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SAT Math skill page

SAT Percent Change Practice

Set percent change against the original amount, not the new amount.

Practice percent change in Dolphin SATPractice questions
10-16 min practice time3 questions on pageProblem Solving and Data Analysis
Practice time10-16 min
Practice questions3 questions
Best forProblem Solving and Data Analysis

What this tests

What to know for this SAT skill

How do you track the base through percent changes?

Name the quantity each percent is taken from before calculating. Recovering an original value and applying successive changes require different operations, even when the stated percentages match.

How do you recover the original amount?

Write final amount = original amount times multiplier. For a p percent increase, the multiplier is 1 + p/100; for a decrease, it is 1 - p/100. Divide the final amount by that nonzero multiplier. Applying the opposite percent to the final amount uses the wrong base. A 100% decrease leaves zero and cannot reveal the original amount on its own.

How do successive changes combine?

When each change applies to the updated amount, multiply the successive multipliers; do not add the stated percentages. To find the overall percent change from a positive starting amount, subtract 1 from the combined multiplier and multiply by 100. A negative result indicates a decrease.

What should you check before calculating?

Read whether each adjustment uses the original amount or the updated amount. Changes explicitly measured from the same original amount can be combined as amounts; they are not automatically successive multipliers. Keep intermediate values unrounded until the question calls for rounding.

References: OpenStax: percent equations and original amounts and College Board SAT Math specifications: percentages. Guidance reviewed .

Dolphin practice questions

Practice your skill

Question 1 of 3Easy
A $40 item is discounted by 25%. What is the sale price?
  1. $10
  2. $25
  3. $30
  4. $35
Show answer and solution
Correct answerC. $30

Solution walkthrough

  1. 25% of 40 is 10, so the discounted price is 40 - 10 = 30.
Question 2 of 3Medium
A value increases from 80 to 100. What is the percent increase?
  1. 20%
  2. 25%
  3. 80%
  4. 125%
Show answer and solution
Correct answerB. 25%

Solution walkthrough

  1. The increase is 20, and 20/80 = 0.25 = 25%.
Question 3 of 3Hard
After a 20% increase, a price is $72. What was the original price?
  1. $54
  2. $57.60
  3. $60
  4. $90
Show answer and solution
Correct answerC. $60

Solution walkthrough

  1. The final price is 120% of the original.
  2. 72 / 1.2 = 60.

Avoid these traps

Common mistakes on this skill

Dividing by the new value

Percent change uses the original value as the denominator.

Using the percent itself as the multiplier

A p percent increase uses 1 + p/100; a decrease uses 1 - p/100.

Study plan

How to practice this skill in Dolphin

  1. Label the original and new values before calculating.
  2. Compute change divided by the original value, or use the appropriate multiplier.
  3. Check that the direction and approximate size of the result match the situation.
Practice percent change in Dolphin SAT

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FAQ

Questions about SAT Percent Change Practice

What is the percent-change formula?

It is (new value - original value) divided by the original value, multiplied by 100 percent.

Do equal percent increases and decreases cancel?

No. They use different base values; for example, up 20 percent and down 20 percent leaves 96 percent of the original.