Percentages and Percent Change Complete SAT Study Guide

What this topic tests

Compute percent of, percent change, and successive percent operations. The College Board groups this topic inside the Problem Solving & Data Analysis content domain. Across a full SAT Math section, you can expect roughly 3–6 questions touching this topic, distributed across the easy, medium, and hard difficulty tiers.

Problem Solving and Data Analysis is where the SAT pretends to be the real world. Every question in this domain is wrapped in context: a recipe, a survey, a clinical trial, a lab measurement, a marketing report. The math itself is rarely harder than middle-school arithmetic — ratios, proportions, percentages, unit conversions, means, medians, scatter plots, two-way tables, and basic probability. What trips students up is the reading. The College Board has spent two decades calibrating these prompts to reward students who slow down on the setup and punish students who rush to compute. ScoreReady's Problem Solving drills isolate each archetype the test reuses: percent-change versus percent-of, weighted versus simple averages, line of best fit interpretation, conditional probability from two-way tables, and density and rate conversions. Every worked solution shows the unit-tracking step explicitly because that is where careless students lose points they should keep. If you can score perfectly here, you have neutralized one of the easiest places on the entire SAT to leave points on the table.

Sub-skills inside Percentages and Percent Change

ScoreReady breaks this topic into four distinct sub-skills, each of which the College Board tests with its own characteristic question patterns. Mastering each sub-skill in isolation is faster than trying to master the whole topic at once.

Percent of a Quantity

The phrase 'p percent of n' translates to (p/100) × n. This single translation handles the majority of SAT percent questions. The trap is the difference between 'percent of' and 'percent more than': 30 percent of 50 is 15, but 30 percent more than 50 is 65. Underline the exact phrasing of the question before computing. Students who default to one interpretation regardless of phrasing get the wrong answer roughly half the time on these questions, and the College Board lists both possibilities as choices.

Percent Increase and Decrease

Percent change is the change divided by the original value, multiplied by 100. The most common error is dividing by the new value instead of the original. A second common error is treating an increase from 50 to 80 as a 30 percent increase (it is actually 60 percent, since 30 is 60 percent of 50). Memorize the formula and always identify the original value before dividing. Wrong-answer choices on these questions are designed to catch each of these specific misreads.

Successive Percent Changes

When two percent changes are applied successively — for example, a 20 percent increase followed by a 20 percent decrease — the net change is not zero. The successive multipliers (1.2 and 0.8 in this case) compound, giving a net multiplier of 0.96, which is a 4 percent decrease. The SAT tests this almost every form. The wrong-answer choice is always the naive sum of the two percentages or the value that assumes the changes cancel. Multiply the multipliers; do not add the percents.

Percent in Word Problems

Word problems involving discounts, taxes, tips, commissions, and markups are all percent problems wrapped in context. Tax of 8 percent on a $50 item adds 8 percent of $50, giving a final price of $54. A 25 percent off sale on a $40 item subtracts 25 percent of $40, giving a final price of $30. The skill is reading the prompt to identify whether the percent is an addition or subtraction, and what the original value is. Underline the original-value phrase before computing.

Score-band drills

Once you have read through the sub-skills, drill the questions filtered to your current score band. The four bands below correspond to the four roughly-equal scoring ranges on the SAT Math section.

Key formulas

p% of n = (p/100) × n
Percent change = (new − old) / old × 100
Successive multipliers compound, not add
Final price after p% tax = original × (1 + p/100)

For longer worked examples that walk through every formula on this list, see the formula reference page.

Common pitfalls

Dividing percent change by the new value instead of the original
Adding successive percent changes instead of multiplying their multipliers
Confusing "p% of n" with "p% more than n"
Using the percent value (p) instead of p/100 in a calculation

Each of these pitfalls maps to a wrong-answer choice the College Board reliably includes on questions in this topic. Read the common pitfalls walkthrough for a worked example of each one.

Suggested study order

Work the four sub-skill drills in the order they are listed above. The first sub-skill is the foundational one, and each subsequent sub-skill assumes fluency with the previous one. After you can clear all four sub-skill drills without notes, take the full topic question bank as a single timed sitting. Aim for at least 90% accuracy at a pace of one question per 75 seconds.