CDS 2024 · PYQ · Data Sufficiency / Mensuration · medium
Area of a rectangle with length x and breadth y is P and area of a parallelogram (which is strictly not a rectangle) with adjacent sides of length x and y is Q. Question: Is P > Q? Statement-I: x : y = 2 : 1. Statement-II: The angle between the two adjacent sides of the parallelogram is 60°.
A.If the Question can be answered by one of the Statements alone, but not by the other.
B.If the Question can be answered by either Statement alone.✓ Correct
C.If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
D.If the Question cannot be answered even by using both Statements together.
Explanation
P = xy and Q = xy sin θ where θ ≠ 90° (parallelogram is strictly not a rectangle). Since sin θ < 1 for θ ≠ 90°, Q < P always. So P > Q regardless. Both statements are individually redundant — the question is answerable without either, so either statement alone (vacuously) suffices. Hence option (b).
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