Math · Problem-Solving and Data Analysis

Percentages on the Digital SAT

Percent questions look like the friendliest problems on the SAT Math section, which is exactly why they cost so many points. Everyone can find 25% of 60. The test knows that, so it asks for percent change instead of percent of, stacks two percent changes on top of each other, or gives you the final price and asks you to work backwards to the original.

The single most useful upgrade for this skill is thinking in multipliers. A 25% discount means multiplying by 0.75. An 8% tax means multiplying by 1.08. Once every percent move becomes a single multiplication, stacked changes are just multiplied multipliers, and reverse problems are just division. That one habit eliminates most of the traps in this category.

You always have the Desmos calculator on the Digital SAT, so none of these questions are about arithmetic speed. They are about whether you chose the right base for the percent, and whether you resisted the urge to add percents that should have been multiplied.

New to the Digital SAT? Start with how the test is structured and scored.

What the SAT actually tests

Finding a percent of a quantity, and finding what percent one quantity is of another.
Percent increase and decrease, where the base is always the starting value, not the ending value.
The difference between "percent of" (a portion) and "percent change" (a comparison to a starting point).
Complementary percentages: since every part of a whole adds up to 100%, you can find a missing category or count "how many did NOT" by subtracting from 100%.
Successive percent changes, like a markup followed by a discount, which multiply rather than add.
Reverse percent problems: recovering the original amount from a total that already includes tax or a discount.
Percent language in context, like interpreting "40% more than" versus "40% as much as."

Strategies that work

Turn every percent move into a multiplier

Write a 30% increase as x1.30 and a 30% decrease as x0.70 before doing anything else. Stacked changes become one expression: 1.30 x 0.70 = 0.91, so the net effect is a 9% drop. This kills the temptation to add and subtract percents, which only works when there is a single change.

Identify the base before you compute

Percent change is always measured against the starting value. If a price goes from 40 to 50, the increase is 10/40 = 25%, not 10/50 = 20%. When you read a percent question, underline the quantity that comes right after "of" or the value the change starts from. That is your denominator.

Work backwards with division, not subtraction

If a total of $86.40 already includes 8% tax, the original price is 86.40 / 1.08, not 86.40 minus 8% of 86.40. Subtracting a percent of the final value uses the wrong base and gives an answer that is close but wrong, which is exactly what one of the choices will be.

Test with 100 when the numbers are abstract

When a question describes percent changes with no starting number, plug in 100. A 20% increase then a 20% decrease takes 100 to 120 to 96, and now you can see the net 4% loss directly instead of reasoning about it in the abstract.

Mistakes to avoid

Adding successive percents: treating a 30% increase followed by a 30% decrease as a net change of zero.
Using the ending value as the base for percent change, which turns a 25% increase into a "20%" answer.
Answering with the discount amount instead of the sale price, or the change instead of the final value.
Undoing a tax or discount by subtracting a percent of the total instead of dividing by the multiplier.
Confusing "40% more than x" (which is 1.4x) with "40% of x" (which is 0.4x).

Practice with Nova, your Math coach

Answer right here and Nova walks you through it, just like in a drill. Difficulty labels are relative within this skill.

Tip: the Calculator button on each question opens the same Desmos graphing calculator you get on the real Digital SAT. Try solving these with it.

Question 1Easy

A jacket has a regular price of $60. During a sale, the price is reduced by 25%.

What is the sale price of the jacket?

Pick an answer to get instant coaching from Nova.

Question 2Medium

The price of a share of stock rose from $40 to $50 over one year.

By what percent did the price of the share increase?

Pick an answer to get instant coaching from Nova.

Question 3Hard

A store increases the price of a backpack by 30%. During a later sale, the store discounts the new price by 30%.

The final price of the backpack is what percent of the original price?

Pick an answer to get instant coaching from Nova.

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The rest of Problem-Solving and Data Analysis

Percentages is one of 7 skills in Problem-Solving and Data Analysis. The ideas build on each other, so it pays to learn them as a set rather than in isolation. See how Problem-Solving and Data Analysis fits together.

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