# Percentages on the SAT: Examples & Practice | 1600.now Source: https://1600.now/sat-skill/percentages --- Math · Problem-Solving and Data Analysis ## Percentages Use the starting quantity as the denominator for percent change. Convert an increase or decrease into a multiplier, and apply successive changes one at a time. Written by [Luke Finigan](https://1600.now/about) 2 min read Updated Oct 2, 2026 ### Choose the base before calculating If a value rises from 80 to 100, its increase is 20 and its percent increase is $\frac{20}{80}\cdot100\%=25\%$. The denominator is the original 80. Reversing the change, from 100 to 80, gives a 20% decrease. The two changes use different bases. A sentence saying that one value is a certain percent of another also names the base: if $a$ is 30% of $b$, then $a=0.30b$. ### Use multipliers for successive changes A 20% increase multiplies by 1.20, and a 20% decrease multiplies by 0.80. Applying both to 100 gives $100(1.20)(0.80)=96$. The changes do not cancel because the decrease acts on 120. For several changes, multiply the factors before converting the final multiplier into an overall percent change. A multiplier of 0.96 represents a 4% decrease from the original value. ### Work backward from the final amount A jacket costs 72 dollars after a 20% discount. Its original price $p$ satisfies $0.80p=72$, so $p=90$. Adding 20% of 72 would give 86.40 dollars and would not undo the discount. Write the equation with the original amount as the unknown. This also works for a final amount after tax, growth, or a markup. ### Separate percentage points from percent change If a success rate rises from 40% to 50%, it rises by 10 percentage points. Relative to the original rate, the percent increase is $\frac{50-40}{40}\cdot100\%=25\%$. Read the requested unit carefully. A percentage-point difference subtracts the two rates; a relative percent change divides that difference by the original rate. ### Check your understanding Try it yourself A price of 50 dollars rises by 10% and then falls by 10%. What is its final value? A 45 dollars B 49.50 dollars C 50 dollars D 55 dollars ### Sample percentages questions Percentages · Easy: If 250% of n is 45, what is the value of $n$? · A $11,250$ B $2,025$ C $1,800$ D $18$ - [Open the question and explanation](https://1600.now/bank/math/be7439d8) Percentages · Easy: 4% of $w$ is 632.86. What is the value of $w$? · A 658.174 B 2,531.44 C 15,821.5 D 60,754.56 - [Open the question and explanation](https://1600.now/bank/math/48826e16) Percentages · Easy If $x$ is a positive integer, the expression $0.23x$ represents what percent of $x$? A 23 B 77 C 123 D 177 - [Open the question and explanation](https://1600.now/bank/math/e95d4d13) ### Practice this skill 1. Circle the base quantity in the stem. 2. Write each percent as a decimal factor before multiplying. 3. For a reverse problem, substitute the original amount back through the change. [Practice percentages](https://1600.now/bank/math/skill/Percentages) [Print the percentages worksheet and worked answers](https://1600.now/sat-percentages-worksheet). Then use a [mixed practice module](https://1600.now/modules) to check whether you can choose this method among other question types. ### Source and question labels The bank label for this guide is "Percentages" in Problem-Solving and Data Analysis. The worked examples above are written for this guide. - [College Board: Types of Math tested](https://satsuite.collegeboard.org/sat/whats-on-the-test/math/types) ### Related skills - **[Ratios, Rates, and Proportions](https://1600.now/sat-skill/ratios-rates-proportions)** Keep the compared quantities in a fixed order and write their units. - **[Nonlinear Functions](https://1600.now/sat-skill/nonlinear-functions)** The form of a nonlinear function tells you what you can read directly. - **[Probability and Conditional Probability](https://1600.now/sat-skill/probability)** Probability compares favorable outcomes with the eligible outcomes.