Percent change questions come up on every SAT. They appear in word problems, data tables, and even calculator section questions. Here's a reliable method that works every time.

The Percent Change Formula

If the result is positive, it's an increase. If negative, it's a decrease.

Example 1: A shirt's price goes from 52. What is the percent increase?

The Multiplier Method (Faster)

Instead of the formula, use multipliers:

Example 2: A $200 item increases by 15%.

Example 3: A $80 item is discounted 25%.

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Finding the Original Price

Example 4: After a 20% increase, a stock is worth $72. What was the original price?


Common trap: students subtract 20% of 72 () and get . That's wrong because 20% of the original is not the same as 20% of the new value.

Successive Percent Changes

When percent changes happen one after another, multiply the multipliers — don't add the percentages.

Example 5: A price increases by 10% and then decreases by 10%. Is it back to the original?

No! It's 99% of the original — a net 1% decrease. This surprises many students.

Example 6: A population grows by 20% one year and 30% the next. What is the total percent increase?

Total increase: 56% (not 50%).

Tax, Tip, and Markup

Example 7: A meal costs $45. With 8% tax and a 20% tip (on the pre-tax amount), what's the total?

Tax: 3.60$
Tip: 9.00$
Total: 57.60$

Or use the multiplier: 57.60$

Practice Problems

Problem 1: A town's population decreased from 8,000 to 6,800. What was the percent decrease?

Solution


The population decreased by 15%.

Problem 2: After a 30% discount, a laptop costs $560. What was the original price?

Solution


800$

Problem 3: A stock increases by 50% and then decreases by 40%. What is the net percent change?

Solution

. Net change: (a 10% decrease).

Key Takeaways

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