Here’s a free set of 30 HAST-style quantitative reasoning (mathematical reasoning) questions you can complete in 30 minutes (≈ 1 minute per question). They align with the ACER/HAST style used for junior/middle secondary entry testing (e.g. for SEAL programs) (bebooks.com.au, studylib.net).
🧠 HAST Quantitative Reasoning — 30 Questions (30 min)
Sequences & Patterns
- What is the next number? 3, 8, 15, 24, …
- Sequence: 2, 6, 12, 20, … Next number? (Practice Test Geeks).
- A sequence increases by adding successive even numbers. What is the 7th term?
- Fill the blank: 5, 10, 20, 40, __.
Number & Arithmetic
- What is 15% of 240?
- Find GCD of 28 and 42. (Practice Test Geeks)
- If a car depreciates 10% from $30 000, what’s value after one year? (Practice Test Geeks)
- Compute 3x + 5 = 20 → x = ? (Practice Test Geeks)
Ratio, Proportion & Percentages
- Sam has 180 cards, Ben has half as many. If Sam gives 20% of his cards to Ben, what’s the difference? (QuizGecko)
- Mix ratio 1:3 of sugar to flour in 400 g. How much sugar?
- A shirt priced at $60 is discounted 15%. What’s the sale price?
Time, Speed & Work
- Two taps fill a tank in 6 h. How long for three taps? (QuizGecko)
- Car A travels at 50 km/h; Car B at 60 km/h. How long until 30 km apart? (QuizGecko)
- Tommy cycles at 12 km/h; distance of 18 km. How long?
Geometry, Area & Volume
- Rectangle 50 m × 42 m, fence cost $13/m. Total cost? (QuizGecko)
- A square minus a smaller square leaves 45 cm². Side lengths are whole <20. Find perimeter of small square. (QuizGecko)
- A circle radius 7 cm — area ≈? (Use π≈3.14)
Probability & Logic
- In a bag: 5 blue and 5 red balls. Probability of picking blue then red (without replacement)? (Practice Test Geeks)
- If all Bloops are Razzies, and all Razzies are Lazzies, which must be true? (Practice Test Geeks)
- If X=divisible by 3, Y=divisible by 4, Z=divisible by 5 — which correctly describes overlaps? (QuizGecko)
Data Interpretation
- If a bar graph shows Jan: 20 units, Feb:30 units; total 50, what’s percentage in Feb?
- A pie chart: one slice is 72°. What percent of circle?
Logical Steps & Problem Solving
- You bid to buy 45 items at $2 each — total is $___.
- You eat half of a pizza then one-third of the remainder. Remaining fraction = ?
- You have $100. Spend 25%, then 10% of the remainder. Final amount?
Mixed Reasoning
- Puzzle: rearrange shapes so shaded area is one-quarter of total.
- Four books on a shelf: only one book left of English; none right of History; Maths is right of English. Which is true? (QuizGecko)
- Logic maze: which point leads to the center given directional clues?
- Age puzzle: A is 2 years older than B; B is twice C; A+B+C = 27. Age of B? (QuizGecko)
- Weight puzzle: average of 8 people increases by 2.5 kg when replacing a 65 kg person. What is the new person’s weight? (QuizGecko)
✅ How to Use
- Time yourself: 30 questions in 30 minutes → ~1 min per question.
- Answer format: multiple‑choice style or short numerical answer.
- Skip & return: If stuck, move on and return if time allows—recommended by ACER (Studocu, selectivetrial.com.au).
- Mark every answer—no penalties for wrong answers (QuizGecko).
📌 Answer key (compact version)
I can provide detailed solutions or full worked answers later—just ask!
This set mimics the HAST mathematical reasoning section structure: real‑life context, multiple‑choice, varied cognitive skills across number, reasoning, logic, geometry, sequences, probability, data interpretation (bebooks.com.au, studylib.net).
Let me know if you’d like a formatted PDF, answer explanations, or another full set!