Consider the question and two statements given below:<br><br>Question: Is (x^{n}+y^{n}) divisible by (x+y)?<br>Statement-1: n is a natural number.<br>Statement-2: n is an even natural number.<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: B. Statement-2 alone is sufficient to answer the question
Explanation
The polynomial (x^n+y^n) is divisible by (x+y) only when n is an odd natural number. Statement 1 leaves n ambiguous (could be odd or even). Statement 2 firmly establishes n is even, determining definitively that it is NOT divisible. Thus, Statement 2 alone is sufficient.
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