Data Sufficiency — Area of a Rectangular Plot What is the area of the rectangular plot? I. The length of the plot is 375 m. II. The length of the plot is thrice its breadth.
Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.
Introduction / Context:We must evaluate whether we can uniquely compute the area of a rectangle from the given statements. The area requires both length and breadth.
Given Data / Assumptions:
- Statement I: Length L = 375 m.
- Statement II: L = 3 * B (i.e., length is thrice breadth).
Concept / Approach:Area A = L * B. Knowing only L (from I) or only the ratio L:B (from II) is not enough. Combined, they yield both dimensions.
Step-by-Step Solution:
From II: B = L/3.Using I in II: B = 375 / 3 = 125 m.Area A = L * B = 375 * 125 = 46,875 m^2 (unique).Verification / Alternative check:Neither statement alone can fix the area: I lacks B; II lacks numerical scale. Together they are sufficient.
Why Other Options Are Wrong:
- I alone sufficient: Wrong — breadth unknown.
- II alone sufficient: Wrong — only ratio known.
- Either alone sufficient: Wrong — each alone fails.
- Even both not sufficient: Wrong — both together fully determine A.
Common Pitfalls:Assuming a default breadth or treating a ratio as if it fixes absolute dimensions. Ratios require at least one absolute measure.
Final Answer:Both statements together are sufficient; neither alone is sufficient.