Data sufficiency reasoning: guide and free practice

Data sufficiency asks whether the supplied facts determine an answer, not merely whether you can form an equation. Test each statement separately before combining them.

Define what must be determined

For a numerical question, sufficient data should force one value. For a yes-or-no question, they should force one answer, even if the exact underlying value remains unknown. A statement establishing that a number is always above a threshold can answer a threshold question without identifying the number.

Reset between statements

Evaluate statement one without importing statement two. Then reset and evaluate statement two alone. Only after those checks should you combine them. Otherwise you can accidentally give a single statement credit for information it does not contain.

Look for two counterexamples

To prove insufficiency, find two cases that satisfy the statement but give different answers. This is often faster than solving every variable. Remember domain restrictions: a positive integer is different from an unrestricted real number.

Use our option convention

Each question below has its own explicit options describing which statements suffice. Read them instead of relying on letter conventions from another test. Some questions distinguish either alone from both together; others deliberately show that even the combined statements fail.

Practise the reasoning, not just algebra

Count unknowns only as a rough guide. Two equations can repeat the same information. Conversely, a bound can settle a yes-or-no question without solving the equation. The explanations identify both a successful calculation and a counterexample where relevant.

Your first practice session

Assess each numbered statement independently first. Then assess the combination if needed. A statement is sufficient only if it forces a unique value or a definite yes/no answer to the exact question.

Try 10 questions with explanations

Worked examples

  1. 1. What is x? (1) x + 4 = 13. (2) x is positive.
    1. Even together insufficient
    2. Statement 1 alone suffices
    3. Statement 2 alone suffices
    4. Only both together suffice

    Reference: q-91b2b8ce-46 · Report this question

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    Answer: B. Statement 1 alone suffices

    Statement 1 fixes x at nine. Positivity alone permits many values, so only statement 1 is sufficient alone.
  2. 2. What is the area of a rectangle? (1) Its length is 8 m. (2) Its width is 5 m.
    1. Statement 1 alone
    2. Statement 2 alone
    3. Only both together
    4. Even together insufficient

    Reference: q-9fb3f11d-78 · Report this question

    Show answer and solution

    Answer: C. Only both together

    Either dimension alone leaves the other unknown. Together the dimensions give 8 times 5 = 40 square metres.
  3. 3. Is integer n even? (1) n is a multiple of four. (2) n is greater than ten.
    1. Statement 2 alone suffices
    2. Only both together suffice
    3. Even together insufficient
    4. Statement 1 alone suffices

    Reference: q-12740687-75 · Report this question

    Show answer and solution

    Answer: D. Statement 1 alone suffices

    Every multiple of four is even. Greater than ten permits both even and odd integers.

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About this practice

These are independently written teaching questions. A practice score helps you review your answers; it is not a validated hiring prediction or an official employer score.