What this page helps you practise
- number sequences and matrix patterns
- logic arithmetic and symbol problems
- data interpretation and proportional reasoning
- multi-step quantitative reasoning under time pressure
EdutestYear 6Numerical Reasoning
Edutest Year 6 Numerical Reasoning Practice
Year 6 Edutest numerical reasoning focuses on mathematical logic rather than routine school exercises. Students need practice finding patterns quickly and applying number sense under pressure.
Year 6 Numerical Reasoning sample questions with worked solutions
Try each question first, then open the worked solution to check your answer and see how to reach it.
1.Find the missing number: 81, 27, 9, 3, __.
- A1
- B0
- C-3
- D1/3
Show answer and working
Answer: A (1)
Each number is divided by 3 to get the next: 81 ÷ 3 = 27, 27 ÷ 3 = 9, 9 ÷ 3 = 3. So the next number is 3 ÷ 3 = 1. The gaps shrink (−54, −18, −6), which signals division rather than subtraction. The answer 0 would subtract 3, which does not match the earlier steps.
2.If 5 apples cost $2.50, how much do 7 apples cost?
- A$3.00
- B$3.50
- C$4.00
- D$4.50
Show answer and working
Answer: B ($3.50)
Find the cost of one apple first: $2.50 ÷ 5 = $0.50 each. Then multiply by 7: 7 × $0.50 = $3.50. This is the unitary method: work out the value of one, then scale up. You could also add 2 more apples (2 × $0.50 = $1.00) to $2.50.
3.Find the missing number: 2, 6, 18, 54, __.
- A108
- B152
- C162
- D216
Show answer and working
Answer: C (162)
The numbers grow quickly, so test multiplication: 2 × 3 = 6, 6 × 3 = 18, 18 × 3 = 54. The rule is multiply by 3, so the next number is 54 × 3 = 162. The answer 108 doubles 54 instead of tripling it, so check that your rule works for every step.
4.What is the next number: 100, 95, 85, 70, __?
- A60
- B55
- C50
- D45
Show answer and working
Answer: C (50)
Look at the gaps: 100 to 95 is −5, 95 to 85 is −10 and 85 to 70 is −15. The amount subtracted increases by 5 each time, so the next gap is −20. 70 − 20 = 50. When the gaps are not equal, check whether the gaps themselves form a pattern.
5.A number is doubled and then 5 is added to get 17. What is the number?
- A5
- B6
- C7
- D8
Show answer and working
Answer: B (6)
Work backwards by undoing each step in reverse order. The last step was adding 5, so subtract 5: 17 − 5 = 12. The first step was doubling, so halve: 12 ÷ 2 = 6. Check: 6 doubled is 12, plus 5 is 17. As an equation this is 2n + 5 = 17.
6.What is the next number: 12, 10, 13, 11, 14, __?
- A11
- B12
- C13
- D15
Show answer and working
Answer: B (12)
The gaps alternate: 12 to 10 is −2, 10 to 13 is +3, 13 to 11 is −2, 11 to 14 is +3. The next step is −2, so 14 − 2 = 12. Another way to see it: every second number (12, 13, 14) goes up by 1, and the numbers between them (10, 11, 12) also go up by 1.
7.The sum of two numbers is 20 and their difference is 4. What are the numbers?
- A10, 10
- B12, 8
- C14, 6
- D15, 5
Show answer and working
Answer: B (12, 8)
The two numbers must add to 20 and differ by 4. Check the options: 12 + 8 = 20 and 12 − 8 = 4, so both conditions work. 14 and 6 add to 20 but differ by 8, and 10 and 10 differ by 0. A quick method: half of (20 + 4) is 12, and 20 − 12 is 8.
8.4 people shake hands with everyone else once. How many handshakes in total?
- A4
- B6
- C8
- D10
Show answer and working
Answer: B (6)
Label the people A, B, C and D and list every pair once: AB, AC, AD, BC, BD, CD. That is 6 handshakes. A shortcut: each person shakes 3 hands, so 4 × 3 = 12, but this counts every handshake twice (A with B and B with A), so divide by 2 to get 6.
9.3 cats catch 3 mice in 3 minutes. How long for 100 cats to catch 100 mice?
- A3 minutes
- B30 minutes
- C100 minutes
- D300 minutes
Show answer and working
Answer: A (3 minutes)
3 cats catch 3 mice in 3 minutes, so each cat catches 1 mouse in 3 minutes. With 100 cats each catching their own mouse at the same time, 100 mice are caught in the same 3 minutes. This is a reasoning trap: the numbers grow, but the time stays the same because the cats work at once.
10.What is the next number: 1, 2, 4, 7, 11, __?
- A14
- B15
- C16
- D17
Show answer and working
Answer: C (16)
Look at the gaps: 1 to 2 is +1, 2 to 4 is +2, 4 to 7 is +3 and 7 to 11 is +4. The amount added goes up by one each time, so the next gap is +5, and 11 + 5 = 16. The answer 15 adds 4 again, which ignores the growing pattern.
Preparation strategy
1
Teach students to write down the pattern rule before calculating.
2
Use mixed reasoning sets rather than only curriculum maths drills.
3
Practise pacing because scholarship tests often reward fast recognition.
Frequently asked questions
How is Year 6 numerical reasoning different from maths?
Numerical reasoning tests flexible problem solving and pattern recognition, while school maths often focuses more on taught procedures.
How should Year 6 students prepare?
They should practise number patterns, logic puzzles, data questions, and timed mixed sets.