UPSC CDS I 2024 Math Paper

Concept:For any convex quadrilateral, joining the midpoints of its sides forms a parallelogram whose area is exactly half of the original quadrilateral's area.Explanation:Let Area of quadrilateral $ABCD$ be $A$ and area of quadrilateral $PQRS$ (midpoint quadrilateral) be $M$.The known midpoint property gives $M = \frac{1}{2}A$.The required difference $D = A - M = A - \frac{1}{2}A = \frac{1}{2}A$.Thus, if either $A$ or $M$ is known, $D$ can be directly calculated.Statement I gives $A = 100$ sq. units, so $D = \frac{1}{2} \times 100 = 50$ sq. units.Statement II gives $M = 50$ sq. units, so $A = 2 \times 50 = 100$ sq. units and $D = 100 - 50 = 50$ sq. units.Therefore, each statement alone is sufficient to determine the difference.Answer:Option B: The question can be answered by either statement alone.