Quantitative Reasoning: Translate Before You Compute
Quantitative Reasoning covers arithmetic, algebra, ratios, percentages, averages, geometry and data interpretation. Most items are word problems: the difficulty usually lies in translation and in avoiding a tempting shortcut, not in advanced mathematics.
Core rules
- Percentage change = (new − old)/old × 100. Successive changes multiply: a 20% rise then a 20% fall gives 1.2 × 0.8 = 0.96, a 4% net fall, not zero.
- Work rates add as reciprocals: if A takes a days and B takes b days, together they take ab/(a+b) days.
- Average speed = total distance ÷ total time; never average two speeds unless the times are equal.
- Sets: |A ∪ B| = |A| + |B| − |A ∩ B|. Add 'neither' only when the question includes people outside both sets.
Worked example
A completes a job in 12 days and B in 18 days. Working together, how long do they take?
Rates: 1/12 + 1/18 = 3/36 + 2/36 = 5/36 of the job per day. Time = 36/5 = 7.2 days. The wrong shortcut is (12 + 18)/2 = 15 days, which would be valid only if the workers split the work equally instead of working simultaneously.
Traps that cost marks
Mixing hours and minutes; taking a percentage of the new value when the question fixes the original base; confusing a ratio such as 3:4 with the fraction 3/4; forgetting to subtract the overlap in set questions; accepting a neat answer that lies outside the feasible range.