Quantitative Word Problems
Word problems present a scenario in text. You must extract the numbers, identify the relationships, set up equations and solve. They appear in numerical reasoning tests and GMAT-style assessments. Here's how to approach them.
Strategy
Read carefully – What is given? What is asked? Underline key numbers and phrases ("twice as much", "increased by 10%", "total of").
Identify unknowns – What do you need to find? Assign a variable (x, y) if helpful.
Translate to math – "A is twice B" → A = 2B. "A increased by 10%" → A × 1.10. "A is 20% of B" → A = 0.20 × B.
Set up equations – One equation per relationship. For one unknown, you need one equation. For two unknowns, two equations.
Solve – Substitute, simplify, or use algebra. Check the answer makes sense.
Common Phrases
| Phrase | Math |
|---|---|
| A is twice B | A = 2B |
| A is 50% more than B | A = 1.5B |
| A is 20% less than B | A = 0.8B |
| A and B total 100 | A + B = 100 |
| A is 3 times the difference of B and C | A = 3(B − C) |
| A increased by 15% | A × 1.15 |
| A decreased by 25% | A × 0.75 |
Problem Types
Rate problems – Distance = Speed × Time. Work = Rate × Time. Identify what you have and what you need.
Mixture problems – (Amount A × Concentration A) + (Amount B × Concentration B) = Total × Final concentration.
Age problems – "In 5 years, A will be twice B" → A + 5 = 2(B + 5). Set up for the relevant time.
Percentage problems – Identify base, part and percentage. Part = Base × (Percentage ÷ 100).
Pitfalls
- Misreading – "A is 20% less than B" means A = 0.8B, not B = 0.8A. The base is B.
- Wrong variable – Solve for what was asked. If the question asks for "total cost", don't stop at "cost per unit".
- Units – Ensure consistency. If speed is km/h and time is minutes, convert.
Practice with numerical reasoning questions and the numerical reasoning test.
Frequently Asked Questions
How do I handle "cannot be determined"?
If the information is insufficient (e.g. two unknowns, one equation), the answer may be "cannot be determined". Or the problem might have a unique answer—check by assuming values.
What if the problem has fractions or decimals?
Work with them as given, or convert. E.g. 1/4 = 0.25. For "1/4 of the total", use Total ÷ 4 or Total × 0.25.
How do I avoid getting lost in long problems?
Break into smaller parts. List what you know. Write equations as you go. Re-read the question at the end to ensure you answered it.