Use examples and totals
Review comparisons, averages, combinations and geometry.
The idea
For a variable comparison, try permitted values from different ranges. For a mean problem, recover the total; for unordered pairs, count each pair once.
A method to try
- Test negative, fractional and positive cases when allowed.
- Draw a simple diagram or list the quantities.
Follow the reasoning.
Compare x² and x when x is a real number greater than zero.
- Test a fraction: x = 1/2 gives x² = 1/4, which is smaller than x.
- Test an integer above one: x = 2 gives x² = 4, which is greater. At x = 1 the quantities are equal.
- All these values satisfy x > 0, so no single comparison follows. One successful example cannot establish a universal relationship; contrasting admissible examples can show that the relationship is undetermined.
Think it through first.
The mean of four values is 9. What is their sum?
Show the explanation
36.
Mean × count recovers the total: 9 × 4 = 36.
Make it your own
After reading, explain the method in your own words and identify the condition that makes it valid. Then try the linked starter practice without referring back to the worked example. Review the reasoning behind an error before repeating the same item; remembering an answer is different from being able to solve a new problem.
This lesson is one part of a short starter pathway. It does not cover the full exam syllabus or establish a predicted score.
Official references
These provider and publisher links explain the exam or underlying concepts. Our lessons and questions are original, independent practice.
View 7 references and checked dates
- ETS — current General Test structure (opens in a new tab)Checked 2026-10-07
- ETS — 2026–27 Information Bulletin (opens in a new tab)Checked 2026-09-29
Live PDF cover: policies effective 1 July 2026–30 June 2027. Search snippets can be stale.
- ETS — General Test registration (opens in a new tab)Checked 2026-09-29
- ETS — appointment scheduling (opens in a new tab)Checked 2026-09-29
Live seats were not checked.
- ETS — POWERPREP products (opens in a new tab)Checked 2026-10-07
- ETS — Quantitative Reasoning overview (opens in a new tab)Checked 2026-10-07
- ETS — Quantitative Reasoning overview (opens in a new tab)Checked 2026-09-29