The mean of five numbers is 14. One number is removed, and the mean of the four numbers left is 12. What number was removed?
Test guide
NSW Selective High School Placement Test
For Year 6 students applying for Year 7 entry to a NSW selective high school. A plain-English guide to what is in the test, how long each question gets, the key dates and how to prepare.
What the test contains
The placement test is computer-based and held in May. It has four tests, each worth 25%. Calculators are not allowed in any of them.
| Test | Questions | Time | Time per question |
|---|---|---|---|
| Reading | 17 (3 with several parts), multiple choice | 45 minutes | About 2 min 39 s |
| Mathematical Reasoning | 35, multiple choice | 40 minutes | About 69 s |
| Thinking Skills | 40, multiple choice | 40 minutes | About 60 s |
| Writing | 1 open response | 30 minutes | 30 minutes for one piece |
Source: NSW Department of Education, selective high school practice tests and placement test pages, checked 11 October 2026. Time per question is the test time divided by the number of questions; Reading questions with several parts take longer.
Key dates for Year 7 entry in 2028
- Applications open
- Expected early November 2026 — not yet published. Verify on education.nsw.gov.au before you plan around it. For 2027 entry, applications ran from 6 November 2025 to 20 February 2026. Source: NSW Department of Education news
- Placement test
- May 2027, in Year 6 — exact dates not yet published. For 2027 entry, the selective test was held on 1–2 May 2026. Source: NSW Department of Education application process
The department notes there may be changes to dates and activities. Always confirm on education.nsw.gov.au.
How AI Scholar Coach helps you prepare
What a new family gets today:
- An NSW selective Year 7 goal you choose when you set up your child’s profile.
- The free Skills Map — a diagnostic across reasoning skills that marks each one Strong understanding, Developing confidence or Building foundations, so you can see where to start.
- Practice sessions by skill, with banked skills coming back for a review in three days.
- Times tables and number facts, useful for a test with no calculator.
- A parent view of your child’s progress.
With a Season Pass or Monthly plan: unlimited sessions, the AI tutor, AI feedback on writing with parent consent, timed practice tests and quests.
Try a sample question
An original question in the style of Mathematical Reasoning. It is not a real test item.
Show the concept and worked answer
Concept: a mean is the total divided by how many numbers there are, so work with totals rather than the means themselves.
- Total of the five numbers: 5 × 14 = 70.
- Total of the four numbers left: 4 × 12 = 48.
- The removed number is the difference: 70 − 48 = 22.
Answer: E, 22
See where your child stands, skill by skill
The Skills Map is free. No card needed.