Problem-Solving & Data Analysis
This domain is about real-world numbers: percents, ratios, rates, and interpreting data. The calculator helps, but you must set up the relationship correctly.
Percentages
- •X percent of Y = (X/100) * Y.
- •Percent change = (new - old) / old * 100. A drop from 80 to 60 is (60-80)/80 = -25%.
- •Increasing by p% multiplies by (1 + p/100); decreasing multiplies by (1 - p/100). A 20% raise then a 20% cut does not return to the start: 1.20 * 0.80 = 0.96, a 4% net loss.
Ratios and proportions
A ratio compares quantities; a proportion sets two ratios equal and is solved by cross-multiplying. Example: If 3 pumps fill a tank in 12 minutes, how long for the same work measured as pump-minutes? 3 * 12 = 36 pump-minutes total.
Unit rates and conversions
Divide to get a per-unit value: 150 miles in 3 hours = 50 miles per hour. Chain unit conversions by multiplying fractions so units cancel.
Reading data
Always read labels, units, and scale before answering. For two-way tables, find the right row and column; for percentages, divide the part by the correct total.
Worked example
A store buys a jacket for 54**. (Or 1.35 * 40 = 54.)
Worked example (percent change)
Enrollment rose from 250 to 320. What is the percent increase? (320 - 250) / 250 = 70/250 = 0.28 = 28%.
Key takeaways
- •Percent change always divides by the original value.
- •Successive percent changes multiply; they do not add.
- •Keep units explicit so they cancel correctly.
- •Read every axis label and table header before computing.
