Proportion and Percentages

What this exam is like

The Proportion and Percentages exam has 38 multiple-choice questions across these levels: Primary (25), Secondary (38). Each attempt draws 10 at random from the level you choose. You get two tries per question, and each answer is explained afterwards. At the end you see your grade.

Sample questions

1. 1. What does 25% mean exactly?

   • 25 out of every 100
   • 25 times more
   • 25 units
   • A quarter of 25
   Show the answer

   ✅ 25 out of every 100

   Per cent literally means "out of a hundred". So a percentage is a fraction with denominator 100: 25% is 25/100, which simplifies to 1/4 and is 0.25 as a decimal. Three ways of writing the same thing.

2. 2. Trousers cost €30 with a 30% discount. How much do you pay?

   • €20
   • €21
   • €27
   • €9
   Show the answer

   ✅ €21

   30% of 30 is €9, and 30 − 9 = €21. The price and the percentage both being 30 is a coincidence that misleads: the discount is not €30 and the final price is not 30%.

3. 3. You mix 2 kg of coffee at €12/kg with 3 kg at €7/kg. What does a kilo of the mix cost?

   • €19/kg
   • €8/kg
   • €9.50/kg
   • €9/kg
   Show the answer

   ✅ €9/kg

   It costs 2 × 12 + 3 × 7 = €45 in total for 5 kg: 45 ÷ 5 = €9/kg. The plain average of 12 and 7 would be 9.50, but that is wrong because there are more kilos of the cheap one: it is a weighted average, like a term grade.