Quantitative Word Problems
Word problems present a scenario in text. You must extract the numbers, identify the relationships, set up equations and solve. 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, 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 increased by 15% | A × 1.15 |
| A decreased by 25% | A × 0.75 |
Problem Types
Rate problems – Distance = Speed × Time. Work = Rate × Time.
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).
Percentage problems – 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.
- Units – Ensure consistency.
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".
What if the problem has fractions or decimals?
Work with them as given, or convert. 1/4 = 0.25.
How do I avoid getting lost in long problems?
Break into smaller parts. List what you know. Write equations as you go.