Mathematical Reasoning Tips

How to Solve the Tricky "Work Rate" Questions in the Selective Maths Test

It's Reasoning, Not Just Maths The section is called "Mathematical Reasoning" for a reason. They won't just ask "What is 12 × 12?" They will give you a word problem where you have to hunt for the maths hidden inside the story.

The "Inverse Proportion" Trap One of the most common question types involves people working together. It usually looks like this: "If 4 gardeners take 3 hours to mow a lawn, how long will it take 6 gardeners?"

The Mistake: Many students think, "More people means more time," or they try to use standard ratios and get confused. They might guess 4.5 hours. Wrong!

The Logic: If you have more helpers, the job should take less time. This is called Inverse Proportion.

How to Solve It (The "Man-Hours" Method) The easiest way to solve this is to figure out the total amount of "work energy" needed. Multiply the original pair: 4 gardeners × 3 hours = 12 "gardener-hours" of work. (Imagine the job takes 12 tokens of energy.) Divide by the new number of people: You have 12 tokens of work, but now you have 6 gardeners to share it. 12 ÷ 6 = 2 hours. Answer: It will take 2 hours.

Other Topics to Watch: Patterns: "What comes next in this sequence?" (Look for two things happening at once, like doubling and subtracting 1). Spatial Vision: "Which cube can be made from this flat shape?" (You need to practice folding shapes in your head).

Want to practice more under timed exam conditions? Try our computer-based Mathematical Reasoning mock exams to see exactly where your child ranks.

How to Solve the Tricky "Work Rate" Questions in the Selective Maths Test | NSW Selective Test Blog | GoTestPrep