Data Sufficiency: Algebraic Sufficiency

Concept Explanation

Algebra DS items test whether equations or inequalities yield a unique value for unknowns.

Standard Answer Choices

• A — Statement I alone is sufficient; Statement II alone is not.
• B — Statement II alone is sufficient; Statement I alone is not.
• C — Both together are sufficient, neither alone.
• D — Either statement alone is sufficient.
• E — Neither alone nor together is sufficient.

Algebraic DS Focus

Count independent equations vs unknowns. Watch for quadratics giving two roots unless extra constraints apply.

DS Decision Flow

1. State exactly what must be determined (number, ratio, yes/no, or comparison).
2. Test Statement I alone—sufficient or insufficient?
3. Test Statement II alone—sufficient or insufficient?
4. If neither alone works, combine both statements.
5. Choose A–E based on sufficiency; never pick a value when data do not fix it uniquely.

Common Traps in Algebra Problems

• Assuming x² = 4 gives unique x (x = ±2).
• Treating dependent equations as independent.
• Ignoring domain restrictions (positive integers, etc.).