Consider the question and two statements given below:<br><br>Let x and y be two real numbers.<br><br>Question: Is xy \gt 0?<br>Statement-1: x^{8}y^{9} \lt 0.<br>Statement-2: x^{9}y^{10} \lt 0.<br><br>Which one of the following is <strong>CORRECT</strong> in respect of the question and the statements?
- A. Statement-1 alone is sufficient to answer the question
- B. Statement-2 alone is sufficient to answer the question
- C. Both Statement-1 and Statement-2 are sufficient to answer the question ✓
- D. Both Statement-1 and Statement-2 are not sufficient to answer the question
Correct Answer: C. Both Statement-1 and Statement-2 are sufficient to answer the question
Explanation
Statement 1 (x^8 y^9 \lt 0) implies y \lt 0 (since x^8 > 0) but leaves the sign of x unknown. Statement 2 (x^9 y^{10} \lt 0) implies x \lt 0 (since y^{10} > 0) but leaves y unknown. Together, they establish x \lt 0 and y \lt 0, definitively proving xy \gt 0.
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