Translate quantities into equations
Choose the correct base, unit and condition before calculating.
The idea
Write what each number measures. A percentage acts on a particular base; a rate measures work per unit of time; an equation may have more than one allowed solution. Use those meanings to build the calculation before looking for a quick numerical shortcut.
A method to try
- For successive percentages, multiply the factors instead of adding percentage points.
- For combined work, add the rates and then invert to recover time.
- For absolute values or comparisons, check every permitted case and any equality boundary.
Follow the reasoning.
A service costs 200 units. It receives a 15% discount, then an 8% charge is added to the discounted amount. What is the final cost?
- The discount leaves 85% of 200: 200 × 0.85 = 170.
- The charge is based on 170: 170 × 1.08 = 183.60.
- The combined factor is 0.918, so the result is 8.2% below the original cost. Subtracting 8 from 15 would wrongly treat the two percentages as having the same base.
Think it through first.
Two workers complete a job in 4 hours and 12 hours respectively, working separately at constant rates. How long do they need together?
Show the explanation
3 hours.
Their combined rate is 1/4 + 1/12 = 1/3 job per hour, so one job takes 3 hours.
Make it your own
When an answer is wrong, label the error before retrying: wrong base, wrong unit, omitted case or arithmetic slip. Then solve a fresh problem with the same structure.
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
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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
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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