Question: In a quadrilateral ABCD, AB = 6 units, BC = 18 units, CD = 6 units, DA = 9 units. What is the length of diagonal BD? Statement I: The length of BD is an integer greater than 13. Statement II: The length of BD is an even integer.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Which one of the following is correct in respect of the above Question and the Statements?
- A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
- B. The Question can be answered by using either Statement alone ✓
- C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- D. The Question can be answered even without using any of the Statements
Correct Answer: B. The Question can be answered by using either Statement alone
Explanation
Applying the triangle inequality to \Delta ABD, 3 < BD < 15. For \Delta BCD, 12 < BD < 24. Combining them gives 12 < BD < 15. Statement I (integer > 13) leaves only 14. Statement II (even integer) leaves only 14. Either statement alone yields BD = 14.
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