Examples of Sets from 2001

Set Two and Set Five are shown here:

2001 SET TWO Time allowed - 30 minutes Kirsty's school locker has a two-digit number on it. The sum of the two digits is 10 and their difference is 2. If the locker number is less than 50, what number is it? When Louise put 25 golf balls in her bag, it was 1/2 full. When Matt put 17 golf balls in his bag, it was 1/3 full. When Nick put 12 golf balls in his bag, it was 1/4 full. Who had the largest bag? The pictures on the right show how matches can be used to make triangular shapes that have one, two and three matches along a side. How many matches are needed to make a triangular shape of the same pattern, which has 6 matches along one side? One rectangular wall of Bob's house contains a door and a window. Bob wants to paint this wall, but not the door (nor the window!). The wall is 7 m by 3 m, the door is 2 m by 1 m, and the window is 2 m by 1.5 m. If each can of paint covers 4 sq m, how many cans should Bob buy for one coat of paint? Tina's house and her school are on the corners of square blocks as shown. The shortest distance from her house to the school is along the sides of 5 blocks. Two such paths are shown. How many different paths are there of this length from Tina's house to her school (including the two paths shown)?

2001 SET FIVE Time allowed - 30 minutes 12 is 20% of what number? A rectangular piece of paper has length A and width B. It is folded in half twice: first left to right and then top to bottom as shown, to make another rectangle. This final rectangle has length B and width C. What is A divided by C? Visitors to a school fair had to guess the number of marbles in a jar. Prizes were awarded on how close the guesses were to the exact number. First prize went to Daniel who guessed 125 marbles, second prize to Jeremy who guessed 140, third prize to Esther who guessed 142, and fourth prize to Gideon who guessed 121. How many marbles were in the jar? A group of girls plan to buy their netball coach a special birthday cake. The cake will cost them $5 each. However, on the day that they collect the money, two of the girls are away sick, and the other girls have to pay $6 each. What is the cost of the cake? A type of key has four places where a notch can be cut out. These are shown shaded in the top picture. For example, the middle key has two notches cut, while the bottom key has all four notches cut. If every key has at least one notch cut, how many different keys can be made?