Percent Increase and Decrease on the Digital SAT

Quick Answer: Percent increase and decrease measures how much a value changes relative to its original amount, typically calculated using the multiplier method. When solving complex percentage problems on the Digital SAT, use the built-in Desmos calculator to quickly evaluate multiplier equations like $y = 1.15x$.

mindmap
  root((Percent Change))
    Formulas
      (New - Old) / Old * 100
      Multiplier Method
    Multipliers
      Increase: 1 + r
      Decrease: 1 - r
    Common Contexts
      Taxes and Tips
      Discounts
      Populations

What Is Percent Increase and Decrease?

Percent increase and decrease problems ask you to determine how a quantity changes relative to its starting value. On the 2026 Digital SAT, these questions appear frequently in the Problem-Solving & Data Analysis domain. You will encounter them in real-world contexts like calculating store discounts, adding sales tax, or modeling population changes over time. According to the College Board, mastering these practical math skills is essential for college readiness.

While you can use the traditional formula—finding the difference and dividing by the original—the most efficient way to handle these problems on the SAT is the multiplier method. A multiplier is a decimal that represents the final percentage of the original amount. For example, a 20% increase means the new value is 120% of the original, so the multiplier is 1.20. A 20% decrease means the new value is 80% of the original, making the multiplier 0.80.

Understanding percent change is closely related to mastering /sat/math/proportions-cross-multiplication and /sat/math/unit-rates, as all of these concepts require you to scale values proportionally.

Step-by-Step Method

1. Step 1 — Identify the original value and the percentage change. Read carefully to see if the value is going up (increase) or down (decrease).
2. Step 2 — Convert the percentage to a decimal by dividing it by 100 (e.g., 8% becomes 0.08).
3. Step 3 — Create your multiplier. For an increase, add the decimal to 1 ($1 + r$). For a decrease, subtract the decimal from 1 ($1 - r$).
4. Step 4 — Multiply the original value by your multiplier to find the new value. If there are multiple percentage changes (like a discount followed by tax), chain the multipliers together by multiplying them sequentially.

Desmos Shortcut

The built-in Desmos Calculator is an incredibly powerful tool for percent problems, especially when you need to work backward from a final amount to an original amount. If a problem states that a price after an 8% tax is $54, you can simply type the equation 1.08x = 54 into Desmos. Desmos will immediately graph the vertical line x = 50, revealing the original price without requiring manual algebra.

If the problem involves repeated percentage changes over time (like compound interest or population growth), you can graph the exponential function (e.g., y = 500(1.04)^x) and use the table feature or click along the curve to find the exact value at any given time.

Worked Example

Question: A local electronics store is having a sale where all laptops are discounted by 15%. A customer buys a laptop during the sale and must also pay an 8% sales tax on the discounted price. If the final amount the customer paid at the register was $734.40, what was the original price of the laptop?

A) $650 B)$800
C) $850 D)$900

Solution:

First, set up the multipliers for both the discount and the tax.

• 15% discount multiplier: $1 - 0.15 = 0.85$
• 8% tax multiplier: $1 + 0.08 = 1.08$

Let $x$ be the original price of the laptop. The customer pays the discounted price multiplied by the tax: $x \times 0.85 \times 1.08 = 734.40$

Combine the multipliers: $0.85 \times 1.08 = 0.918$

$0.918x = 734.40$

Divide both sides by 0.918 to solve for $x$: $x = \frac{734.40}{0.918} = 800$

The original price of the laptop was $800.

Correct Answer: B

Common Traps

1. Forgetting to convert percentages to decimals — Based on Lumist student data, 25% of errors on percentage and compound interest problems occur because students forget to convert the percentage to a decimal. For example, using $1 + 5$ instead of $1 + 0.05$ for a 5% increase will completely derail your answer.

2. Adding sequential percentages together — Our data shows that 60% of students initially confuse growth and decay factors when dealing with multiple percent changes. If an item is discounted by 20% and then another 10%, students often assume it is a 30% total discount. You must multiply the factors ($0.80 \times 0.90 = 0.72$, which is a 28% discount) rather than adding the raw percentages. This same logic applies to /sat/math/direct-and-inverse-variation when multiple variables scale at once.

FAQ

How do I calculate percent increase or decrease?

Subtract the original value from the new value, divide that difference by the original value, and multiply by 100. A positive result is an increase, while a negative result is a decrease.

What is a multiplier in percent problems?

A multiplier, or growth/decay factor, is the decimal you multiply an original amount by to get the new amount. For a 15% increase, the multiplier is 1.15; for a 15% decrease, it is 0.85.

Can I just add or subtract percentages directly?

Usually no. If a price increases by 20% and then decreases by 20%, you do not end up at the original price because the second percentage is calculated from the new, higher amount.

How many Percent Increase and Decrease questions are on the SAT?

Problem-Solving & Data Analysis makes up approximately 15% of the Digital SAT Math section. On Lumist.ai, we have 30 practice questions specifically focusing on percent increase and decrease to help you prepare.