Write “of what?” beside every percentage
A percentage is incomplete until its base is clear. A price may change relative to its original value, its current value or a competitor’s value. Before calculating, write the denominator in words. This small annotation is especially useful when a question moves between two groups or two points in time.
Consider a price of €80 that rises by 25% and then falls by 20%. The increase is €20 because its base is €80. The decrease is also €20 because its base is now €100. The final price is €80. Adding the percentage changes would instead produce a misleading net increase.
Reverse a change with the inverse multiplier
A 25% increase multiplies a quantity by 1.25. To return to the starting value, divide by 1.25, or multiply by 0.80. That is a 20% decrease. The inverse operation is determined by multiplication, not by attaching the opposite sign to the same percentage.
Try a second original example before looking at the answer: a price drops by 20% from €50 to €40. What percentage increase restores €50? The required €10 increase is 25% of the current €40. Always name the current base before calculating the reverse percentage.
Combine groups by counts before percentages
Suppose 30% of a group of 20 people and 60% of a group of 80 people meet a condition. The counts are 6 and 48. Together, 54 of 100 people meet it, so the combined percentage is 54%. The simple average, 45%, wrongly gives the small and large groups equal weight.
A useful check is to see which group contributes more people. Here the larger group has the higher percentage, so the combined value should sit closer to 60% than to 30%. This does not replace the calculation, but it can catch a denominator mistake quickly.
Notice when information changes the available outcomes
The same habit matters in probability. From a bag with three red and two blue tokens, a red first draw leaves two red among four tokens if the draw is without replacement. The second conditional probability is 2/4, so the chance of two reds is (3/5)(2/4) = 3/10.
Finish a practice answer with three checks: name each base; write the change or condition as an operation; compare the result with a rough bound. The cited sources explain ratios, proportions and probability rules. The examples and checking routine here are original study guidance, rather than official GMAT questions or a claim about how often a trap appears.
Check the underlying concepts
The sources support these concepts. The numerical examples and suggested routines are original Keiko study guidance, with no promise of a particular score outcome.
- A percent expresses a comparison relative to a base. Prealgebra 2e, Section 6.5: Solve Proportions and Their Applications (checked 2026-09-13).
- Rates and ratios describe relationships between quantities. Prealgebra 2e, Section 5.6: Ratios and Rate (checked 2026-09-13).
- A conditional probability uses the outcomes remaining under the stated condition. Introductory Statistics 2e, Section 3.3: Two Basic Rules of Probability (checked 2026-09-13).
Put this into practice
Sources
Every source below was accessed on the listed date. Pages — especially department admissions pages — change without notice; the links go to the live versions.
- Prealgebra 2e, Section 6.5: Solve Proportions and Their Applications — OpenStax. Accessed 2026-07-11.
- Prealgebra 2e, Section 5.6: Ratios and Rate — OpenStax. Accessed 2026-07-11.
- Introductory Statistics 2e, Section 3.3: Two Basic Rules of Probability — OpenStax. Accessed 2026-08-02.
Related guides
Sources and corrections
Sources last checked 2026-09-13Every source cited on this page was checked on the date shown, and we update the page when a source changes. If something looks wrong, tell us and we'll recheck it.