## August 2017 Logic & Maths Problems

1. What is the missing number in this sequence?
0, 4 __, 48, 100, 180

2. Daniel, my son, is exactly one fifth of my age. In 21 years’ time, I will be exactly twice his age. My wife is exactly seven times older than my daughter, Jessica. In 8 years’ time, my wife will be three times older than Jessica. How old are Daniel and Jessica now?

3. What is the maximum number of chess knights that you can place in a chess board so that none of them can attack each other in one move?

4. Three volumes of an encyclopaedia are stacked on a shelf as shown.

Each volume has pages numbered from 1 to 100.
A bookworm begins eating at page 1 of volume 1 and eats his way straight through to volume 3 page 100, where he stops. Ignoring covers and flyleaves, how many pages has he eaten?

5. Which is the door to freedom? There are 6 doors in a line.

Yellow door’s clue: This door is 3 spaces away from the purple door.

Blue door’s clue: This door is at the far left.

Red door’s clue: The doors are in a sequence.

Green door’s clue: This door is directly between the blue and yellow doors. It is three spaces away from the door to freedom.

Purple door’s clue: This door is next to the door to freedom.

Orange door’s clue: This door is directly next to the yellow door.

What colour door leads to freedom?

6. Consider this set of numbers: 3, 3, 18, 19 and 22
a. What is the mean of this set of numbers?
b. What is the median of this set of numbers?
c. What is the mode of this set of numbers?

7.

8. Four boys had a race.

• Keith was fourth.
• Adrian is not the oldest, but is older than Duncan, who was not second.
• The child who was next in age to the youngest, finished second.
• The child who finished in third place is older than the child who finished first.
• Billy is younger than the child who finished in third place.

(a) Who is oldest?
(b) In what position did the youngest child place?
(c) Who placed third?

9. You have three bags, each containing two marbles.
Bag A contains two white marbles
Bag B contains two black marbles
Bag C contains one white marble and one black marble.
You pick a random bag and take out one marble.
It is a white marble.
Is the probability that the remaining marble from the same bag is also white:

nil     1/5     1/3      2/5      1/2      3/5     2/3      4/5      certain

(choose one)

10.
This diagram shows two similar triangular pyramids (i.e. they have identical shapes)

The one on the left has a volume of 1000 m3 and is twice as high as the one on the right.

What is the volume of the triangular pyramid on the right?

SOLUTIONS