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

SAT Ratios, Rates and Units Practice: Questions and Answers

Practice part-to-part ratios, recipe scaling and unit conversions in three original SAT-style questions, with clear setups and complete answer explanations.

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The short answer

A ratio compares quantities, while a rate compares quantities with units, often per one unit. Decide whether a ratio is part-to-part or part-to-whole before using it. For a fixed proportional relationship, find a unit rate or scale both quantities by the same factor. Carry units through a conversion so unwanted units cancel. A constant rate is an assumption, not a rule for every situation. Check whether your result should be a quantity, a rate or a dimensionless ratio.

Method at a glance

  1. 1Name the compared quantities
  2. 2Find the common scale factor
  3. 3Use a unit rate when helpful
  4. 4Arrange conversion factors

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 compared quantities

    Write the ratio in the given order and label its units. For a part-to-part ratio, add the parts to find the whole.

  2. Step 2: Find the common scale factor

    Divide a known total or corresponding amount by its ratio units. Multiply every part by the same factor.

  3. Step 3: Use a unit rate when helpful

    Divide the output quantity by the input quantity to obtain a per-unit rate, then scale to the requested amount.

  4. Step 4: Arrange conversion factors

    Place each unit you want to remove opposite itself in a fraction. Check that only the requested unit remains.

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

Blue and white paint are mixed in a 3:5 ratio by volume. The mixture contains 64 liters total. How many liters are blue paint?

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Correct answer

Choice A: 24 liters

Explanation

The ratio has 3 + 5 = 8 total parts. Each part represents 64/8 = 8 liters. Blue paint uses 3 parts, so its volume is 3 × 8 = 24 liters. White paint accounts for the remaining 40 liters.

Why each choice is right or wrong

  1. Choice A

    Correct answer

    Correct: 3/8 of the 64-liter mixture is 24 liters.

  2. Choice B

    This divides the mixture equally despite the unequal ratio parts.

  3. Choice C

    40 liters is the white paint amount, not the blue amount.

  4. Choice D

    This multiplies the whole by 3 without dividing by the total ratio parts.

Question 2 of 3

A recipe uses 2.5 cups of flour for 6 servings. If every ingredient is scaled proportionally, how many cups of flour are needed for 15 servings?

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Correct answer

Choice B: 6.25 cups

Explanation

The serving scale factor is 15/6 = 2.5. Apply the same factor to the flour: 2.5 × 2.5 = 6.25 cups. The assumption of proportional scaling is explicitly given.

Why each choice is right or wrong

  1. Choice A

    This doubles the flour, which would make 12 rather than 15 servings.

  2. Choice B

    Correct answer

    Correct: scaling by 15/6 gives 6.25 cups.

  3. Choice C

    9 is the increase in servings, not the required flour amount.

  4. Choice D

    This multiplies by 15 without dividing by the original 6 servings.

Question 3 of 3

A vehicle travels at 18 meters per second. What is that speed in kilometers per hour?

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Correct answer

Choice D: 64.8 km/h

Explanation

Convert seconds to hours and meters to kilometers: 18 meters/second × 3,600 seconds/hour × 1 kilometer/1,000 meters = 64.8 kilometers/hour. The meters and seconds cancel, leaving the requested units.

Why each choice is right or wrong

  1. Choice A

    This divides by 3.6, converting in the wrong direction.

  2. Choice B

    The numerical value changes when the distance and time units change.

  3. Choice C

    This does not apply the stated meter-to-kilometer and second-to-hour factors.

  4. Choice D

    Correct answer

    Correct: 18 × 3,600/1,000 = 64.8 km/h.

Common mistakes

  • Treating a 3:5 ratio as 3/5 of the total. The whole contains 3 + 5 = 8 ratio parts.

  • Scaling only one quantity in a proportional relationship. Both quantities must use the same factor.

  • Reversing a unit conversion factor. Write units explicitly and cancel them before calculating.

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Common questions

How do I turn a part-to-part ratio into a fraction of the whole?

Add the ratio parts for the denominator. In a 3:5 mix, the first part occupies 3/(3 + 5) of the whole.

When can I assume proportional scaling?

When the problem states or establishes a constant ratio or rate. A changing rate can invalidate a simple proportion.

Why should I write units inside the calculation?

They show which factors belong in the numerator or denominator and whether the final quantity has the requested unit.

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