May 2015 Logic & Maths Problems – Solutions

1. 2/3: You know that you do not have Bag B (two black marbles) so there are three possibilities
You chose Bag A, first white marble. The other marble will be white
You chose Bag A, second white marble. The other marble will be white
You chose Bag C, the white marble. The other marble will be black
So 2 out of 3 possibilities are white.
Why not 1/2? You are selecting marbles, not bags.

2. 6 hectares

3. 0.06%

4. (a) green 22 cents; (b) blue 17 cents; (c) yellow 50 cents; (d) red 18 cents

5. a. Everton b. Liverpool c. Watford, Spurs, Norwich

6. The cone section is about 4% bigger than the sphere.
Cone section: You can use the formula for the frustrum of a cone.
Assuming that the shape has been achieved by cutting the top off a whole cone. This “original” cone must have been 40 cm high.
The formula for the volume of a cone is 1/3 X π x (radius of base squared) x height
So volume of the cone section = volume of the original cone – volume of the conical tip

= 1/3 X π x (20 x 20) x 40 – 1/3 X π x (10 x 10) x 20

= 1/3 X π x (1600 – 2000)

= 4667 π cubic centimetres

Sphere: The volume of a sphere is given by the formula 4/3 X π x (radius of sphere cubed)

= 4/3 X π x (15 X 15 X 15)

= 4/3 X π x (15 X 15 X 15)

= 4/3 X π x (3375)

= 4500 π cubic centimetres

7. Andrew and Dolly Gould live in Brisbane; Brian and Edna Hedges live in Sydney, and Colin and Flo Jacobs hail from Perth.

8. a. red, b. black, c. purple, d. black

9. 2 of diamonds, 3 of hearts, 6 of clubs, 8 of spades, 9 of hearts

10. A up B down C down D up E up

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