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, because 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.