May 2012

Problem
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

Situation
The solid pole shown in the figure is loaded with a vertical load P = 25 kN and lateral load H = 0.95 kN. The pole is 3 m high, 300 mm diameter and weighs 22 kN/m³.
 

Problem
The area of a park on a map is 600 mm². If the scale of the map is 1 to 40,000 determine the true area of the park in hectares (1 hectare = 10⁴ m²).

Problem
Given the following equations:

$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$

Find the value of $a + b + c$.