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 11Numerical Reasoning
Edutest Year 11 Numerical Reasoning Practice
Year 11 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 11 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: 1, 3, 7, 15, 31, __?
- A61
- B62
- C63
- D64
Show answer and working
Answer: C (63)
Each term is double the previous one plus 1: 1 → 3 → 7 → 15 → 31, so the next is 31 × 2 + 1 = 63. Another view: each term is one less than a power of two (2² − 1 = 3, 2³ − 1 = 7 and so on), and 2⁶ − 1 = 63. The gaps also double: +2, +4, +8, +16, +32.
2.A laptop depreciates by 20% per year. If it costs $1500 new, what is its value after 3 years?
- A$750
- B$960
- C$768
- D$900
Show answer and working
Answer: C ($768)
Depreciation compounds, so multiply by 0.8 each year. Year 1: $1500 × 0.8 = $1200. Year 2: $1200 × 0.8 = $960. Year 3: $960 × 0.8 = $768. The answer $600 would subtract 20% of the original price each year ($300 × 3 = $900 lost), and $960 stops after two years.
3.A train travels from A to B at 60km/h and returns at 90km/h. What is the average speed for the whole journey?
- A75 km/h
- B72 km/h
- C70 km/h
- D80 km/h
Show answer and working
Answer: B (72 km/h)
Average speed is total distance ÷ total time, not the average of the speeds. Let the distance each way be 180 km. Going takes 180 ÷ 60 = 3 hours, and returning takes 180 ÷ 90 = 2 hours. Total: 360 km in 5 hours = 72 km/h. The trap answer 75 averages 60 and 90 directly.
4.In a class, 60% are boys. 20% of boys and 30% of girls wear glasses. What percentage of the class wears glasses?
- A24%
- B25%
- C26%
- D50%
Show answer and working
Answer: A (24%)
Imagine a class of 100: 60 boys and 40 girls. 20% of 60 boys is 12, and 30% of 40 girls is 12. So 12 + 12 = 24 students out of 100 wear glasses, which is 24%. The answer 25% averages 20% and 30%, which ignores that there are more boys than girls.
5.What is the next number in the sequence: 2, 4, 10, 28, 82, __?
- A244
- B246
- C248
- D250
Show answer and working
Answer: A (244)
Each term is three times the previous term minus 2: 2 × 3 − 2 = 4, 4 × 3 − 2 = 10, 10 × 3 − 2 = 28, 28 × 3 − 2 = 82. The next is 82 × 3 − 2 = 244. The gaps (+2, +6, +18, +54) are tripling, which confirms the next gap is +162, and 82 + 162 = 244.
6.A stock increases by 10%, then decreases by 10%. The final price is $99. What was the original price?
- A$99
- B$100
- C$101
- D$98.01
Show answer and working
Answer: B ($100)
A 10% increase then a 10% decrease multiplies the price by 1.1 × 0.9 = 0.99, so the final price is 99% of the original. If 0.99 × original = $99, then original = $99 ÷ 0.99 = $100. Check: $100 → $110 → $99. The answer $99 assumes the two changes cancel, but they do not.
7.The sum of 5 consecutive integers is 150. What is the largest integer?
- A30
- B31
- C32
- D33
Show answer and working
Answer: C (32)
For consecutive integers, the middle number is the average. 150 ÷ 5 = 30, so the five numbers are 28, 29, 30, 31 and 32. The largest is 32. Check: 28 + 29 + 30 + 31 + 32 = 150. The answer 30 is the middle number, not the largest.
8.A product is sold for $120, making a 25% profit on the cost price. What was the cost price?
- A$90
- B$96
- C$100
- D$150
Show answer and working
Answer: B ($96)
A 25% profit means the selling price is 125% of the cost price. So 1.25 × cost = $120, giving cost = $120 ÷ 1.25 = $96. Check: 25% of $96 is $24, and $96 + $24 = $120. The answer $90 subtracts 25% of $120, which uses the selling price as the base instead of the cost.
9.A shopkeeper mixes 2kg of tea costing $10/kg with 3kg of tea costing $15/kg. What is the cost per kg of the mixture?
- A$12
- B$12.50
- C$13
- D$13.50
Show answer and working
Answer: C ($13)
Find the total cost and divide by the total mass. 2 kg at $10 costs $20, and 3 kg at $15 costs $45. Together: $65 for 5 kg, so $65 ÷ 5 = $13 per kg. The answer $12.50 averages $10 and $15 equally, which ignores that there is more of the dearer tea.
10.A test has 50 questions. You get 2 marks for a correct answer and lose 1 mark for a wrong answer. If you score 70, how many did you get right?
- A35
- B38
- C40
- D42
Show answer and working
Answer: C (40)
Let c be the number correct, so 50 − c are wrong. Score = 2c − (50 − c) = 3c − 50. Setting 3c − 50 = 70 gives 3c = 120, so c = 40. Check: 40 right earns 80 marks, 10 wrong loses 10, and 80 − 10 = 70. This assumes every question was attempted.
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 11 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 11 students prepare?
They should practise number patterns, logic puzzles, data questions, and timed mixed sets.