Selective Test Sample Questions with Worked Solutions

The NSW Selective High School test rewards clear reasoning under time pressure across Reading, Mathematical Reasoning and Thinking Skills. Below are five original, Selective-style questions (Year 6 level) from the two most practisable areas — Maths Reasoning and Thinking Skills — each with a full worked solution. Encourage your child to attempt each one before reading the answer.

Mathematical Reasoning

1. Rates

Q. A tap fills a 24-litre bucket in 6 minutes. At the same rate, how long would it take to fill a 40-litre bucket?

Insight: find the rate first — how many litres per minute — then scale up.
Method: 24 ÷ 6 = 4 litres per minute, so 40 ÷ 4 = 10 minutes.
Check: 4 litres/min × 10 min = 40 litres. ✓

2. Ratio

Q. In a class, the ratio of boys to girls is 3 : 5. If there are 15 boys, how many students are in the class altogether?

Insight: the ratio splits the class into equal "parts"; find what one part is worth.
Method: 3 parts = 15 boys, so 1 part = 5. Total parts = 3 + 5 = 8, so 8 × 5 = 40 students.
Check: girls = 5 × 5 = 25, boys = 15, and 15 : 25 simplifies to 3 : 5. ✓

3. Adding a long run of numbers

Q. What is 1 + 2 + 3 + … + 20?

Insight: don't add one at a time — pair the smallest with the largest. 1 + 20 = 21, 2 + 19 = 21, and so on.
Method: there are 10 such pairs, each adding to 21, so 10 × 21 = 210.
Check: the shortcut n × (n + 1) ÷ 2 gives 20 × 21 ÷ 2 = 210. ✓

Thinking Skills

4. Logical ordering

Q. Four friends ran a race with no ties. Mia finished ahead of Sam. Sam finished ahead of Ben. Ben finished ahead of Zoe. Who came third?

Insight: line the clues up into a single order rather than juggling them separately.
Method: Mia → Sam → Ben → Zoe. That's 1st, 2nd, 3rd, 4th, so third is Ben.
Check: every clue still holds: Mia beat Sam, Sam beat Ben, Ben beat Zoe. ✓

5. What must follow

Q. Every student who passed the test had studied for it. Priya did not study for the test. What can we conclude about Priya?

Insight: turn the rule around. If "passed" guarantees "studied", then "did not study" guarantees "did not pass".
Method: since Priya did not study, she cannot be one of the students who passed — so Priya did not pass the test.
Check: if Priya had passed, the rule says she must have studied — which contradicts what we're told. ✓

Practise more like these

These questions reward finding the right idea — the rate, the "part", the pairing, the single order, the turned-around rule — rather than a memorised procedure. PrepPath offers unlimited Selective test practice and OC test practice across Reading, Mathematical Reasoning and Thinking Skills, with every question explained in full and progress tracking that shows which areas need work. For the bigger picture, see How to Prepare for the OC and Selective Tests and OC vs Selective: What's the Difference?

PrepPath is an independent educational platform and is not affiliated with, endorsed by, or associated with the NSW Department of Education. These are original, Selective-style practice questions written by PrepPath — not real test papers.