SAT Math · Problem-Solving & Data Analysis

Percentages on the Digital SATWhat it tests, how to approach it, and where students get trapped

Percent change, percent of a quantity, reverse-percentage problems, and multi-step percent scenarios like tax-plus-discount.

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Percentages in Our Question Bank

46

Total questions

18

Easy

16

Medium

12

Hard

These counts cover the full Grind1600 bank. On the Free plan you get the first 5 easy, 5 medium, and 5 hard questions in Problem-Solving & Data Analysis.

What the SAT Actually Tests

Percent questions span simple ("what is 15% of 80") to genuinely tricky: successive percent changes, reverse percentages ("after a 20% discount the price was $60 — what was the original?"), and percent-of-a-percent comparisons between groups in a table.

Convert every percent operation to a multiplier: +15% is ×1.15, −20% is ×0.80. This makes successive changes a single multiplication and makes reverse problems a division (60 ÷ 0.80), not a subtraction. For comparison questions, be precise about the base — "A is 25% more than B" means A = 1.25B, and B is not 25% less than A.

Common Percentages Question Patterns

Pattern 1Find a percentage of a quantity or convert a part-to-whole relationship to a percent.
Pattern 2Apply percent increase, decrease, discount, tax, markup, growth, or decline.
Pattern 3Reverse a percentage or compare quantities when the reference base changes.

A Step-by-Step Strategy

  1. 1

    Identify the base

    Name the original or reference quantity before applying a percent.

  2. 2

    Convert to a multiplier

    Use 1 + r for an increase, 1 − r for a decrease, and r for a percent of.

  3. 3

    Build one equation

    Represent successive changes by multiplying factors and reverse changes by dividing.

  4. 4

    Check the direction

    Confirm that an increase produced a larger value and that the answer uses the requested base.

Original Percentages Practice Questions

These fixed public samples come from Grind1600's original question bank. Choose an answer and check your reasoning before reading the explanation.

Question 1easy
A student answered 36 out of 45 questions correctly on a test. What percentage of questions did the student answer correctly?
Question 2medium
In January, the price of a vintage record was $85. In February, the price of the vintage record was $102. The price of the vintage record in February was w% of the price of the vintage record in January. What is the value of w?
Question 3medium
A store originally priced a couch at $800. During a sale, the price was reduced by 30%. A week later, the sale price was further reduced by an additional 20%. What was the final price of the couch?

Traps to Avoid

  • Solving reverse-percentage problems by taking the percent of the final value instead of dividing by the multiplier.
  • Adding successive percent changes (+10%, +10% is not +20% — it's ×1.21).
  • Using the wrong base in comparisons: 'X% more than' and 'X% of' produce different equations.

Difficulty Progression

1. Foundation

Calculate a percent of a number and translate fractions or decimals to percents.

2. Developing

Solve percent-change, tax, discount, markup, and reverse-percent problems.

3. Advanced

Handle successive changes and comparisons where 'more than,' 'less than,' and 'of' use different bases.

Official taxonomy: College Board Math skills and question descriptions. Strategy and progression labels are Grind1600 editorial guidance. Last reviewed August 29, 2026.

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More Problem-Solving & Data Analysis Skills

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Setting up proportions, converting units, and reasoning with rates — the most common word-problem machinery on the SAT Math section.

Data Distributions & Measures of Center

Mean, median, mode, range, and standard deviation — and how outliers or skew change them — read from lists, tables, and frequency plots.

Scatterplots & Two-Variable Data

Reading scatterplots, lines of best fit, interpreting slope in context, and distinguishing linear from exponential association.

Probability

One-event and conditional probability, usually read out of two-way frequency tables — the key is identifying the correct restricted group.

Inference & Margin of Error

What sample results let you conclude about a population, how margin of error works, and why sample size changes confidence.

Evaluating Statistical Claims

Judging what a study design supports: random sampling vs. random assignment, causation vs. correlation, and generalizability.

Continue With Problem-Solving & Data Analysis Practice

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Last reviewed August 29, 2026 · Grind1600 Editorial Team