Ratios, Rates, and Percentages in Context

What the SAT Tests in This Domain

Problem Solving and Data Analysis is 15% of SAT Math — roughly 4 questions per module. Unlike Algebra, these questions rarely require setting up equations. Instead, they test your ability to interpret data, reason proportionally, and evaluate statistical claims.

Ratios and Proportions

A ratio compares two quantities. On the SAT, ratios always appear in context.

Setting up proportions: If 3 printers can print 120 pages in 10 minutes, how many pages can 5 printers print in 10 minutes?

$\frac{3 \text{ printers}}{120 \text{ pages}} = \frac{5 \text{ printers}}{x \text{ pages}}$

Cross-multiply: $3x = 600$, so $x = 200$ pages.

SAT Trap: Make sure the units match across the proportion. A common distractor results from mixing up which quantity goes in the numerator.

Rates and Unit Conversion

Rate problems ask you to convert between units or combine rates.

Example: A car travels at 55 miles per hour. How many feet does it travel in 30 seconds?

$55 \frac{\text{mi}}{\text{hr}} \times \frac{5{,}280 \text{ ft}}{1 \text{ mi}} \times \frac{1 \text{ hr}}{3{,}600 \text{ sec}} \times 30 \text{ sec} = 2{,}420 \text{ ft}$

Strategy: Write out every conversion factor and cancel units. The SAT gives conversion factors in the problem — use them.

Percentages

The SAT tests three percent skills:

Type	Formula	Example
Percent of a number	$\text{part} = \frac{p}{100} \times \text{whole}$	30% of 250 = 75
Percent change	$\frac{\text{new} - \text{old}}{\text{old}} \times 100$	From 80 to 100 = 25% increase
Successive percent changes	Multiply factors	20% up then 10% down: $1.20 \times 0.90 = 1.08$ (8% net increase)

SAT Pattern: "A price increases by 20% and then decreases by 20%. Is the final price the same as the original?"

No. $1.20 \times 0.80 = 0.96$, so the final price is 96% of the original — a 4% net decrease. This is a perennial SAT question.