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.
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AStatement I alone is sufficient; Statement II alone is not sufficient.
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BStatement II alone is sufficient; Statement I alone is not sufficient.
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CBoth statements I and II together are sufficient, but neither alone is sufficient.
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DEither statement I alone or statement II alone is sufficient.
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EEven both statements together are not sufficient.
Answer
Correct Answer: Both statements I and II together are sufficient, but neither alone is sufficient.
Explanation
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.