20 medium SAT Ratios, rates, proportions, units questions
Medium is where most scores are actually won and lost. These questions are not tricky for the sake of it, but every one of them has a wrong answer built to catch a specific shortcut.
Every question below is a real item from the SAT Climb bank, tagged medium by the same difficulty model the app uses to build your practice. Pick an answer before you open the explanation.
Math · Problem-Solving and Data Analysis~2 per testMedium tier
A printer produces 450 pages in 15 minutes. At this rate, how many pages does the printer produce in 1 hour and 20 minutes?
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Why D is right
The printer produces 450 pages in 15 minutes, so the rate is 450/15 = 30 pages per minute. Converting 1 hour and 20 minutes to 80 minutes, the printer produces 30 × 80 = 2400 pages.
Why the others are wrong
AThis results from treating 1 hour 20 minutes as 60 minutes only, yielding 450 × 60/15 = 1800.
BThis results from doubling the time incorrectly, treating 1 hour 20 minutes as 2 hours (120 minutes), yielding 450 × 120/15 = 3600.
CThis results from inverting the calculation structure, dividing 450 by 80 instead of computing the correct multiplication.
Question 2Medium
A car travels 150 kilometers in 2 hours. At this same rate, how many meters does the car travel in 4 minutes? 1 kilometer = 1000 meters
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Why B is right
The car travels 150 kilometers in 2 hours, which is 150 ÷ 2 = 75 kilometers per hour. Converting to meters per hour gives 75 × 1000 = 75000 meters per hour. Converting 4 minutes to hours gives 4 ÷ 60 = 1/15 hours. Therefore, the car travels 75000 × 1/15 = 5000 meters in 4 minutes.
Why the others are wrong
AThis incorrectly calculates 75 × 4 = 300 by treating 4 minutes as 4 hours and failing to convert kilometers to meters.
CThis inverts the calculation by dividing 4 by 75000 instead of multiplying 75000 by the fraction of an hour.
DThis applies an incorrect negative sign to the otherwise correct result.
Question 3Medium
Steel has a density of 7.85 grams per cubic centimeter. A cube of steel has a mass of 3925 grams. To the nearest centimeter, what is the edge length of the cube?
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Why A is right
Using mass = density × volume, the volume is 3925 ÷ 7.85 = 500 cubic centimeters. For a cube with edge length s, volume = s3, so s3 = 500 and s = ∛500 ≈ 7.94, which rounds to 8 centimeters.
Why the others are wrong
BThis is the volume of the cube in cubic centimeters. The student computed volume but did not take the cube root to find edge length.
CThis results from taking the square root of the volume instead of the cube root, computing √500 ≈ 22.4, then likely an arithmetic error, or from computing 8² = 64.
DThis results from using mass ÷ density incorrectly with an additional arithmetic error, or from using the wrong root operation.
Question 4Medium
A factory produces 1260 units in 9 hours. At this rate, how many units does the factory produce in 6 hours and 45 minutes?
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Why C is right
The factory produces 1260 units in 9 hours, so the rate is 1260/9 = 140 units per hour. Converting 6 hours and 45 minutes to 6.75 hours, the factory produces 140 × 6.75 = 945 units.
Why the others are wrong
AThis results from using only the 6-hour portion and ignoring the 45 minutes, yielding 140 × 6 = 840.
BThis results from inverting the calculation structure, dividing 9 by 6.75 and treating the result as the answer.
DThis results from treating 45 minutes as 0.75 hours but adding instead of multiplying correctly, or rounding 6.75 to 7.5.
Question 5Medium
A scale model of a building is constructed such that 2 inches on the model represents 15 feet on the actual building. If a window on the model is 0.8 inches tall, how many feet tall is the actual window?
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Why B is right
The scale is 2 inches on the model to 15 feet on the actual building, so each inch on the model represents 15 ÷ 2 = 7.5 feet. A window that is 0.8 inches tall on the model is 0.8 × 7.5 = 6 feet tall on the actual building.
Why the others are wrong
AThis results from incorrectly dividing 0.8 by 7.5 instead of multiplying, inverting the scale relationship.
CThis results from using the conversion factor of 7.5 feet per inch but failing to multiply by 0.8.
DThis results from incorrectly multiplying 15 by 0.8 without first determining the scale factor per inch.
Question 6Medium
Titanium has a density of 4.5 grams per cubic centimeter. A solid sphere of titanium has a radius of 3 centimeters. To the nearest gram, what is the mass of the sphere? (The volume of a sphere with radius r is given by 34πr3.)
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Why B is right
The volume of the sphere is 34π(33) = 34π(27)=36π cubic centimeters. Using mass = density × volume, the mass is 4.5×36π=162π≈508.9 grams, which rounds to 509 grams.
Why the others are wrong
AThis results from computing 4.5 × 36 but omitting the factor of π in the volume calculation.
CThis results from using an incorrect volume formula, such as πr³ instead of (4/3)πr³, giving 4.5 × 27π ≈ 127.
DThis results from dividing the correct answer by 2, or from using half of the density when computing mass.
Question 7Medium
A machine fills containers at a rate of 18 containers per minute. How many containers does the machine fill in 12 minutes and 20 seconds?
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Why C is right
The machine fills 18 containers per minute. Converting 12 minutes and 20 seconds to 12.333... minutes (or 12 + 1/3 minutes), the number of containers filled is 18 × (37/3) = 222 containers.
Why the others are wrong
AThis results from using only the 12-minute portion and ignoring the 20 seconds, yielding 18 × 12 = 216.
BThis results from treating 20 seconds as 30 seconds (0.5 minutes), yielding 18 × 12.5 = 225, with rounding to 226.
DThis results from inverting the calculation structure, dividing 12.333 by 18 instead of multiplying.
Question 8Medium
A solution contains 24 grams of salt dissolved in 600 milliliters of water. How many grams of salt are dissolved in 900 milliliters of water at the same concentration?
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Why B is right
The concentration is 24 grams of salt in 600 milliliters of water, so the concentration is 24 ÷ 600 = 0.04 grams per milliliter. In 900 milliliters of water, there are 0.04 × 900 = 36 grams of salt.
Why the others are wrong
AThis results from incorrectly multiplying 24 by 600 and dividing by 900, inverting the proportion.
CThis results from adding the difference in volume (300 mL) divided by some factor to 24 without proper scaling.
DThis results from incorrectly adding the increase in volume (300 mL) scaled by some factor to 24.
Question 9Medium
Gold has a density of 19.3 grams per cubic centimeter. A rectangular bar of gold has a mass of 1930 grams and dimensions 5 centimeters by 4 centimeters by h centimeters. What is the value of h?
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Why D is right
Using mass = density × volume, the volume is 1930 ÷ 19.3 = 100 cubic centimeters. The volume of the bar is 5×4×h=20h, so 20h=100 and h=5 centimeters.
Why the others are wrong
AThis results from dividing 10 by 5, possibly from confusing which dimensions to use or from incorrectly setting up the ratio.
BThis is the volume of the bar in cubic centimeters. The student computed volume but did not divide by the product of the known dimensions.
CThis results from dividing volume by only one of the two known dimensions (100 ÷ 10 = 10) instead of by their product.
Question 10Medium
A printing press produces 2400 copies of a newspaper in 3 hours. At this rate, how many copies will the press produce in 50 minutes?
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Why B is right
First convert 3 hours to 180 minutes to match units. Set up the proportion: 2400 copies / 180 minutes = x copies / 50 minutes. Cross-multiplying gives 180x=120000, so x=666.67 copies.
Why the others are wrong
AThis results from adding 50 to 2400 instead of using the proportional rate with proper unit conversion.
CThis results from inverting the ratio and computing 2400 ÷ 50 × 3 or similar miscalculation.
DThis incorrectly applies a negative sign to the correct calculation.
Question 11Medium
A medication has a concentration of 250 milligrams per 5 milliliters. A patient requires a dose of 3 grams of this medication. How many milliliters of the medication should be administered? 1 gram = 1000 milligrams
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Why C is right
Converting 3 grams to milligrams gives 3 × 1000 = 3000 milligrams. The concentration is 250 milligrams per 5 milliliters, which is 250 ÷ 5 = 50 milligrams per milliliter. Therefore, 3000 ÷ 50 = 60 milliliters should be administered.
Why the others are wrong
AThis fails to convert grams to milligrams, incorrectly calculating 3 × 5 = 15 milliliters.
BThis inverts the ratio by dividing 3 by 50 instead of 3000 by 50.
DThis applies an incorrect negative sign to the otherwise correct calculation.
Question 12Medium
Copper has a density of 9 grams per cubic centimeter. A solid copper cube has a mass of 5832 grams. To the nearest centimeter, what is the length of one edge of the cube?
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Why B is right
Using volume = mass ÷ density, the volume is 5832÷9=648 cubic centimeters. For a cube with volume V = s3, the edge length is s = 3648=9 centimeters.
Why the others are wrong
AThis results from taking the cube root of the density times some partial calculation, rather than correctly finding the volume first.
CThis results from finding the square root of the volume (√648 ≈ 25.5) and then making an arithmetic error, or from doubling the correct edge length.
DThis is the volume of the cube in cubic centimeters, not the edge length in centimeters.
Question 13Medium
A cyclist travels 18 kilometers in 45 minutes. At this rate, how many kilometers will the cyclist travel in 2 hours?
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Why B is right
First convert 2 hours to 120 minutes to match units. Set up the proportion: 18 kilometers / 45 minutes = x kilometers / 120 minutes. Cross-multiplying gives 45x=2160, so x=48 kilometers.
Why the others are wrong
AThis results from adding 2 to 18 instead of using the proportional rate with proper unit conversion.
CThis incorrectly applies a negative sign to the correct calculation.
DThis results from inverting the calculation and computing 45 ÷ 18 × 2.
Question 14Medium
A solution contains 45 milligrams of medication per 15 milliliters of liquid. How many milligrams of medication are in 80 milliliters of this solution?
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Why D is right
The solution contains 45 milligrams per 15 milliliters, so the concentration is 45/15 = 3 milligrams per milliliter. In 80 milliliters, there are 3 × 80 = 240 milligrams of medication.
Why the others are wrong
AThis results from computing 80/(45/15) instead of (45/15) × 80, inverting the ratio.
BThis results from adding 45, 15, and 80 and dividing incorrectly, missing the proportional relationship.
CThis results from computing (45/15) × 80 but then subtracting 30, introducing a sign error.
Question 15Medium
Ice has a density of 0.92 grams per cubic centimeter. A cylindrical ice sculpture has a radius of 15 centimeters and a height of 40 centimeters. To the nearest hundred grams, what is the mass of the sculpture? (Use 3.14 for π.)
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Why A is right
The volume of the cylinder is π×152×40=3.14×225×40=28260 cubic centimeters. Using mass = density × volume, the mass is 0.92 × 28260 = 25999.2 grams, which rounds to 26000 grams.
Why the others are wrong
BThis is the volume of the cylinder in cubic centimeters, not the mass in grams.
CThis results from using the reciprocal of the density (dividing volume by 0.92 instead of multiplying).
DThis is the product of the radius and height (15 × 40), a partial computation that omits π and the density relationship.
Question 16Medium
A cyclist travels 84 kilometers in 4 hours. At this rate, how many kilometers does the cyclist travel in 2 hours and 30 minutes?
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Why B is right
The cyclist travels 84 kilometers in 4 hours, so the rate is 84/4 = 21 kilometers per hour. Converting 2 hours and 30 minutes to 2.5 hours, the distance is 21 × 2.5 = 52.5 kilometers.
Why the others are wrong
AThis results from using only the 2-hour portion and ignoring the 30 minutes, yielding 21 × 2 = 42.
CThis results from inverting the calculation, dividing 4 by 2.5 instead of performing the correct multiplication.
DThis results from treating 2 hours 30 minutes as 3 hours, yielding 21 × 3 = 63.
Question 17Medium
A recipe for 8 servings calls for 3 cups of flour. How many cups of flour are needed to make 56 servings of this recipe?
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Why B is right
To find the number of cups needed for 56 servings, set up the proportion: 3 cups / 8 servings = x cups / 56 servings. Cross-multiplying gives 8x=168, so x=21 cups.
Why the others are wrong
AThis results from dividing 56 by 3 instead of using the correct proportion with the original serving size.
CThis results from inverting the ratio, multiplying 56 × 8 ÷ 3 instead of 56 × 3 ÷ 8.
DThis incorrectly applies a negative sign to the correct calculation.
Question 18Medium
Copper has a density of 8.96 grams per cubic centimeter. A cylindrical copper wire has a length of 50 centimeters and a circular cross-sectional area of 0.2 square centimeters. To the nearest gram, what is the mass of the wire?
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Why B is right
The volume of the cylinder is cross-sectional area × length = 0.2 × 50 = 10 cubic centimeters. Using mass = density × volume, the mass is 8.96 × 10 = 89.6 grams, which rounds to 90 grams.
Why the others are wrong
AThis results from multiplying density by an incorrectly computed quantity, such as 8.96 × (50 ÷ 4) or from using an arithmetic error in combining the given values.
CThis is the volume of the wire in cubic centimeters. The student computed volume but did not multiply by density.
DThis results from dividing the correct answer by 2, or from using half of the volume when computing mass.
Question 19Medium
A pump removes 320 liters of water from a pool in 8 minutes. At this rate, how many liters of water does the pump remove in 1 hour and 15 minutes?
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Why B is right
The pump removes 320 liters in 8 minutes, so the rate is 320/8 = 40 liters per minute. Convert 1 hour and 15 minutes to minutes: 60 + 15 = 75 minutes. Total water removed is 40 × 75 = 3000 liters.
Why the others are wrong
AThis results from using 60 minutes instead of 75 minutes.
CThis results from incorrectly adding 320 to an intermediate calculation.
DThis results from multiplying 320 by 12.5 instead of finding the per-minute rate first.
Question 20Medium
Brass has a density of 8.5 grams per cubic centimeter. A rectangular block of brass has dimensions 12 centimeters by 5 centimeters by 4 centimeters. To the nearest kilogram, what is the mass of the block?
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Why D is right
The volume of the block is 12 × 5 × 4 = 240 cubic centimeters. Using mass = density × volume, the mass is 8.5 × 240 = 2040 grams, which equals 2.04 kilograms and rounds to 2 kilograms.
Why the others are wrong
AThis is the volume in cubic centimeters, not the mass in kilograms. The student computed volume but did not multiply by density or convert units.
BThis is the mass in grams. The student correctly computed mass but did not convert from grams to kilograms.
CThis results from rounding 2.04 down to 1 instead of using standard rounding, or from an error in unit conversion.
What to do after medium
Medium is the tier that decides most scores. If these are landing, the hard set is where the remaining points are.
Questions are written by SAT Climb and drawn from its own item bank. SAT® is a registered trademark of College Board, which is not affiliated with and does not endorse SAT Climb.