angle x◦ to the sides and then folded
underneath forming an angle of 20◦ as shown.
..
... ...
... .....
... ...
... .
... ...
....... ...
...
... ...
... ...
... ...
... ...
... ...
... ...
.... ...
... ...
... ...
... ...
... ...
... ...
... ...
... ...
... ...
.... ...
... ...
... ..
..... ... ... ... ... ... ..... ..
.. ... ..
x◦....... =⇒
...
...
...
... ...
...
...
.. .... ..
.. ... ...
.. ....

..... ...
... ..... ......
... ... ... ..
... ... . ..
... ... .. .. ....
.
..
.. ........ ...
=⇒ ....
... ....
....
...

20◦ ... ...

.... ....
........ ......
.
....
. ...
...... ....
....
... ....
...
... .
......
... ....
... .......
The value of x is ....

(A) 60 (B) 65 (C) 70 (D) 75 (E) 80

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. A two-digit number ab and its reversal ba are both prime. For example, 13 and 31
are both prime. What is the largest possible sum of these two numbers ab and ba?

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27. Given a regular heptagon (7-sided polygon), how many obtuse-angled triangles are
there, where the vertices of each triangle are vertices of the heptagon?

28. A rectangular prism 6 cm by 3 cm by 3 cm is made up by stacking 1 cm by 1 cm

by 1 cm cubes. How many rectangular prisms, including cubes, are there whose
vertices are vertices of the cubes, and whose edges are parallel to the edges of the
original rectangular prism? (Rectangular prisms with the same dimensions but in
different positions are different.)

29. Let us call a sum of integers cool if the first and last terms are 1 and each term
differs from its neighbours by at most 1. For example, the sum 1 + 2 + 3 + 4 + 3 +
2 + 3 + 3 + 3 + 2 + 3 + 3 + 2 + 1 is cool.
How many terms does it take to write 2008 as a cool sum if we use no more terms
than necessary?

30. A monument has been constructed from identical stone cubes. The views from
above, the front f and the side s are shown.

f
above view front view side view
What is the largest number of stones in the monument consistent with these views?

***

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