SAT Math · Problem-Solving and Data Analysis · Skill 2 of 7

Percentages, done fast

Find a percent of anything, turn every increase and decrease into a single multiplier, and work backwards to an original price. One idea handles almost every SAT percent question.

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Hi, I’m Io. Percent just means “out of 100”. Everything else follows.
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The percent bar

Explore · 5 min

Percent means per hundred, so 35% is 35/100 = 0.35. The whole is always 100%, and a part is that decimal times the whole. Parts can be bigger than the whole too: 125% of something is more than all of it.

part = (percent ÷ 100) × whole

Three kinds of question

Practise · 5 min

Every simple percent question gives you two of part, percent and whole, and asks for the third. The word “of” points to the whole.

  • Find the part: what is 30% of 70? 0.3 × 70 = 21
  • Find the percent: 12 is what percent of 48? 12 ÷ 48 = 0.25 = 25%
  • Find the whole: 15 is 20% of what number? 15 ÷ 0.2 = 75

One multiplier for every change

Learn · 4 min

To increase by 15%, you keep the whole 100% and add 15%, so you multiply by 1.15. To decrease by 15%, you keep 85%, so you multiply by 0.85. This one step replaces “find 15%, then add or subtract it”.

new = old × (1 ± r)

Percent change

Practise · 4 min

To find a percent increase or decrease, divide the change by the original value, the one you started from.

percent change = (new − original) ÷ original × 100
Worked example: a ticket price rises from $40 to $46.
  1. Change: 46 − 40 = 6
  2. Divide by the original: 6 ÷ 40 = 0.15
  3. So the price rose by 15%
  4. Check with the multiplier: 40 × 1.15 = 46

Changes on top of changes

Explore · 5 min

When one percent change follows another, the second is taken from the new amount. So the multipliers multiply: up 10% then down 10% is 1.1 × 0.9 = 0.99, a 1% drop overall. Try it with a $100 price.

Finding the original

Practise · 4 min

If you know the amount after a change, write the change as a multiplier and divide by it. The percent was taken from the original, so it has to be undone the same way.

Worked example: after a 20% increase, a price is $72. What was it before?
  1. A 20% increase means original × 1.2 = 72
  2. Divide: original = 72 ÷ 1.2
  3. So the original price was $60
  4. Check: 60 × 1.2 = 72

Percentage points and percent of a percent

Learn · 4 min

When the values are themselves percents, two phrases matter:

  • Percentage points are a plain subtraction: 4% to 6% is up 2 percentage points.
  • Percent change still divides by the original: from 4 to 6 is a (6 − 4) ÷ 4 = 50% increase.
  • Percent of a percent multiplies: 25% of 40% of a group is 0.25 × 0.4 = 10% of the group.

Real-life percentages

Scenarios · 6 min

Shopping, pay and surveys are where the SAT hides its percent questions. Pick a scenario and answer each question.

Spot the trap

Detective · 3 min

These three slips are the most common wrong answers on SAT percent questions. Find the faulty step in each.

Final challenge

8 questions · 10 min

Key ideas to carry in
Partpart = (percent ÷ 100) × whole.
MultipliersUp r%: 1 + r. Down r%: 1 − r.
Percent changeChange ÷ original.
Stacked changesMultiply the multipliers.
Working backwardsDivide by the multiplier.
Points4% to 6% is 2 points, and a 50% increase.
Challenge