Solving Percentage Questions on the SAT

The one equation that solves every percent question

Nearly every percent question on the Digital SAT — find a percent, find a part, find a whole, or find a percent change — comes from the same relationship: Part = Percent × Whole, where the percent is written as a decimal. The skill is translating English into that equation correctly.

Translate word-by-word: “is” becomes an equals sign, “of” becomes multiplication, and “what percent” or “what number” becomes your unknown. “18 is what percent of 20” becomes 18 = (x/100)(20). Once it’s an equation, solving is ordinary algebra.

Walk through that exact question below, then try one yourself.

That translate-then-solve habit is the whole method. The rest of this guide is just applying it to specific phrasings: change, reversal, and repeated change.

Percent increase and decrease

To apply a percent change forward, multiply the original value by (1 + rate) for an increase or (1 − rate) for a decrease. A $64 shirt marked up 25% costs 64 × 1.25 = $80. A $64 shirt marked down 25% costs 64 × 0.75 = $48. Building the multiplier (1.25 or 0.75) in one step avoids the common error of calculating the change and forgetting to add it back.

If you’re instead given the before-and-after values and asked for the rate, use Percent change = (New − Original) / Original × 100. The denominator is always the original value — using the new value there is a frequent trap.

Reverse percent: working backward from the result

A reverse-percent question gives you the value after a change and asks for the value before it. The trap is treating the final value as if you should undo the percent by simple addition or subtraction. Instead, write the same multiplier equation and solve for the original.

If a $56 jacket reflects a 20% discount, the original price satisfies 0.8 × Original = 56, so Original = 56 / 0.8. Dividing by the multiplier — not multiplying the final price by the discount rate — recovers the original.

Successive percent changes — why they don't add

When a value changes by one percent and then by another, resist the urge to add or subtract the percents. Instead, multiply the two multipliers together. A 20% increase followed by a 15% decrease is 1.20 × 0.85 = 1.02 — a net increase of only 2%, not the 5% you’d get by naively subtracting 20 − 15.

This is also why an equal percent increase followed by the same percent decrease never returns you to the start (unless the percent is 0%): the multipliers (1 + r) and (1 − r) multiply to 1 − r², which is always a little less than 1.

Classify each pair of changes below by its net effect before you compute anything precisely.

Now put it together in a full question — multiply the factors, then convert back to a percent.

Practice until it's automatic

Translate first, then compute. These mix all three variations — forward, reverse, and successive — so you build the habit of identifying which one you’re looking at before you start calculating.

Once these feel quick, the next natural step is applying the same “part over whole” thinking to ratios and rates, where the denominator isn’t fixed at 100.

Practice questions

Here are five practice problems that help you hone your skills. Use the same method we learned earlier above to solve these problems. Remember, practice makes perfect.