Quantitative Reasoning: Setup Before Arithmetic
Core concepts
Quantitative Reasoning covers arithmetic (fractions, percentages, ratios, averages), algebra (linear equations, inequalities, substitution), geometry (perimeter, area, angles, similar triangles), rates and work, and data interpretation from tables and charts. You also need number properties: factors, multiples, divisibility, remainders, and parity.
Traps
Unit mismatches - minutes versus hours, centimetres versus metres - cause more errors than any other single issue. Percent language is another: a 20% increase followed by a 20% decrease does not return to the original value, and "percent more than" differs from "percent of". Average speed is total distance divided by total time, not the average of the two speeds. In ratio problems, check whether the parts sum to the whole or whether a remainder is unaccounted for. Overlapping-set questions tempt you to add percentages that double-count the overlap. Geometry figures are not drawn to scale unless stated, so compute rather than measure.
Rule of thumb: estimate, then backsolve
Before computing, estimate a rough answer; if your calculation lands far from it, recheck the setup. When an algebra problem feels messy, plug in the answer choices - starting with the middle value - or pick convenient numbers for the variables.
Worked example
A shirt costs $80. It is discounted 20%, then a further 10% off the reduced price. What is the final price? After 20%: $64. After 10% of $64: $57.60. The total discount is 28%, not 30%, because the second discount applies to the smaller amount.