A numerical reasoning test measures how well a student thinks with numbers: finding patterns, working out rules and solving unfamiliar problems. It isn't a test of times tables or school methods. Most questions use simple arithmetic, but they ask your child to work out what to do, not just do it.
This guide covers numerical reasoning in school entrance and scholarship tests. Graduate job aptitude tests use the same name but test data interpretation for adults.
Which tests include numerical reasoning?
| Test | Section name | Year |
|---|---|---|
| EduTest (scholarships, SEAL) | Numerical reasoning | Years 4 to 10 |
| Victorian selective entry exam | Mathematics and quantitative reasoning | Year 8 |
| WA ASET | Quantitative reasoning | Year 6 |
| ACER HAST | Mathematical reasoning | Years 4 to 10 |
| NSW selective and OC tests | Mathematical reasoning and thinking skills | Years 4 and 6 |
The names differ, but the thinking is the same: spot the pattern, find the rule, check it works.
The eight question types
1. Number series
What comes next? 5, 9, 17, 33, ... A. 49 B. 57 C. 65 D. 66
2. Growing differences
What comes next? 2, 3, 5, 8, 12, ... A. 15 B. 16 C. 17 D. 18
3. Alternating series
What comes next? 10, 4, 12, 6, 14, 8, ... A. 10 B. 15 C. 16 D. 18
4. Number matrices
| 2 | 4 | 8 |
| 3 | 6 | 12 |
| 5 | 10 | ? |
What is the missing number? A. 15 B. 18 C. 20 D. 25
5. Function machines
A number is multiplied by 4, then 3 is added. The result is 31. What was the number? A. 6 B. 7 C. 8 D. 9
6. Symbols and balances
◆ + ◆ = 18 and ◆ + ● = 14. What is ●? A. 4 B. 5 C. 6 D. 9
7. Missing operations
The same symbol makes both true: 6 ? 3 = 18 and 8 ? 2 = 16. What is the symbol? A. + B. − C. × D. ÷
8. Word problems and averages
The mean of 4, 8, 15 and a fourth number is 10. What is the fourth number? A. 10 B. 11 C. 13 D. 15
Answers and explanations
| Q | Answer | Why |
|---|---|---|
| 1 | C | Double, then subtract 1: 33 × 2 − 1 = 65. Check every step: 5 × 2 − 1 = 9 and 9 × 2 − 1 = 17. |
| 2 | C | The gaps grow by one: +1, +2, +3, +4, then +5. 12 + 5 = 17. |
| 3 | C | Two series take turns: 10, 12, 14, 16 and 4, 6, 8. Next is the first series: 16. |
| 4 | C | Each number in a row is double the one before: 10 × 2 = 20. |
| 5 | B | Work backwards: 31 − 3 = 28, then 28 ÷ 4 = 7. |
| 6 | B | ◆ = 9, so ● = 14 − 9 = 5. |
| 7 | C | 6 × 3 = 18 and 8 × 2 = 16. |
| 8 | C | Four numbers with a mean of 10 total 40. 4 + 8 + 15 = 27, so the fourth is 13. |
A method for any series question
- Write the differences between each pair of numbers underneath the series.
- If the differences are equal, add the same amount. If they grow, look at the differences of the differences.
- If the numbers grow fast, try multiplying instead (×2, ×3), possibly with a small adjustment (±1).
- If the series jumps up and down, split it into two series taking turns.
- Check your rule on every step, not just the first two. That's where most wrong answers come from.
How to prepare
- Fluent arithmetic first. Times tables to 12 and quick halving and doubling free up thinking time. Calculators aren't allowed in any of these tests.
- Learn the families of question. Most numerical reasoning questions fall into the eight types above. Once your child recognises the type, half the work is done.
- Practise working backwards. Function machines, ages and "think of a number" problems all reward it.
- Explain answers aloud. A child who can say why the rule works will spot it faster next time.
- Add time last. EduTest numerical reasoning gives about 30 minutes. In the ASET, there are 35 questions in 35 minutes.
Deeper guides on our site
- Number series and matrices
- Coding and word problems in numerical reasoning
- Word problems in selective school maths
- Abstract reasoning: the shapes version of the same pattern-spotting skill
- Verbal reasoning test: the word-based equivalent
Practise in test conditions
- EduTest practice tests: full numerical reasoning papers with worked explanations
- HAST practice tests and NSW Selective practice tests
- Sample questions for EduTest, ASET and the Victorian selective entry exam
Frequently asked questions
What is a numerical reasoning test? A test of how well you think with numbers: finding patterns and rules, and solving unfamiliar problems, rather than recalling school methods.
Is numerical reasoning the same as maths? Not quite. Maths tests what you've learned. Numerical reasoning tests how you reason, usually with simple arithmetic.
Can you use a calculator? No. School entrance and scholarship tests don't allow calculators.
Example questions written by Practice Tests & Exams.