Mathematical Reasoning: Rates, Percents, and Multi-Step Problems
The GED Mathematical Reasoning test rewards careful reading as much as calculation. You need fluency with arithmetic on rational numbers, ratio and proportion, percent change, order of operations, evaluating expressions, and linear relationships (slope, intercepts, interpreting a graph). Geometry questions cover perimeter, area, volume, the Pythagorean theorem, and angle relationships; data questions cover mean, median, mode, range, and reading tables, bar graphs, and scatter plots. A short constructed-response item asks you to set up and solve a problem and explain your reasoning.
Traps to watch
- Percent change vs. percent of. "Increased by 20%, then decreased by 20%" does not return to the original value.
- Unit mismatches. Minutes versus hours, cents versus dollars, inches versus feet.
- Answering the wrong question. Many items ask for a remaining amount or a difference, not the total.
- Rounding too early. Carry decimals through and round only at the end.
Worked example
A jacket costs $80 and is marked down 25%, then an additional 10% is taken off the sale price. Final price? First discount: $80 x 0.75 = $60. Second discount: $60 x 0.90 = $54. Rule of thumb: successive percent changes multiply - here 0.75 x 0.90 = 0.675, so the buyer pays 67.5% of the original price, a 32.5% total discount, not 35%.