Arithmetic Reasoning
Turning words into equations
Arithmetic Reasoning is word problems: percentages, ratios, averages, rates, unit conversions, simple interest, and multi-step shopping or travel scenarios. The arithmetic is easy; the difficulty is translation and organization. Write an equation for every sentence that carries a number, and label each quantity with its unit.
Core formulas
- Percent change = (new - old) / old x 100.
- Average = sum / count, so total = average x count.
- Distance = rate x time; combined work rates add as 1/a + 1/b per hour.
- Simple interest = principal x rate x time.
Traps
- Percent increases and decreases use the original value as the base. A price that rises 20% then falls 20% ends 4% below where it started, not even.
- Average speed over two legs is total distance / total time, not the average of the two speeds.
- Answers may be offered in the wrong units (minutes instead of hours, cents instead of dollars).
- Distractors often come from a single wrong operation, such as adding where you should divide.
- Tax or tip usually applies to a discounted price, not the original.
Worked example
A jacket costs $80 and is marked down 25%, then 8% sales tax is added. Discounted price = 80 x 0.75 = $60. Tax = 60 x 0.08 = $4.80. Total = $64.80. The tax applies to the sale price, not the original.
Rule of thumb
Estimate first, then compute. If the exact answer is far from your estimate, you slipped somewhere. When stuck, plug the answer choices back into the problem - the choices are usually friendly numbers.