2003 Junior

JUNIOR DIVISION

Questions 1 - 10, 3 marks each

1. 3004 − 2003 equals

(A) 999 (B) 991 (C) 1001 (D) 2001 (E) 2003

2. Which of the following is closest to 9?

(A) 9.2 (B) 8.17 (C) 8.7 (D) 9.21 (E) 8.71

P
3. The size of 6 RSQ, in degrees, is
(A) 120 (B) 130 (C) 140 110◦
100◦ a
(D) 150 (E) 160 S aaa Q

4. The temperature at Cooma rose from 7◦ C yesterday morning to

15◦ C yesterday afternoon. The number of degrees the temperature
rose was

(A) 5 (B) 7 (C) 8 (D) 10 (E) 12

5. Which of the following is equal to 50?

(A) 15 + (10 × 2) (B) 100 ÷ 5 (C) 2 × (5 × 10)

(D) (20 + 80) ÷ 10 (E) 200 ÷ 4

6. In the diagram, the size of P

6 P QT , in degrees, is L
37◦L
(A) 74 (B) 107 (C) 111 L
◦ L
(D) 101 (E) 121 74 L
R Q T

2003
7. equals
20.03
(A) 0.01 (B) 100 (C) 0.1 (D) 1 (E) 10
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8. The smallest number that 4, 5 and 7 will divide into is

(A) 70 (B) 140 (C) 210 (D) 280 (E) 1400

9. A square piece of paper is folded along the diagonals twice as shown.

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

...
- -
...
...
....
.....
s ......
@ ....>
...
..... @
...@ @
...

@ @

A cut is made along the dotted line in the third diagram to remove
the corner. When the paper is unfolded, which of the following
diagrams shows how the paper appears?

(A) (B) @ (C) @

@ @

(D) (E)
@

1 3
10. If of a number is 6, then of this number is
4 8
(A) 6 (B) 8 (C) 9 (D) 12 (E) 15

Questions 11 - 20, 4 marks each

11. Schoolteacher Mr Jones drove 54 kilometres from his house in the

country to the school. If the trip takes him 45 minutes, what is his
average speed in kilometres per hour?

(A) 72 (B) 60 (C) 48 (D) 75 (E) 84

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12. On the number line below, where would 0.12 be placed?

P Q R S

1 1 1 1
7 6 5 4

(A) To the right of S (B) Between R and S (C) Between Q and R

(D) Between P and Q (E) To the left of P

13. When George recently visited Latvia, one Latvian lat was worth
$US1.50, while $A1 was worth $US0.60. In this case, a Latvian lat
was worth

(A) $A1.80 (B) $A2.50 (C) $A2.75 (D) $A2.00 (E) $A3.00

n 1 1
14. If lies between and and n is an integer, then n equals
24 6 4
(A) 5 (B) 6 (C) 7 (D) 8 (E) 9

15. If S is the sum of the remainders when each of the numbers 30, 31,
32, 33, 34 and 35 is divided by 6, then what is the remainder when
S is divided by 6?

(A) 0 (B) 1 (C) 2 (D) 3 (E) 5

16. If it is 9am now, what time will it be in 2003 hours from now?

(A) 11pm (B) 8pm (C) 8am (D) 11am (E) 12noon

17. At Utopia High, each of the 1516 students voted either ‘YES’ or
‘NO’ on whether to change the school uniform. There were 1162
more ‘YES’ votes than ‘NO’ votes. The number of students who
voted ‘NO’ was

(A) 344 (B) 254 (C) 177 (D) 172 (E) 127
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18. The side of each of the equilateral .......

.......
.......
triangles in the figure is twice the .......
.......
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.....
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.................... ....
side of the central regular hexagon. .
.....
.
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.
....
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What fraction of the total area of ..
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the six triangles is the area of the .......
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hexagon? ...
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........ . .
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1 1 3 ... .. ...
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6 12 4 ............. .......
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1 2 .......
(D) (E)
4 3

19. When written in the dd/mm/yyyy format, the recent dates

10/02/2001 and 20/02/2002 are palindromic, as the digits read
the same forwards and backwards. The sum of the digits in the
first palindromic date nearest to and before 2000 is

(A) 26 (B) 32 (C) 16 (D) 28 (E) 30

20. Natasha buys 4 double icecreams and 2 single icecreams and pays
$16. The next day she buys 2 double icecreams and 4 single ice-
creams and pays $14. The cost of a double icecream is

(A) $1.50 (B) $2.00 (C) $2.50 (D) $3.00 (E) $3.50

Questions 21 - 30, 8 marks each correct response, 0 marks

each incorrect response, 3 marks each no response,
30 marks minimum for this section guaranteed

21. Our water supply comes from rainwater tanks filled by the rain
which lands on our roof. We find that 25 mm of rain puts 5000
litres of water in our tanks. If 80% of the water which lands on our
roof reaches the tanks, what is the ground area, in square metres,
covered by our roof? (1000 cm3 is 1 litre.)

(A) 25 (B) 2500 (C) 2000 (D) 250 (E) 200

22. Mum, Dad and their two children arrive at the river where there
is a boat that will hold one adult or two children. What is the
minimum number of trips across the river in either direction to get
the family across?

(A) 7 (B) 9 (C) 11 (D) 13 (E) 15

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23. A triangle is called scalene if no two sides are the same length.
The number of scalene triangles whose vertices are the vertices of
a given cube is
(A) 8 (B) 18 (C) 24 (D) 36 (E) 40

24. In a mathematical competition consisting of 12 problems, 8 marks

are given for each correct response, 0 marks for each incorrect re-
sponse and each no response is awarded 3 marks. Vicki scored
35 marks in this competition. The largest number of incorrect
responses she could have had is
(A) 1 (B) 8 (C) 11 (D) 2 (E) 7

25. The numbers from 1 to 15 are arranged in a triangular fashion, one

such arrangement is shown.
1
6 7
2 13 4
5 11 3 15
12 8 14 10 9
If they are arranged so that the sum of the numbers along each
side of the triangle is the same and is as small as possible what is
that sum?
(A) 20 (B) 24 (C) 28 (D) 32 (E) 36

26. Steve has a broken calculator. When just turned on, it displays
0. If the + key is pressed it adds 51. If the − key is pressed it
subtracts 51. If the × key is pressed it adds 85. If the ÷ key is
pressed it subtracts 85. The other keys do not function. Steve
turns the calculator on. The number closest to 2003 that he can
get using this calculator is
(A) 1989 (B) 2001 (C) 2002 (D) 2004 (E) 2006

27. A 10 cm × 10 cm × 10 cm cube is cut into 1 cm × 1 cm × 1 cm

cubes. As many of these cubes as needed are glued together to
form the largest possible cube which looks solid from any point on
the outside but is hollow inside. The maximum number of smaller
cubes left over is
(A) 81 (B) 32 (C) 66 (D) 125 (E) 134
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28. How many numbers less than 10 000 have the product of their digits
equal to 84?

(A) 24 (B) 30 (C) 42 (D) 72 (E) 84

29. A 3 × 3 square is divided up into nine 1 × 1 unit squares. Different

integers from 1 to 9 are written in these 9 unit squares. For each
two squares sharing a common edge, the sum of the integers in them
is calculated. The minimum possible number of different sums is

(A) 3 (B) 4 (C) 5 (D) 6 (E) 7

30. What is the largest number of cars which can leave in some order
from P and arrive in the reverse order at Q if movement is allowed
only from left to right and no car can pass another as the roads are
too narrow?
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(A) 6 (B) 5 (C) 8 (D) 4 (E) 7

Answer to AMC test paper (Junior 2003)