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 10Numerical Reasoning
Edutest Year 10 Numerical Reasoning Practice
Year 10 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 10 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: 1, 2, 6, 24, 120, __.
- A600
- B720
- C840
- D960
Show answer and working
Answer: B (720)
Each term is multiplied by the next whole number: 1 × 2 = 2, 2 × 3 = 6, 6 × 4 = 24, 24 × 5 = 120. The next is 120 × 6 = 720. These are factorials: 5! = 120 and 6! = 720. When the multiplier increases by 1 each step, the sequence grows very quickly.
2.A clock shows 3:15. What is the smaller angle between the hour and minute hands?
- A0°
- B7.5°
- C15°
- D22.5°
Show answer and working
Answer: B (7.5°)
At 3:15 the minute hand points at 3, which is 90° from 12. The hour hand has moved a quarter of the way from 3 to 4. The gap between hour marks is 30°, so the hour hand is 30° × ¼ = 7.5° past the 3. The angle between the hands is therefore 7.5°, not 0°.
3.A book has 200 pages. How many digits are used to number all the pages?
- A392
- B489
- C492
- D500
Show answer and working
Answer: C (492)
Count by number of digits. Pages 1–9 use 9 digits. Pages 10–99 are 90 pages × 2 digits = 180. Pages 100–200 are 101 pages × 3 digits = 303. Total: 9 + 180 + 303 = 492. A common error is counting 100 three-digit pages instead of 101 (100 to 200 inclusive).
4.Which number is the odd one out?
- A27
- B64
- C125
- D100
Show answer and working
Answer: D (100)
27 = 3³, 64 = 4³ and 125 = 5³ are all cube numbers. 100 is 10², a square number, but it is not a cube, because 4³ = 64 and 5³ = 125, so no whole number cubes to 100. That makes 100 the odd one out. (64 is also a square, but it still belongs to the cube group.)
5.What is the next number in the sequence: 1, 5, 13, 29, __?
- A55
- B59
- C61
- D63
Show answer and working
Answer: C (61)
Each term is double the previous one plus 3: 1 × 2 + 3 = 5, 5 × 2 + 3 = 13, 13 × 2 + 3 = 29. The next is 29 × 2 + 3 = 61. Checking the gaps confirms it: +4, +8, +16 double each time, so the next gap is +32, and 29 + 32 = 61.
6.In a group of 60 people, 35 like coffee, 40 like tea, and 20 like both. How many like neither?
- A0
- B5
- C10
- D15
Show answer and working
Answer: B (5)
Use the inclusion–exclusion principle: people who like coffee or tea = 35 + 40 − 20 = 55. The 20 who like both are subtracted once because they were counted in both groups. So 60 − 55 = 5 people like neither. A Venn diagram makes this clear: 15 coffee only, 20 both, 20 tea only.
7.A car's value depreciates by 10% each year. If it's worth $20,000 now, what will it be worth in 2 years?
- A$16000
- B$18000
- C$16200
- D$17000
Show answer and working
Answer: C ($16200)
Depreciation compounds, so each year's 10% is taken from the new, lower value. After year 1: $20,000 × 0.9 = $18,000. After year 2: $18,000 × 0.9 = $16,200. The answer $16,000 subtracts 10% of the original price twice ($2,000 each year), which ignores the shrinking base.
8.What is the next number in the sequence: 360, 180, 60, 15, __?
- A5
- B3
- C1
- D0
Show answer and working
Answer: B (3)
The divisor increases by 1 each step: 360 ÷ 2 = 180, 180 ÷ 3 = 60, 60 ÷ 4 = 15. The next step is ÷ 5, so 15 ÷ 5 = 3. If the gaps are irregular but the numbers shrink quickly, test division and look at how the divisor changes from step to step.
9.A train leaves at 8:00 AM traveling at 60km/h. A second train leaves at 9:00 AM at 90km/h on the same track. At what time will they meet?
- A10:00 AM
- B10:30 AM
- C11:00 AM
- D11:30 AM
Show answer and working
Answer: C (11:00 AM)
By 9:00 AM the first train has travelled 60 km. The second train is 90 − 60 = 30 km/h faster, so it closes the gap at 30 km per hour. Closing 60 km takes 60 ÷ 30 = 2 hours, so it catches up at 11:00 AM. Check: by then the first train has gone 180 km and the second 2 × 90 = 180 km.
10.If 10% of x is 20% of y, what is the ratio of x to y?
- A1:2
- B2:1
- C1:1
- D1:5
Show answer and working
Answer: B (2:1)
Write the statement as an equation: 0.1x = 0.2y. Divide both sides by 0.1: x = 2y. So x is twice y, giving the ratio x:y = 2:1. The answer 1:2 reverses the ratio. A quick check: if y = 10, then 20% of y is 2, and x = 20 because 10% of 20 is also 2.
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 10 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 10 students prepare?
They should practise number patterns, logic puzzles, data questions, and timed mixed sets.