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Math: Problem-Solving and Data Analysis, 3 original questions

SAT Percentage Practice: Questions and Answers

Practice reverse percentages, decimal conversions and percent change with three original SAT-style questions, explained answers and common percentage-base mistakes.

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The short answer

A percentage expresses an amount relative to a specific base. Convert p% to p/100 before calculating, and name the whole to which it applies. A percent change compares the difference with the original amount, not the new amount. If the final amount and growth factor are known, divide to recover the original. Distinguish a percentage from a percentage-point difference. Write the relationship first, then use the requested unit; a dollar difference by itself is not a percentage.

Method at a glance

  1. 1Name the base quantity
  2. 2Convert between percent and decimal
  3. 3Write a multiplier equation
  4. 4Check what the question requests

Try the 3 questionsRead the full method

Step-by-step method

Use these steps in order, then apply them to the questions below.

  1. Step 1: Name the base quantity

    Identify what represents 100%. For percent change, the base is the original amount.

  2. Step 2: Convert between percent and decimal

    Divide a percent by 100 to use it as a decimal multiplier. Multiply a decimal by 100 to express it as a percent.

  3. Step 3: Write a multiplier equation

    An increase of p% gives new = original × (1 + p/100). Divide by the multiplier when solving for the original.

  4. Step 4: Check what the question requests

    Separate an amount, a decimal proportion, a percent change and a percentage-point change. Attach the correct unit to the result.

Try 3 SAT-style questions

These are original SAT-style questions written by PeakSAT, not official College Board questions. Choose an answer and check it to see why each choice is right or wrong, or open the worked answer.

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Question 1 of 3

An item's price increases by 20% and becomes $84. What was its original price?

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Correct answer

Choice B: $70

Explanation

Let the original price be P. A 20% increase gives 1.20P = 84, so P = 84/1.20 = 70. Checking: 20% of $70 is $14, and $70 + $14 = $84.

Why each choice is right or wrong

  1. Choice A

    Subtracting $20 treats a percentage as a dollar amount.

  2. Choice B

    Correct answer

    Correct: dividing the final price by 1.20 gives $70.

  3. Choice C

    This applies another 20% increase to the final price.

  4. Choice D

    This doubles the final price instead of reversing the stated multiplier.

Question 2 of 3

Which percentage is equivalent to the decimal 0.004?

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Correct answer

Choice B: 0.4%

Explanation

To write a decimal as a percent, multiply by 100: 0.004 × 100 = 0.4. Thus 0.004 = 0.4%. Checking in reverse, 0.4/100 = 0.004.

Why each choice is right or wrong

  1. Choice A

    0.04% equals 0.0004, which is ten times smaller.

  2. Choice B

    Correct answer

    Correct: multiplying the decimal by 100 gives 0.4%.

  3. Choice C

    4% equals 0.04, which is ten times larger.

  4. Choice D

    40% equals 0.4, which is one hundred times larger.

Question 3 of 3

A club's membership increases from 40 to 52. What is the percentage increase?

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Correct answer

Choice C: 30%

Explanation

The increase is 52 − 40 = 12 members. Divide by the original 40: 12/40 = 0.30, or 30%. The new membership is 130% of the original, but the increase alone is 30%.

Why each choice is right or wrong

  1. Choice A

    12 is the member-count increase, not the percent increase.

  2. Choice B

    This divides the change by the new amount 52 rather than the original 40.

  3. Choice C

    Correct answer

    Correct: 12/40 × 100 = 30%.

  4. Choice D

    130% describes the new amount as a percent of the original, including the original 100%.

Common mistakes

  • Dividing a change by the final amount. Percent increase or decrease uses the original amount as its denominator.

  • Subtracting the stated percent from a final amount to undo growth. Divide by the growth factor instead.

  • Moving the decimal only one place in a percent conversion. Percent means per hundred, so conversion uses a factor of 100.

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Common questions

How do I reverse a percentage increase?

Divide the final amount by 1 plus the decimal increase. Subtracting that percent of the final amount uses the wrong base.

Are percent change and percentage-point change the same?

No. A move from 20% to 25% is 5 percentage points, but it is a 25% increase relative to the original 20%.

Why is the original amount the percent-change denominator?

The question asks how large the change is relative to where the quantity started. State that reference amount before dividing.

Sources

  1. College Board: Math section overviewsatsuite.collegeboard.org
  2. College Board: Student Question Bank Math skillssatsuite.collegeboard.org

Sources are linked for reference; they do not endorse PeakSAT. How we prepare our guides