Question: Area of a rectangle with length x and breadth y is P and area of a parallelogram (which is strictly <strong>NOT</strong> a rectangle) with adjacent sides of length x and y is Q. Is P \gt Q?<br>Statement-I: x:y=2:1<br>Statement-II: The angle between the two adjacent sides of the parallelogram is 60^{\circ}.

Consider the following for the next ten (10) items that follow : Each item contains a Question followed by two Statements. Answer each item using the following instructions : Choose option (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. (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.

  1. A. If the Question can be answered by one of the Statements alone, but not by the other.
  2. B. If the Question can be answered by either Statement alone.
  3. C. If the Question can be answered by using both the Statements together, but cannot be answered by using either Statement alone.
  4. D. If the Question cannot be answered even by using both Statements together. ✓

Correct Answer: D. If the Question cannot be answered even by using both Statements together.

Explanation

The area of the rectangle is P = xy. The area of the parallelogram is Q = xy \sin \theta, where \theta is the included angle. Since it is strictly not a rectangle, \theta \neq 90^{\circ}, which means \sin \theta \lt 1. Therefore, Q \lt P is a universal geometric property for these shapes. Because the question can be answered definitively as "Yes" using just the information in the problem prompt itself, neither statement is actually required to answer the question.

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