  # Recent Examples of Sets  ### 2015

#### SET THREE Time allowed - 30 minutes

1. 544 and 760 are both three-digit numbers whose digits add to 13.

What is the smallest three-digit number whose digits add to 13? 2. Bob managed to colour the different regions in this map using just three colours: red, green and blue. He did it so that no two adjacent regions had the same colour.

If he coloured region 1 blue and region 2 red, what colour did he use for region X?

3. Supa Cycles make both two-wheeled bicycles and three-wheeled tricycles. Last week they made 12 in total, and used 31 wheels. How many tricycles did they make? 4. Enter one A, one B and one C in each row and column of this design of 16 squares, leaving four squares empty. When viewed along one of the arrows the first letter you must see is the letter given.

Give the last row from left to right, using * for the empty square (e.g. A*BC).

5. One-tenth of the cars in a car park are yellow. Another car arrives and now one-ninth of the cars are yellow. How many cars are now in the car park?  ### 2015

#### SET FOUR Time allowed - 30 minutes

1. Jeremy pays the exact amount for his new \$17 T-shirt using \$5 notes and \$2 coins only.

In how many different ways can he do this?

2. There are three children in the Fong family and only one is a teenager. When their ages are multiplied together the result is 140.

How old is the teenager? 3. The three symbols in this design stand for numbers, where each row and each column has the total given.

What is the value of ?

4. The pages of a book are numbered 1, 2, 3, ... . In total, it takes 489 digits to number all the pages of the book.

What is the number on the last numbered page? 5. An isosceles triangle is one which has two sides of equal length.

How many different isosceles triangles of perimeter 25 units can be formed with all sides having lengths that are whole numbers?