What is the area of the piece of glass? Statements: I. The glass is…

Concept

In a data-sufficiency problem you do not compute a final number; you only decide whether the information given is enough to pin down a unique answer. A statement (or combination) is "sufficient" only if it forces exactly one possible value of the quantity asked. The area of a rectangle is length × breadth, so to fix the area you must know BOTH of its two perpendicular dimensions.

Application

1. The quantity asked is the area of the glass, which needs two dimensions (a base and a height).

2. "The glass is rectangular in shape" fixes the formula to use (length × breadth) but gives no measurement at all, so it cannot produce a number on its own.

3. "The base of the glass is 25 cm" supplies only one dimension. Even assuming a rectangle, the height is still unknown, so the area is not fixed on its own.

4. Taking both together, we know the shape is a rectangle and one side is 25 cm, but the second dimension (height) is still missing. Area = 25 × height stays undetermined because height can be any positive value.

Cross-check

A 25 cm × 10 cm glass gives 250 cm², while a 25 cm × 20 cm glass gives 500 cm². Both fit every piece of information given, yet the areas differ — so even with both statements the area is not uniquely determined.

Hence even both statements together are not sufficient to find the area.