Mathematics and Numerical Reasoning
What this domain tests
This domain covers arithmetic fluency, fractions and decimals, percentages, ratios and proportions, basic algebra, averages, and interpreting tables or word problems without a calculator in many cases.
Concepts to master
- Order of operations (PEMDAS) and signed-number rules.
- Fraction and decimal conversion, including simplifying and finding common denominators.
- Percent change: change divided by original, times 100. Distinguish percent of from percent increase.
- Ratios and unit rates: set up a proportion and cross-multiply.
- Mean, median, and mode, and how outliers shift the mean.
- Solving linear equations: isolate the variable by inverse operations.
- Estimation to sanity-check an answer.
Common traps
- Percent-change direction: a 20% increase followed by a 20% decrease does not return to the start.
- Adding denominators in fractions (1/2 + 1/3 is not 2/5).
- Unit mismatch: minutes versus hours, cents versus dollars.
- Misreading "percent of" versus "percentage points."
- Rushing the last step and answering for the wrong quantity (e.g., finding the discount instead of the final price).
Rule of thumb
Write the units beside every number, underline what the question asks for, and estimate first. If your exact answer is far from the estimate, recheck the setup.
Worked example
A jacket costs $80 and is discounted 25%, then sales tax of 10% is added to the sale price. Sale price = 80 × 0.75 = $60. Tax = 60 × 0.10 = $6. Final = $66. Note that applying tax first would give a different, wrong answer, and 80 × 0.85 = $68 is a common distractor.