DATA INSIGHTS · GMAT-DI-DSALG · DRAFT

Data Sufficiency: Algebra and Inequalities

Build the concept, interpret evidence, and apply it in a separate assessment pool.

Learn: Evidence and decisions

Treat each statement as a set of possible values

Solve or interpret the statement, then ask whether every value in that set gives the same answer to the target question.

Domain restrictions can resolve ambiguity

An equation may allow several roots. A second condition may eliminate all but one, but it must be combined only in the final step.

Learning Objectives

Translate a sufficiency prompt into a set of candidate values.
Test whether multiple candidate values remain under each statement.
Use the combined statements only after individual analysis.

Prerequisite Knowledge

Solving a factored equation.
The meaning of a nonzero restriction.

Worked Examples

Test the requested property, not just the value

Is a real number greater than four? Statement (1): its square equals twenty-five. Statement (2): it is positive.

Solving the first statement produces one Yes case and one No case. $x^{2} = 25 ⟹ x \in {- 5, 5}$
The second statement also allows opposite answers to the target question. $0 < 2 < 4 < 5$
Only after testing each separately, combine them: the positive root is the only remaining candidate. $x \in {- 5, 5}, x > 0 ⟹ x = 5 > 4$

Conclusion: Together the statements are sufficient; neither is sufficient alone. Keep both roots until a stated condition excludes one.

Two possible values can still be sufficient

Is the square of a real number greater than sixteen? Statement (1): its absolute value equals five. Statement (2): the number is greater than four.

The first statement permits two values, but both give the same answer to the actual question. $∣ x ∣ = 5 ⟹ x^{2} = 25 > 16$
Independently, the second statement restricts the number to positive values whose squares exceed sixteen. $x > 4 ⟹ x^{2} > 16$

Conclusion: Each statement alone is sufficient. An exact value is unnecessary when every allowed value gives the same Yes/No answer.

Guided Practice: Try, then check

Work through each question on paper before opening its hint or explanation. This learning activity is separate from the scored Practice and Simulation pools.

Guided case: more than one value, one answer

For a real number, is its square greater than nine?

Sortable data table. Select a column heading to sort.

(1)	Its absolute value is four.
(2)	The number is less than negative three.

What values does statement one permit, and what does the question ask?
Show hint
The question asks about the square rather than the sign.
Check reasoning
The two possible values have the same square. Both answer Yes, so statement one is sufficient.
$∣ x ∣ = 4 ⟹ x \in {- 4, 4} ⟹ x^{2} = 16 > 9$
Evaluate statement two independently.
Show hint
A number below negative three has magnitude greater than three.
Check reasoning
Every allowed number has a square greater than nine. An exact value is unnecessary.
$x < - 3 ⟹ ∣ x ∣ > 3 ⟹ x^{2} > 9$
Which sufficiency choice applies?
Show hint
Do not combine statements that are already sufficient separately.
Check reasoning
Each statement alone is sufficient. The statements are compatible: negative four satisfies both.

Count answers to the target question, not merely candidate values of the variable. Multiple values can all produce the same required answer.

Think Like a GMAT Test-Taker

Solve the equation fully before evaluating sufficiency.

List all roots, including zero and negative values when permitted.

Check whether a restriction removes every alternative or only some alternatives.

Common Traps

Dropping a root without a stated restriction.

Treating one possible solution as the only solution.

Using an unstated positive-value assumption.