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 8Numerical Reasoning
Edutest Year 8 Numerical Reasoning Practice
Year 8 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 8 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.What is the next number in the sequence: 2, 6, 12, 20, 30, ...?
- A40
- B42
- C44
- D46
Show answer and working
Answer: B (42)
Look at the gaps: 2 to 6 is +4, 6 to 12 is +6, 12 to 20 is +8, 20 to 30 is +10. The gaps go up by 2 each time, so the next gap is +12, and 30 + 12 = 42. These are also n × (n + 1): 1×2, 2×3, 3×4, 4×5, 5×6 and 6×7 = 42.
2.Find the missing number: 2, 5, 10, 17, 26, __.
- A35
- B36
- C37
- D38
Show answer and working
Answer: C (37)
Each number is one more than a square number: 1² + 1 = 2, 2² + 1 = 5, 3² + 1 = 10, 4² + 1 = 17, 5² + 1 = 26. The next is 6² + 1 = 37. The gaps (+3, +5, +7, +9) are the odd numbers, so the next gap is +11, and 26 + 11 = 37 as well.
3.A rectangle's length is twice its width. If the perimeter is 30cm, what is the length?
- A5cm
- B10cm
- C15cm
- D20cm
Show answer and working
Answer: B (10cm)
Let the width be w, so the length is 2w. Perimeter = 2 × (length + width) = 2 × (2w + w) = 6w. If 6w = 30, then w = 5 cm and the length is 2 × 5 = 10 cm. Check: 10 + 5 + 10 + 5 = 30. The answer 5 cm is the width, not the length.
4.If you write down all the numbers from 1 to 50, how many times will you write the digit '4'?
- A10
- B11
- C14
- D15
Show answer and working
Answer: D (15)
Count the 4s in the ones place and the tens place separately. Ones place: 4, 14, 24, 34, 44 gives 5. Tens place: 40 to 49 gives 10 numbers with a 4 in the tens. So the total is 5 + 10 = 15. The number 44 has two 4s, and this method counts both correctly.
5.A number is halved and then 4 is subtracted, giving 10. What is the number?
- A28
- B24
- C32
- D36
Show answer and working
Answer: A (28)
Work backwards, undoing each step in reverse order. The last step subtracted 4, so add 4: 10 + 4 = 14. The first step halved the number, so double it: 14 × 2 = 28. Check: half of 28 is 14, and 14 − 4 = 10. As an equation this is n/2 − 4 = 10.
6.If 4 painters can paint a house in 6 days, how long would it take 3 painters?
- A7 days
- B8 days
- C9 days
- D10 days
Show answer and working
Answer: B (8 days)
This is inverse proportion: fewer painters take longer. The total work is 4 painters × 6 days = 24 painter-days. With 3 painters, 24 ÷ 3 = 8 days. The trap answer 7 days adds one day for one fewer painter, but the work must be shared, so multiply and divide instead.
7.What is the next number in the sequence: 1, 10, 2, 9, 3, __?
- A4
- B7
- C8
- D10
Show answer and working
Answer: C (8)
Two sequences are interleaved. Read every second number: 1, 2, 3 counts up by 1. The numbers in between, 10, 9, count down by 1. The next position belongs to the second sequence, so after 10, 9 comes 8. Splitting alternating patterns into two lists makes them much easier to see.
8.If a quarter of a number is 12, what is one-third of the same number?
- A12
- B16
- C24
- D48
Show answer and working
Answer: B (16)
If a quarter of the number is 12, the whole number is 12 × 4 = 48. One third of 48 is 48 ÷ 3 = 16. The answer 12 assumes a third equals a quarter, and 48 is the whole number rather than a third of it. Always find the whole first, then take the new fraction.
9.What is the next number in the sequence: 1, 4, 27, 256, __?
- A625
- B1024
- C3125
- D1296
Show answer and working
Answer: C (3125)
Each term is a number raised to its own power: 1¹ = 1, 2² = 4, 3³ = 27, 4⁴ = 256. The next term is 5⁵ = 5 × 5 × 5 × 5 × 5 = 3125. The answer 625 is 5⁴, which uses the wrong power. When numbers grow extremely fast, test powers rather than simple multiplication.
10.A tap fills a bath in 20 minutes. A second tap fills it in 30 minutes. If both are open, how long to fill the bath?
- A10 minutes
- B12 minutes
- C15 minutes
- D25 minutes
Show answer and working
Answer: B (12 minutes)
Work out how much of the bath each tap fills in one minute. Tap 1 fills 1/20 and tap 2 fills 1/30. Together: 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12 of the bath per minute, so the bath fills in 12 minutes. The answer must be less than 20, because the faster tap alone takes 20.
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 8 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 8 students prepare?
They should practise number patterns, logic puzzles, data questions, and timed mixed sets.