SECTION ONE - (3 points problems)

1. Four chocolate bars cost 6 EUR more than one chocolate bar. What is the cost of one chocolate bar? (A) 1 EUR (B) 2 EUR (C) 3 EUR (D) 4 EUR (E) 5 EUR

2. 11.11 − 1.111 = (A) 9.009 (B) 9.0909 (C) 9.99 (D) 9.999 (E) 10

3. A watch is placed face up on a table so that its minute hand points north-east. How many minutes pass before the minute hand points north-west for the ﬁrst time? (A) 45 (B) 40 (C) 30 (D) 20 (E) 15

4. Mary has a pair of scissors and ﬁve cardboard letters. She cuts each letter exactly once (along a straight line) so that it falls apart in as many pieces as possible. Which letter falls apart into the most pieces?

(A)

(B)

(C)

(D)

(E)

5. A dragon has ﬁve heads. Every time a head is chopped oﬀ, ﬁve new heads grow. If six heads are chopped oﬀ one by one, how many heads will the dragon ﬁnally have? (A) 25 (B) 28 (C) 29 (D) 30 (E) 35

6. In which of the following expressions can we replace each occurrence of the number 8 by the same positive number (other than 8) and obtain the same result? (A) (8 + 8) : 8 + 8 (D) (8 + 8 − 8) · 8 (B) 8 · (8 + 8) : 8 (E) (8 + 8 − 8) : 8 (C) 8 + 8 − 8 + 8

7. Each of the nine paths in a park is 100 m long. Ann wants to go from A to B without going along any path more than once. What is the length of the longest route she can choose? 1 of 7

International Kangaroo Mathematics Contest 2012 – Cadet B

A (A) 900 m (B) 800 m (C) 700 m (D) 600 m (E) 400 m

8. The diagram shows two triangles. In how many ways can you choose two vertices, one in each triangle, so that the straight line through the vertices does not cross either triangle? (A) 1 (B) 2 (C) 3 (D) 4 (E) more than 4

9. Werner folds a sheet of paper as shown in the ﬁgure and makes two straight cuts with a pair of scissors. He then opens up the paper again. Which of the following shapes cannot be the result?

(A)

(B)

(C)

(D)

(E)

10. A cuboid is made of four pieces, as shown. Each piece consists of four cubes and is a

single colour. What is the shape of the white piece?

(A)

(B)

(C)

(D)

(E) 2 of 7

International Kangaroo Mathematics Contest 2012 – Cadet

SECTION TWO - (4 points problems)

11. Kanga forms two 4-digit natural numbers using each of the digits 1, 2, 3, 4, 5, 6, 7 and 8 exactly once. Kanga wants the sum of the two numbers to be as small as possible. What is the value of this smallest possible sum? (A) 2468 (B) 3333 (C) 3825 (D) 4734 (E) 6912

12. Mrs Gardner grows peas and strawberries. This year she has changed the rectangular pea bed to a square by lengthening one of its sides by 3 metres. As a result of this change, the area of the strawberry bed was reduced by 15 m2 . What was the area of the pea bed before Last year This year Peas

Peas

Strawberries the change? (A) 5 m2 (B) 9 m2

Strawberries (C) 10 m2 (D) 15 m2 (E) 18 m2

13. Barbara wants to complete the diagram by inserting three numbers, one in each empty cell. She wants the sum of the ﬁrst three numbers to be 100, the sum of the three middle numbers to be 200 and the sum of the last three numbers to be 300. What number should Barbara insert in the middle cell of the diagram?

10

(A) 50 (B) 60

130

(C) 70 (D) 75 (E) 100

14. In the ﬁgure, what is the value of x? 3 of 7

International Kangaroo Mathematics Contest 2012 – Cadet

100◦ 58◦ (A) 35

93◦ x◦

(B) 42

(C) 51

(D) 65

(E) 109

15. Four cards each have a number written on one side and a phrase written on the other. The four phrases are ”divisible by 7”, ”prime”, ”odd” and ”greater than 100”, and the four numbers are 2, 5, 7 and 12. On each card, the number does not correspond to the phrase on the other side. What number is written on the same card as the phrase ”greater than 100”? (A) 2 (B) 5 (C) 7 (D) 12 (E) impossible to determine

16. Three small...