2022 · Q30
Consider the question and two statements given below : Let x and y be two real numbers.Question : Is xy > 0?
Statement 1x⁸y⁹ < 0.
Statement 2x⁹y¹⁰ < 0.
Which one of the following is correct in respect of the question and the statements?
Elementary MathematicsNumber System
- AStatement-1 alone is sufficient to answer the question
- BStatement-2 alone is sufficient to answer the question
- CBoth Statement-1 and Statement-2 are sufficient to answer the question
- DBoth Statement-1 and Statement-2 are not sufficient to answer the question
Explanation
Statement 1: x⁸y⁹ < 0 forces x ≠ 0 and y < 0, but the sign of x is free — insufficient. Statement 2: x⁹y¹⁰ < 0 forces y ≠ 0 and x < 0, but the sign of y is free — insufficient. Together x < 0 and y < 0 give xy > 0, answering the question. The keyed option is C.