Problem-Solving and Data Analysis · Math

Ratios, rates, proportions, and units

Ratios, proportional reasoning, unit rates, and unit conversion.

18 questions in the bank · 5 easier · 9 medium · 4 harder · this domain is ≈15% of the section

Learn it in the Guide

What to watch for

Scale both quantities by the same factor, and keep the units attached through the whole calculation — the unit is usually what tells you whether to multiply or divide.

How the question is worded

These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.

  • A recipe uses 3 cups of flour to make 4 loaves of bread. At this rate, how many cups of flour are needed to make 24 loaves of bread?
  • A recipe uses 4 liters of paint to make 8 fence panels. At this rate, how many liters of paint are needed to make 56 fence panels?
  • A recipe uses 5 bags of soil to make 6 planter boxes. At this rate, how many bags of soil are needed to make 48 planter boxes?
  • A recipe uses 5 meters of fabric to make 8 tote bags. At this rate, how many meters of fabric are needed to make 40 tote bags?

Worked examples

easyA recipe uses 3 cups of flour to make 4 loaves of bread. At this rate, how man…

A recipe uses 3 cups of flour to make 4 loaves of bread. At this rate, how many cups of flour are needed to make 24 loaves of bread?

  • A. 9
  • B. 18
  • C. 24
  • D. 38

Answer: B. 18

Explanation

24 is 6 times 4, so scale the other quantity by the same factor: 3 × 6 = 18. Keeping the two quantities locked to the same multiplier is the whole idea of a rate.

mediumThe ratio of x to 42 is equal to the ratio of 11 to 7. What is the value of x?

The ratio of x to 42 is equal to the ratio of 11 to 7. What is the value of x?

  • A. 46
  • B. 77
  • C. 66
  • D. 294/11

Answer: C. 66

Explanation

Write the proportion x/42 = 11/7. Multiply both sides by 42: x = 42·11/7 = 66. Setting up the fractions in a consistent order is what the inverted wrong answer gets wrong.

hardMachine A produces 330 parts in 5 hours. Machine B produces 180 parts in 2 hou…

Machine A produces 330 parts in 5 hours. Machine B produces 180 parts in 2 hours. Which machine produces parts at a faster rate, and by how much?

  • A. Machine B, by 150 parts per hour
  • B. Machine A, by 3 parts per hour
  • C. Machine B, by 24 parts per hour
  • D. Machine A, by 24 parts per hour

Answer: C. Machine B, by 24 parts per hour

Explanation

Compute each unit rate: A = 330/5 = 66 parts per hour; B = 180/2 = 90. Machine B is faster by 24 parts per hour. Comparing raw totals ignores that the times differ.