Problem Solving & Data Analysis · SAT Math

Percent Problems on the Digital SAT

Percentages show up in roughly 1 in 7 Digital SAT math questions — almost always wrapped in a word problem about discounts, taxes, population growth, or interest. The math is straightforward; the setups are the trap. This lesson covers the four percent question types you'll see, the multiplier trick that beats every successive-percent question, and 8 practice problems.
By the Prepiii Editorial TeamUpdated 2026-05-23~10 min read

Percent basics: convert before you compute

Percent literally means "per 100." To convert a percent to a decimal, move the decimal point two places left: 15% = 0.15, 2.5% = 0.025, 300% = 3.0.

The percent equation:

part = percent × whole

Rearrange to find any one given the other two.

Three forms of the same question:

  • What is 15% of 200? → part = 0.15 × 200 = 30
  • 30 is what percent of 200? → percent = 30 / 200 = 0.15 = 15%
  • 30 is 15% of what number? → whole = 30 / 0.15 = 200

Percent change: increase or decrease

Percent change measures how much something grew or shrank. The formula:

% change = (new − old) / old × 100

Critical: the denominator is always the original value, not the new one. Mix this up and your answer will be close but wrong.

Example. A stock goes from $50 to $65. The percent change is (65 - 50) / 50 = 15/50 = 0.30 = 30% increase.

If the stock then drops back from $65 to $50, the percent change is (50 - 65) / 65 ≈ -23.1%. Notice it's not -30% — because the denominator is now 65, not 50. A 30% gain followed by a 23% loss returns you to the start.

The multiplier trick (memorize this)

Instead of computing increases as "original + percent," multiply directly:

X% increase → multiply by (1 + X/100).

15% increase → multiply by 1.15

8% increase → multiply by 1.08

X% decrease → multiply by (1 − X/100).

15% decrease → multiply by 0.85

8% decrease → multiply by 0.92

Why this matters: for successive percent changes, you multiply the multipliers — never add. A 10% increase followed by a 20% increase is 1.10 × 1.20 = 1.32, a 32% increase total (not 30%).

Discount, tax, and tip patterns

Word problems with discounts, taxes, and tips are just percent-change problems in disguise. Use multipliers:

  • Discount: a 25% off sale → multiply by 0.75.
  • Tax: 8% sales tax → multiply by 1.08.
  • Tip: 20% tip on a meal → multiply by 1.20.
  • Discount AND tax: 25% off then 8% tax → multiply by 0.75 × 1.08 = 0.81.

Reverse problems. "After a 20% discount, the price is $48. What was the original?" Set up: 0.80 × original = 48, so original = 48 / 0.80 = $60. Don't mistakenly add 20% back to $48 — you'll get $57.60, which is wrong.

Stuck on a percent problems problem?

Prepiii's AI tutor watches your scratchwork and tells you exactly where the logic broke — not just whether the answer was right.

Start Free

Solving with Desmos

Desmos turns percent problems into one-line calculations. Three techniques:

1. Find percent of a number

For "15% of 240," just type 0.15 * 240. Desmos returns 36.

2. Percent change

For "by what percent did 80 increase to 100?," type (100 - 80) / 80. Desmos returns 0.25 → 25% increase.

3. Successive changes

For "200 increased by 10%, then decreased by 5%," type 200 * 1.10 * 0.95. Desmos returns 209. Chain multipliers — never add percentages.

For the full set of Desmos techniques across the entire test, see our Desmos & Test Tools guides.

Common mistakes

Adding percentages instead of multiplying

A 10% increase followed by a 20% increase is NOT a 30% increase. It's 1.10 × 1.20 = 1.32, or a 32% increase. Successive percent changes multiply, never add.

Wrong denominator in percent change

The denominator is always the ORIGINAL value, not the new one. Going from $50 to $65 is a 30% increase (15/50). Going from $65 back to $50 is a ~23% decrease (15/65), not a 30% decrease.

Reversing a discount by adding back the same percent

If a $48 item is the price AFTER a 20% discount, the original was $48 / 0.80 = $60. Adding 20% to $48 gives $57.60 — wrong.

Forgetting that 'percent of' multiplies but 'percent more than' adds

'15% of 200' is 0.15 × 200 = 30. '15% more than 200' is 200 + 0.15(200) = 230 (or 1.15 × 200). Read the question carefully.

Practice problems

8 problems adapted from College Board released questions and internal Prepiii sets. Click each one to reveal the solution.

1

What is 30% of 240?

  1. 48
  2. 60
  3. 72
  4. 84

Click to reveal solution →

Answer: (C) 72

0.30 × 240 = 72.

2

What is 18 expressed as a percentage of 75?

  1. 18%
  2. 20%
  3. 24%
  4. 30%

Click to reveal solution →

Answer: (C) 24%

18 / 75 = 0.24 = 24%.

3

The price of a jacket is reduced by 25% from $80. What is the new price?

  1. $55
  2. $60
  3. $65
  4. $70

Click to reveal solution →

Answer: (B) $60

Multiplier for 25% off: 0.75.

80 × 0.75 = 60.

4

A population was 8,000 and grew by 15%. What is the new population?

  1. 8,150
  2. 8,800
  3. 9,200
  4. 9,600

Click to reveal solution →

Answer: (C) 9,200

8000 × 1.15 = 9200.

5

After a 10% discount and an 8% sales tax (applied to the discounted price), a phone costs $324. What was the phone's original price?

Click to reveal solution →

Answer: $333.33

The combined multiplier is 0.90 × 1.08 = 0.972.

original × 0.972 = 324 → original = 324 / 0.972 ≈ 333.33.

6

A stock's value increased by 20% in January and then decreased by 20% in February. By what percent did the stock change overall from the start of January to the end of February?

  1. 0% (no change)
  2. 4% decrease
  3. 4% increase
  4. 10% decrease

Click to reveal solution →

Answer: (B) 4% decrease

Combined multiplier: 1.20 × 0.80 = 0.96. That's a 4% decrease (0.96 = 1 - 0.04). Don't fall for the trap that +20% and -20% cancel.

7

If 45 is 30% of x, what is the value of x?

  1. 75
  2. 100
  3. 120
  4. 150

Click to reveal solution →

Answer: (D) 150

0.30 × x = 45 → x = 45 / 0.30 = 150.

8

A car's value depreciates by 12% each year. If the car is worth $20,000 today, what will it be worth in 2 years (rounded to the nearest dollar)?

Click to reveal solution →

Answer: $15,488

Multiplier per year: 0.88. After 2 years: 20000 × 0.88² = 20000 × 0.7744 = 15488.

Frequently asked questions

How do I calculate a percent of a number?

+
Convert the percent to a decimal (move the decimal point two places left), then multiply. For example, 15% of 200 is 0.15 × 200 = 30.

What's the formula for percent change?

+
Percent change = (new value − original value) / original value × 100. The denominator is always the original value, not the new one.

Why can't I add percentages for successive changes?

+
Because each percent change applies to a different base. A 10% increase followed by a 20% increase isn't a 30% increase — it's 1.10 × 1.20 = 1.32, or 32%. Always multiply the multipliers, never add the percentages.

How do I reverse a percent change to find the original?

+
Divide, don't subtract. If a $48 item is the price after a 20% discount, the original is $48 / 0.80 = $60. Adding 20% back gives the wrong answer.

Discount then tax — does the order matter?

+
Mathematically, no. (0.75 × 1.08) × price equals (1.08 × 0.75) × price — multiplication is commutative. But the SAT will usually apply tax after the discount, so do the discount first.

Keep going

Ratios and proportions

The other core problem-solving topic

All SAT Math topics

Browse every Digital SAT math topic

Want unlimited percent problems practice?

Prepiii generates new problems on demand and walks you through your scratchwork. Free to start, no credit card.

Start Free