Percentages: compute a percent of a number, percent increase and decrease, percent change, successive percent changes, and find an original amount from a percentage (reverse percent).

What this skill is asking

A percent is a fraction out of 100. The Digital SAT (Problem-Solving and Data Analysis domain) tests finding a percent of a number, computing percent increase and decrease, finding the percent change between two values, chaining successive percentages, and the trickier reverse-percent problem of recovering an original amount from a known percentage of it.

The percent toolkit

Almost every percent question reduces to a multiplier.

A worked successive-percentage

Chained percentages multiply, which surprises many students.

Percent change and direction

The percent change formula always divides by the original (old) value, not the new one: $\frac{\text{new} - \text{old}}{\text{old}} \times 100\%$. A positive result is an increase and a negative result is a decrease. A frequent SAT trap is dividing by the wrong base; the percent change from $40$ to $50$ is $\frac{50 - 40}{40} = 25\%$, but from $50$ to $40$ it is $\frac{40 - 50}{50} = -20\%$, so the "up" and "down" percentages differ even though the absolute change is the same. Always anchor the denominator on the starting value.

Reverse percent: the most missed type

The hardest percent questions give you the result of a percent change and ask for the original. The mistake is to take the percentage of the result. Instead, recognise the multiplier and divide. If a $20\%$ increase produced $7200$, the original satisfies $1.20 \times \text{original} = 7200$, so original $= \frac{7200}{1.20} = 6000$, not $7200 - 0.20 \times 7200$. The same logic handles reverse discounts: if a $25\%$-off sale price is \60$, the original is$\frac{60}{0.75} = \$80$. Writing the multiplier equation first and dividing is the reliable route through every reverse-percent question.

Percent in tables, taxes and tips

Many SAT percent questions arrive dressed as everyday money problems: sales tax, tips, commissions, and markups, sometimes layered. A price plus an $8\%$ tax is the price times $1.08$; a bill plus a $15\%$ tip is the bill times $1.15$. When two percentages apply, decide whether they stack (multiply the factors) or apply to different bases. For instance, a \200$item with a$10%$discount and then$8%$tax on the discounted price is$200 \times 0.90 \times 1.08 = \$194.40$, because the tax is charged on the already-discounted amount. Percent questions also appear inside two-way tables and survey data, where "what percent of the juniors play a sport" means dividing the relevant cell by the junior total and multiplying by $100$. The constant skill across all of these is identifying the correct base (the "percent of what?") before you multiply or divide.