Quantitative Word Problems and Applied Reasoning
Translate, then solve
Word problems test whether you can turn prose into arithmetic. Underline the quantity asked for, list the given quantities with their units, and assign a letter to the unknown. Decide whether a single equation, a ratio, or a before-and-after table is the cleanest model. Multi-step problems often involve a remainder: after spending 3/8 of a stock, the next fraction applies to what is left, not to the original. Where answer choices are numerical, backsolving - substituting a choice into the conditions - can be faster and safer than algebra.
Traps
Answer the question actually asked: many items produce an intermediate value and ask for a different one. Watch for hidden constraints such as whole numbers of people or items, “at least” versus “exactly”, and inclusive counting (days from Monday to Friday inclusive). Ignore deliberately irrelevant data. In work-rate problems, add rates, not times, and remember that combined time is the reciprocal of the combined rate.
Worked example
A store has 480 books. Three-eighths are fiction; 25% of the remaining books are science; the rest are history. How many are history? Fiction = 3/8 × 480 = 180. Remaining = 300. Science = 0.25 × 300 = 75. History = 300 − 75 = 225.
Rule of thumb: after solving, reread the final sentence and check that your number answers that exact sentence.