Data sufficiency

Mental model

You are auditing the clues, not solving the crime.

Your goal isn't to find the final numerical answer, but to determine exactly which pieces of information guarantee a single, unique solution. Evaluate each clue in strict isolation before combining them.

Method

1. Read the question stem carefully to determine exactly what constitutes 'sufficient' (e.g., a single unique number, or a definitive 'Yes/No').
2. Evaluate Statement 1 completely on its own, forcefully ignoring Statement 2. Does it guarantee a single answer?
3. Evaluate Statement 2 completely on its own, forcefully ignoring Statement 1. Does it guarantee a single answer?
4. If neither statement alone is sufficient, combine both statements to see if the overlapping data provides a unique answer.
5. Select the final option (1 alone, 2 alone, either alone, both required, neither sufficient) based on these independent checks.

Worked example

Problem: What is the value of x? Statement 1: x^2 = 25. Statement 2: x > 0.

1. Define sufficiency: The question asks for 'the value of x', meaning we need a single, unique number.
2. Evaluate Statement 1 alone: x^2 = 25 yields x = 5 or x = -5. Because there are two possible values, it is NOT sufficient.
3. Evaluate Statement 2 alone: x > 0. This gives an infinite number of possible values (1, 2, 3.5, etc.), so it is NOT sufficient.
4. Combine statements: We know x^2 = 25 AND x > 0. The only value that satisfies both constraints simultaneously is x = 5.
5. Conclusion: A unique answer is found only when both pieces of data are used together.

Answer: Both statements 1 and 2 together are sufficient.

Common mistakes

• Carrying over information: Reading Statement 1, holding that information in your head, and unconsciously using it while evaluating Statement 2 alone.
• Actually calculating the final answer: Wasting time doing complex math to find the exact final value when you already know that the data provides a unique path to solve it.

Glossary

sufficiency

Having exactly enough information to guarantee one single answer.

isolation

Looking at something completely on its own, without letting other information mix in.

guarantee

To make absolutely certain that something is true.

Recall questions

• What is the very first step in solving a Data Sufficiency problem?
• How should you treat Statement 2 initially?
• When should you combine the information from Statement 1 and Statement 2?

Questions & answers

Is integer y even? Statement 1: y + 3 is odd. Statement 2: 2y is an even integer.

Statement 1 alone is sufficient.

Approach: Goal: definitive Yes or No. Stmt 1: y+3 = odd -> y must be even. Sufficient (gives definite 'Yes'). Stmt 2: 2y is even. True for any integer y (even or odd). Not sufficient.

What is the speed of the train? Statement 1: It crosses a pole in 10 seconds. Statement 2: It is 200 meters long.

Both statements together are sufficient.

Approach: Speed = Distance / Time. Stmt 1 gives Time but not Distance. Stmt 2 gives Distance but not Time. Combined, you have both.

Return to Aptitude Roadmap