Successive Percentage Changes on the Digital SAT

Quick Answer: Successive percentage changes involve applying multiple percentage increases or decreases in sequence using decimal multipliers. A key tip is to multiply these decimals together using the built-in Desmos calculator rather than adding the raw percentages.

graph LR
    A[Original Value] --> B[Method 1: Step-by-Step]
    A --> C[Method 2: Multipliers]
    B --> D[Calculate 1st Change] --> E[Calculate 2nd Change] --> F[Final Answer]
    C --> G[Multiply: Original * M1 * M2] --> F

What Is Successive Percentage Changes?

Successive percentage changes occur when a value undergoes a percentage increase or decrease, and then the new value undergoes another percentage change. The most important rule for the Digital SAT is that successive percentages are multiplicative, not additive. If a shirt is marked up by $20\%$ and then discounted by $20\%$, it does not return to its original price.

Understanding this concept is essential for the Problem-Solving & Data Analysis domain, as outlined by the College Board for the 2026 Digital SAT format. It builds heavily on your foundational knowledge of unit rates and requires you to think about how values scale proportionally.

Instead of calculating the exact amount of each increase or decrease step-by-step, the most efficient strategy is to use decimal multipliers. Much like setting up proportions and cross-multiplication, using multipliers allows you to set up a single, clean equation that can be solved in one step.

Step-by-Step Method

1. Step 1 — Identify the original starting value (or use a placeholder like $x$ or $100$ if no starting value is given).
2. Step 2 — Convert the first percentage change into a decimal multiplier. Add the percentage to $100\%$ for an increase (e.g., $+20\% = 1.20$), or subtract from $100\%$ for a decrease (e.g., $-10\% = 0.90$).
3. Step 3 — Convert the second percentage change into its own decimal multiplier using the same logic.
4. Step 4 — Multiply the original value by all of the decimal multipliers in sequence.
5. Step 5 — If the question asks for the overall percentage change, compare your final combined multiplier to $1.00$. (For example, a final multiplier of $1.08$ means an overall $8\%$ increase).

Desmos Shortcut

The built-in Desmos Calculator is your best friend for successive percentage changes. Instead of doing scratchpad math, simply type your chain of multipliers directly into a Desmos cell. For example, if a $150$ item is marked up by $30\%$ and then discounted by $15\%$, just type 150 * 1.30 * 0.85 into Desmos. It will instantly output the final value, completely eliminating the risk of arithmetic errors.

Worked Example

Question: A store marks up the wholesale price of a jacket by $40\%$. During a clearance sale, the store discounts the marked-up price by $25\%$. What is the final price of the jacket as a percentage of the original wholesale price?

A) $105\%$ B) $115\%$ C) $15\%$ D) $150\%$

Solution:

Let the original wholesale price be $x$.

First, convert the $40\%$ markup into a decimal multiplier: $100\% + 40\% = 140\% = 1.40$

Next, convert the $25\%$ discount into a decimal multiplier: $100\% - 25\% = 75\% = 0.75$

Multiply the multipliers together to find the combined effect on the original price: $1.40 \times 0.75 = 1.05$

The final price is $1.05x$. To convert this back to a percentage, multiply by $100$, giving us $105\%$.

The correct answer is A.

Common Traps

1. Adding the percentages together — Based on Lumist student data, when dealing with compound interest and successive changes, 25% of students forget to convert percentages to decimal multipliers. Instead, they fall into the trap of simply adding $+40\%$ and $-25\%$ to get a $+15\%$ overall change. Always multiply the decimal forms!

2. Applying the second percentage to the original amount — Another common error occurs when students fail to recognize how values scale in direct and inverse variation or successive scenarios. If you calculate $25\%$ of the original wholesale price instead of the new marked-up price, your final calculation will be entirely incorrect. Always chain your multipliers so the second change applies to the updated value.

FAQ

Do I add the percentages together for successive changes?

No, you should never simply add successive percentages together. Instead, you must apply each percentage change to the new, updated value, which is easiest to do by multiplying their decimal multipliers.

How do I turn a percentage decrease into a multiplier?

Subtract the percentage from 100% and convert it to a decimal. For example, a 15% decrease leaves 85% of the original amount, so your multiplier is 0.85.

Can I use Desmos for successive percentage questions?

Yes! The built-in Desmos calculator is perfect for quickly multiplying a chain of decimal multipliers, ensuring you avoid manual arithmetic errors.

How many Successive Percentage Changes questions are on the SAT?

Problem-Solving & Data Analysis makes up approximately 15% of the SAT Math section. On Lumist, we currently have 18 practice questions specifically focused on successive percentage changes to help you prepare.