June 2015 Logic & Maths Problems

1. A survey of a town revealed the following data:

60% of the population were female.
70% of the population had blue eyes
80% of the population had blonde hair.

What is the SMALLEST POSSIBLE percentage of the population which is CERTAIN to be blue-eyed, blonde-haired females?

2. Untitled Capture-15
State whether each of these ropes would form a knot when the ends are pulled apart.

3. The table below represents a Mastermind game, based on digits rather than colours. The secret code is a five-digit number. The opponent, (the “code breaker”) has to crack the code in as few trials (guesses) as possible. In this game, the codebreaker can crack the code after only five trials. (Digits may be repeated – for example, 12343 would be a possible answer.
Untitled Capture-16
Write the 5-digit code

4. Small cubes of this size

Untitled Capture-18a

are being used to assemble the large cube below.

Untitled Capture-18

How many more small cubes are required to finish the job?
You can assume that any cubes hidden in the drawing are there.

5. Peter met Gail 16 years ago. At that time, Gail was half Peter’s age. Now she is two-thirds of Peter’s age.
How old was Peter when he first met Gail?

6. Which five consecutive numbers add up to 490?

7. Which are the lowest five consecutive numbers not to include a prime number?

8. Untitled Capture-19
The picture shows a stack of identical wooden planks. How many planks are visible?

9. A man counted his savings and found that he had the same number of ten, twenty and fifty dollar notes making a total of $2560.
How many notes did he have?

10. Untitled Capture-21
Which ONE of the above nets can be folded to form a cube?


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