What is the area of the rectangle? a) The length is 10 b) The width is 5

Concept: In a data-sufficiency question, the goal is to decide whether the given statements together provide enough information to answer the question, not to compute the final number by itself. For the area of a rectangle, the formula area = length × width means both the length and the width must be known before the area can be found.

Application: Statement (a) gives only the length (10); the width is unknown, so the area cannot be found from (a) alone. Statement (b) gives only the width (5); the length is unknown, so the area cannot be found from (b) alone. Only when both statements are combined do we know length = 10 and width = 5, so area = 10 × 5 = 50 can be computed.

Cross-check:

• Statement A alone fails because it never reveals the width.

• Statement B alone fails because it never reveals the length.

• Neither statement can be derived from the other (no ratio or relation links length and width here), so "either statement alone is sufficient" also fails.

Since both dimensions are required and neither statement alone supplies the other, both statements together are needed to answer the question.