Quantitative - Arithmetic Reasoning and Math Knowledge
Translate, then compute
Arithmetic reasoning tests translation from words to equations; math knowledge tests recall and manipulation. For word problems, identify the unknown, assign a variable, and write units beside every number. Watch for rate problems (distance = rate × time, work rates add), proportions, percent change, weighted averages, and mixtures. Percent change uses the original amount as the base: an increase from 80 to 100 is 20/80 = 25%, not 20%. Average is total ÷ count, so if a problem gives an average and count, multiply to recover the total. In geometry, distinguish perimeter from area and radius from diameter; in algebra, apply order of operations and check inequality direction when multiplying or dividing by a negative. No calculator is allowed, so estimate and backsolve from answer choices when exact computation is slow.
Worked example: A shirt costs $80 and is marked up to $100. What is the percent increase? Increase = 20; base = original 80; 20/80 = 0.25 = 25%. Choosing 20% uses the new price as the base-a classic trap.
Another trap is extraneous information and unit mismatches (minutes vs hours, cents vs dollars). Convert before calculating.
Rule of thumb: label every quantity, and if two answer choices differ only by a unit or a base, re-read the question before selecting.