Inequalities
Inequalities Data Sufficiency problems test your ability to determine if given statements provide enough information to compare values, determine ranges, or analyze signs. You must assess sufficiency using inequality rules, number line concepts, and logical deduction.
What You'll Learn
Introduction to Inequalities
Inequalities Data Sufficiency problems test your ability to determine if given statements provide enough information to compare values, determine ranges, or analyze signs. You must assess sufficiency using inequality rules, number line concepts, and logical deduction.
Prerequisites
How to Solve Inequalities Problems
Step 1: Identify what is being asked (is x > y?, range of x, sign of x, etc.)
Step 2: Translate each statement into inequality conditions
Step 3: Check if Statement (1) alone gives a unique answer
Step 4: Check if Statement (2) alone gives a unique answer
Step 5: Combine statements if needed
Step 6: Test counterexamples to check sufficiency
Step 7: Select the appropriate DS answer choice
Example Problem
Example: Is x > y? Statement (1): x² > y² Statement (2): x³ > y³ Solution: Step 1: Question asks if x > y Step 2: Statement (1): x² > y² → |x| > |y|, but x could be less than y if both negative (e.g., x=-3, y=2) → NOT sufficient alone Step 3: Statement (2): x³ > y³ → since cube preserves order, x > y → SUFFICIENT alone Answer: Statement (2) alone is sufficient
Pro Tips & Tricks
- Adding same number to both sides preserves inequality
- Multiplying by positive number preserves inequality
- Multiplying by negative number flips inequality sign
- Squaring loses sign information (x² > y² means |x| > |y|)
- Cubing preserves inequality (x³ > y³ ↔ x > y)
- Transitive property: if x > y and y > z, then x > z
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master Inequalities. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Inequalities is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Inequalities?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: