Data Sufficiency and Logical Validation of Numerical Statements
Data-sufficiency items supply a question plus two statements and ask whether the statements, alone or together, determine the answer. You are not required to compute the value - only to establish that exactly one value exists. Related items ask you to judge whether a written numerical claim is supported by the accompanying data.
The answer structure
Typical options are: (A) statement 1 alone suffices; (B) statement 2 alone suffices; (C) both together suffice but neither alone; (D) each alone suffices; (E) even together they do not suffice. Confirm the structure used in the paper you are sitting before starting.
Core rules
- Test each statement alone first, ignoring the other. Do not carry information across.
- A ratio plus an absolute total determines every absolute component. A ratio alone does not.
- A percentage without a base determines nothing absolute. Two percentages without bases still determine nothing absolute, though they may fix a relative comparison.
- Directional information is not numeric information. Knowing that X's total exceeds Y's says nothing about the ratio of their averages, because the headcounts are unknown.
- Check for multiple solutions: if two configurations satisfy the statements and give different answers, the data is insufficient.
- Validate claims against the stated definition: "spending rose in real terms" requires growth above inflation, not merely a nominal increase.
Worked example
Is the average salary in Unit X higher than in Unit Y? (1) X has more employees than Y. (2) X's total salary bill is higher than Y's.
Average = total / headcount. Statement (1) gives no salary data; statement (2) gives no headcount data. Together we know only directions: X has both a larger numerator and a larger denominator. Try X: total 300, 10 staff, average 30; Y: total 100, 5 staff, average 20 - X is higher. Try X: total 200, 10 staff, average 20; Y: total 100, 5 staff, average 20 - the averages are equal. Both configurations satisfy (1) and (2) but give different answers, so the data is insufficient - answer (E).
Traps
- Completing the full calculation when only sufficiency was asked, and running out of time.
- Assuming more statements always mean more information; two statements can be redundant.
- Accepting a percentage comparison as proof of an absolute one.
- Overlooking a second valid configuration that produces a different answer.