Setting up proportions, converting units, and reasoning with rates — the most common word-problem machinery on the SAT Math section.
46
Total questions
30
Easy
9
Medium
7
Hard
The workhorse of SAT word problems: recipe ratios, speed and distance, unit prices, currency and unit conversions, and scale drawings. The math is rarely hard — the skill is setting up the proportion correctly and keeping units straight through multi-step conversions.
Write every rate as a labeled fraction (miles/hour, dollars/ounce) and let the units guide the setup: arrange fractions so unwanted units cancel. For ratio-splitting problems (a 3:5 ratio of a 96-item total), add the parts (8), find one part's size (12), then scale. Slowing down for ten seconds to label units prevents nearly every error in this category.
Straight from the Grind1600 question bank — try each one before revealing the answer.
Correct answer: C
Choice C is correct. If the ship traveled 4,800 nautical miles in 160 days, then it traveled, on average, 4,800 nautical miles / 160 days = 30 nautical miles per day.
Choice A is incorrect. This is approximately the average amount of time, in days, it took the ship to travel one nautical mile: 160 days / 4,800 nautical miles = 0.033 days per nautical mile.
Choice B is incorrect and may result from an arithmetic error.
Choice D is incorrect. This is the number of hours in a day rather than the number of nautical miles traveled per day.
Correct answer: C
Choice C is correct. The volume of the barrel is approximately 20 fluid ounces. Marcus has 1.5 gallons = 1.5 × 128 = 192 fluid ounces. He could fill the barrel 192 / 20 = 9.6 times. Since the barrel must be completely filled, Marcus could fill it 9 times.
Choice A is incorrect because Marcus would need 20 × 20 = 400 fluid ounces to fill the barrel 20 times.
Choice B is incorrect because 12 × 20 = 240, which exceeds the 192 fluid ounces available.
Choice D is incorrect because 6 × 20 = 120, which underestimates the number of complete fills possible.
Percentages
Percent change, percent of a quantity, reverse-percentage problems, and multi-step percent scenarios like tax-plus-discount.
Data Distributions & Measures of Center
Mean, median, mode, range, and standard deviation — and how outliers or skew change them — read from lists, tables, and frequency plots.
Scatterplots & Two-Variable Data
Reading scatterplots, lines of best fit, interpreting slope in context, and distinguishing linear from exponential association.
Probability
One-event and conditional probability, usually read out of two-way frequency tables — the key is identifying the correct restricted group.
Inference & Margin of Error
What sample results let you conclude about a population, how margin of error works, and why sample size changes confidence.
Evaluating Statistical Claims
Judging what a study design supports: random sampling vs. random assignment, causation vs. correlation, and generalizability.
46 Ratios, Rates & Units questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.
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