Arithmetic Reasoning: Word Problems
Arithmetic Reasoning tests your ability to translate real-world situations into calculations. The core operations are addition, subtraction, multiplication, division, fractions, decimals, percentages, ratios, averages, and rates (distance = rate × time). Most errors come from misreading the problem, not from bad arithmetic.
Strategy
- Identify what is asked. Underline the question-often the last sentence.
- List the given numbers with units.
- Choose an operation. Look for keywords: total, altogether (add); difference, how many more (subtract); each, per, times (multiply); split, per person (divide).
- Estimate first. Round numbers to check whether your answer is reasonable.
- Check units and the reasonableness of the result.
Traps
- Extra information: problems often include a number you do not need.
- Unit mismatch: minutes vs. hours, cents vs. dollars.
- Reverse percentage: "price increased 20%, then decreased 20%" does not return to the original-multiply by 1.20 then 0.80.
- Answering the wrong quantity: you may be asked for the remainder, not the total.
Worked example
A worker earns $14.50 per hour and works 6 hours on Monday and 4.5 hours on Tuesday. What are total earnings? Total hours = 6 + 4.5 = 10.5. Earnings = 10.5 × $14.50. Estimate: 10 × 14.50 = 145; plus 0.5 × 14.50 = 7.25; total = $152.25. The estimate ($145–$160) confirms the answer is reasonable.
Rule of thumb
After computing, ask: "Does this answer make sense in the real-world situation described?" If not, reread the problem.