3.21 Final Exam-Day Tips for Percentage Questions

• Identify the base before writing a single number. Read the sentence once purely to locate the phrase “of what” or “compared to what” — that noun phrase is your denominator. Only after fixing the base should you plug numbers into a formula.
• Default to the successive-change formula for any “two changes, one after another” question, whether it is phrased as price and consumption, two discounts, two years of population change, or markup-and-discount. Recognizing the pattern instantly (rather than re-deriving by multiplying decimals) is the single biggest time-saver in this chapter.
• For pass/fail and election problems with exactly one unknown (the maximum marks or total votes), use the unitary “value of 1%” shortcut (Trick 9) instead of setting up algebra — it is faster and less error-prone when only one relationship is given.
• When two scenarios and two unknowns are given (two students, two candidates), set up two linear equations and subtract them to eliminate one variable — this is the standard technique used in Worked Example 3 and 4 of Section 3.11 and is worth practicing until it becomes automatic.
• Sanity-check every answer for direction. If the question describes an increase, your final percentage or value must be larger than the original; if it describes a net loss or decrease, it must be smaller. A surprising number of calculation errors are caught simply by asking “does this direction make sense?” before marking the final answer.
• Keep a mental exact-fraction library, not just decimals, especially for 1/3, 1/6, 1/7, 1/9, and 1/11 through 1/19 — these recur constantly in “successive discount,” “population,” and “DI table” questions, and rounding them early causes small errors that compound across multiple steps.
• Practice mental 10%–5%–1% decomposition until it is faster than reaching for a decimal multiplication — under exam time pressure (roughly 45–60 seconds per question), this decomposition alone can save 15–20 seconds per calculation-heavy question, which adds up to several extra minutes across a full quantitative section.

With the formulas, worked examples, shortcuts, and two full practice sets in this chapter thoroughly internalized, you now have the complete toolkit needed not only for direct Percentage questions but also for the Profit-Loss and Interest chapters that follow — both of which are, at their core, percentage problems wearing different labels.