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M2 Percentages

One of the SAT's published Math skills, inside Problem-Solving & Data Analysis. 101 questions here, across 12 distinct question types.

Problem-Solving and Data Analysis covers the math you use in everyday and scientific situations: ratios, rates, percentages, proportions, unit conversions, and reading data from tables, graphs, and scatterplots. It also includes basic statistics like mean, median, and interpreting trends. One concrete tip: always check the units and labels on a graph or table before you calculate, because a misread axis is a common way to lose an easy point. On this page you'll find a short lesson on ratios, percentages, and reading data accurately, plus free interactive practice with instant explanations so you can get comfortable pulling the right numbers from real-world contexts and computing with confidence.

This domain is all about ratios, rates, percentages, proportions, and statistics — the "real-world math" questions. They're wordy, so careful reading beats clever tricks.

Percent translation: "of" → multiply, "is" → equals, "what" → the variable. "15 is 20% of what?" becomes 15 = 0.20 × n.

The essentials

  • Percent change = (new − old) / old × 100. Always divide by the original.
  • Discount: a 25% discount means you pay 75%. Final = 0.75 × original.
  • Rate = quantity ÷ time. Set up a proportion for "at that rate" questions.
  • Mean = sum ÷ count → so sum = mean × count. This rearrangement unlocks most average questions.
  • Median = middle value when ordered; resistant to outliers, unlike the mean.
Two-step percent trap: A price up 20% then down 20% is NOT back to start — it's 0.80 × 1.20 = 0.96, a 4% net drop. Percentages don't cancel.

Worked examples

A jacket costs $80 after a 20% discount. What was the original price?

  1. A 20% discount means you pay 100% − 20% = 80% of the original price.
  2. So $80 is 80% of the original: 80 = 0.80 × p.
  3. Divide: p = 80 ÷ 0.80 = $100.
  4. Check: 20% of $100 is $20, and $100 − $20 = $80 ✓. (Note: it is NOT $80 + 20% = $96 — that's the classic trap.)

The average of 6 numbers is 15. If one number, 25, is removed, what is the new average?

  1. Use sum = mean × count: the total of all 6 numbers is 15 × 6 = 90.
  2. Remove 25: the new sum is 90 − 25 = 65.
  3. There are now 5 numbers, so the new average is 65 ÷ 5 = 13.

A price rises 20%, then falls 20%. What is the net change?

  1. Start with $100 to make it concrete.
  2. Up 20%: 100 × 1.20 = $120.
  3. Down 20% from $120: 120 × 0.80 = $96.
  4. Net change: $96 vs $100 — a 4% DECREASE. Percent increases and decreases do not cancel out.

Common mistakes to avoid

  • Dividing by the new value instead of the original when computing percent change. Always divide by the ORIGINAL.
  • Assuming a 20% increase followed by a 20% decrease returns to the starting value. It does not — you end up 4% lower.
  • Confusing 'percent of' with 'percent more than.' 'B is 20% of A' and 'B is 20% more than A' are completely different.
  • Forgetting to put numbers in order before finding the median.

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Frequently asked questions

What is Problem-Solving and Data Analysis on the SAT?

It's the math area focused on real-world quantitative reasoning: ratios, proportions, rates, percentages, and unit conversions, along with reading and interpreting data in tables, graphs, and scatterplots. It also includes basic statistics like mean and median and understanding trends. These questions test whether you can work with the kinds of numbers and charts you meet in science, business, and daily life.

How do I solve percentage problems fast?

Translate the words into an equation: percent means divide by 100, of means multiply, and is means equals. For percent change, use the difference divided by the original amount, then convert to a percent. Be clear about which number is the whole. Watch for percent-of-a-percent traps and increases followed by decreases, where you can't just add and subtract the percentages.

How do I read graphs and tables without making mistakes?

Before calculating, read the title, the axis labels, and the units, and note any scale that doesn't start at zero or counts in large steps. Confirm you're pulling the value the question asks for. For scatterplots, look at the overall trend and any line of best fit. Many errors here come from misreading the chart, not from the math, so slow down at the start.

What's the difference between mean and median?

The mean is the average: add all values and divide by how many there are. The median is the middle value when the numbers are ordered. The median resists extreme values, so a few very large or small numbers pull the mean but barely move the median. If a question mentions outliers or a skewed set, think about how each measure responds.