Digital SAT · Percentages

How to Solve Percentages on the Digital SAT

Percent questions translate straight into arithmetic. "Part is percent of whole" becomes part equals percent times whole, and any one of the three follows from the other two. For a change, use the difference over the original. When changes stack, like a discount and then a tax, multiply their factors rather than adding. Set the relationship up, then let Desmos run the numbers, since a fair share are grid-ins.

Written from Perfect1600’s analysis of every percentages question in our bank·Method checked against the current Bluebook test

per test: 1 per test
typical difficulty: Easy to medium
practice questions: 112

How we counted

Frequency reflects how often this question type appears on a full-length Digital SAT. The difficulty mix reflects every question of this type across our bank.

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What the question bank shows

translate

Is/of/what percent

"Is" is equals, "of" is times, "what percent" is the unknown.

70%

Do it in Desmos

Set up the relationship and the calculator finishes it.

×, not +

Stack by multiplying

Successive changes multiply their factors; adding percentages is the classic error.

How to recognize percentages questions

The words is, of, and what percent appear, or there is an increase, decrease, discount, or tax.
You are asked for a part, a whole, a percent, or a percent change.
Steps chain, such as a discount followed by a tax.
Answers are numbers, and roughly four in ten are grid-ins.

Why students miss these

The setup is simple but easy to misdirect. A percent gets taken of the wrong base, successive percentages get added instead of multiplied as factors, or percent change gets confused with percentage points. A 25 percent discount then an 8 percent tax is not a 17 percent change; it is 0.75 times 1.08. On a grid-in a slip like that has nothing to catch it.

The step-by-step method

1
Translate the words
"Is" becomes equals, "of" becomes times, "what percent" is the unknown: part equals percent times whole.
2
Use change over original
For a percent increase or decrease, compute the difference divided by the original, then convert to a percent.
3
Multiply factors when they stack
Apply each change as a factor, like 0.75 for a 25 percent discount and 1.08 for an 8 percent tax, in order.
4
Answer the exact quantity
Compute in Desmos, and confirm whether the final amount, the change, or the percent is wanted.

Solving it on Desmos

Type the relationship. Enter it directly, like 15/60 for "15 is what percent of 60", and read the decimal.
Chain the factors. For stacked changes, type the base times each factor, like 120 * 0.75 * 1.08.
Convert to a percent. Multiply a decimal by 100, and confirm you reported what was asked.

Full Desmos walkthrough for percentages→

When to use it: With the relationship set up, the calculator handles the arithmetic and keeps a grid-in clean. Translating the words and choosing the right base are the parts you own.

See it live: open a real question in the same Desmos calculator you get on Perfect1600, with the equations already typed in.

Worked examples

Easy example

15

is what percent of

60

4\%

25\%

45\%

75\%

A: Incorrect. $4\%$ divides $60$ by $15$ ; the part goes over the whole.

B: Correct. $\frac{15}{60}=0.25=25\%$ .

C: Incorrect. $45\%$ uses the difference $60-15$ .

D: Incorrect. $75\%$ is the complementary part, not $15$ of $60$ .

Explanation

15/60 = 0.25 = 25%.

Medium example

The number of members of a club decreased from 500 to 460. What was the percent decrease in the number of members?

8

9.2

40

92

A: Correct. The decrease is $\frac{500 - 460}{500} = \frac{40}{500} = 0.08 = 8\%$ .

B: Incorrect. This divides the change by 460 instead of 500.

C: Incorrect. This gives the raw change, 40, not the percent.

D: Incorrect. This computes $\frac{460}{500}$ , the remaining percent.

Explanation

$\frac{40}{500} = 8\%$ .

Hard example

A jacket priced at 120 dollars is discounted by 25%, and then a 8% sales tax is applied to the discounted price. What is the final price, in dollars?

90.00

97.20

99.60

129.60

A: Incorrect. This applies the discount but omits the sales tax.

B: Correct. $120 \times 0.75 \times 1.08 = 97.20$ dollars.

C: Incorrect. This combines the percents into a single 17% reduction.

D: Incorrect. This applies the 8% tax but omits the discount.

Explanation

$120 \times 0.75 \times 1.08 = 97.20$ .

Detailed explanation

The 25% discount multiplies by 0.75 to give 90, and the 8% tax multiplies by 1.08 to give $90 \times 1.08 = 97.20$ . Forgetting the tax gives 90, and forgetting the discount gives 129.60.

The common traps

Pattern	What it does	The tell
Wrong base	Took the percent of the wrong number, like the discounted price instead of the original.	Reread which amount the percent is of before multiplying.
Added successive percents	Combined a discount and a tax by adding the percentages.	Stacked changes multiply their factors; they do not add.
Percent versus percentage points	Confused a change in percent with a change in percentage points.	A rise from 20 to 25 percent is 5 percentage points but a 25 percent increase.
Wrong quantity	Gave the final amount when the change was asked, or the reverse.	Confirm whether the amount, the change, or the percent is wanted.

Try it: two real questions

Question 1easy

What is 10% of 470?

Question 2easy

A container holds 320 marbles. Of these marbles, 10% are red. How many of the marbles are red?

Question 3 is ready when you are

Keep going with more questions of this type, each with the same step-by-step reasoning. Free to start.

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Common questions

How do you solve percent problems on the SAT?

Translate the words into part equals percent times whole, and solve for the missing piece. On the digital test, type the arithmetic into Desmos, especially on grid-ins.

How do I calculate percent increase or decrease?

Use the difference over the original, then multiply by 100. A drop from 500 to 460 is 40 over 500, an 8 percent decrease.

How do I handle a discount and then a tax?

Multiply the base by each factor in order. A 25 percent discount is 0.75 and an 8 percent tax is 1.08, so the price is base times 0.75 times 1.08, not one combined percent.

What is the difference between percent and percentage points?

Percentage points are the raw gap between two percents; percent change is relative. Going from 20 to 25 percent is 5 percentage points, a 25 percent increase.

Can Desmos do percent calculations?

Yes. Type the arithmetic, like 15/60 or 120 * 0.75 * 1.08, and read the value. It keeps a grid-in from a careless slip.

Practice percentages the way it is tested

Start with the free 16-question diagnostic, then drill this type with step-by-step reasoning on every question.

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What the question bank shows

How to recognize percentages questions

Why students miss these

The step-by-step method

Translate the words

Use change over original

Multiply factors when they stack

Answer the exact quantity

Solving it on Desmos

Worked examples

The common traps

Try it: two real questions

Question 3 is ready when you are

Often confused with

Related reading

Common questions

How do you solve percent problems on the SAT?

How do I calculate percent increase or decrease?

How do I handle a discount and then a tax?

What is the difference between percent and percentage points?

Can Desmos do percent calculations?

Practice percentages the way it is tested