Use the conditions, not a first impression
Connect geometry, probability and data questions to a complete model.
The idea
A diagram, average or probability is only useful when its conditions are preserved. State the total population, count or geometric relationship. Decide whether selections replace earlier objects, whether group sizes differ, and whether you need a whole length or half of it.
A method to try
- Recover totals from a group mean by multiplying by the group size.
- Count equally likely outcomes consistently as ordered or unordered.
- Use geometric relationships and stated measurements; do not estimate an unstated length from a sketch.
Follow the reasoning.
A group of 12 students has a mean score of 70. A separate group of 8 has a mean of 85. What is the combined mean?
- Recover the totals: 12 × 70 = 840 and 8 × 85 = 680.
- Combine totals and counts: (840 + 680)/(12 + 8) = 1,520/20 = 76.
- The answer lies between 70 and 85 and is closer to 70 because the lower-scoring group is larger. The unweighted mean, 77.5, would describe two equally sized groups.
Think it through first.
Four scores total 32. A fifth score is added and the new mean is 9. What was the added score?
Show the explanation
13.
The new total is 5 × 9 = 45. Subtract the original total: 45 − 32 = 13.
Make it your own
After solving, check the size and units of the answer. For probability it must be between 0 and 1; for a weighted mean it must lie between the group means.
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
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- 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
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- 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