February 2014 Logic & Maths Problems Solutions

1. The water level of the pool will fall. The cannonball is much denser than the water. Let the cannonball have a volume of x litre. Assume the cannonball is ten times as dense as the water. Its mass will therefore be 10x kg. When the cannonball is placed in the boat, the boat settles by an amount which displaces 10 kg of water or 10x litres of water. However, when the cannonball is taken out of the boat and placed directly in the water, it only displaces its own VOLUME of water or x litres. This will have the same effect on the water level of the pool as taking 9x litres out.
2. Treble = 18, double = 4, single = 13
3. 2519 prisoners
4. The rule is: double the first number then take away 8. The answer is therefore 20
5. 13 triangles
6. 30 picknickers
7. a. 54m b. 6th c. 11th d. 22 times
8. Direction A (The doors must be on the other side or kerb side, & they drive on the right)
9. $20
10. (a) Keep Still (b) Call a Cab

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