A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.<br><br>Question : Is 327^n+173^n divisible by 500?<br><br>Statement-I: n is odd natural number<br><br>Statement-II: n is a positive integer<br><br>Which one of the following is correct in respect of the above Question and the Statements?

  1. A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone ✓
  2. B. The Question can be answered by using either Statement alone
  3. C. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
  4. D. The Question can be answered even without using any of the Statements

Correct Answer: A. The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone

Explanation

By algebra, a^n+b^n is perfectly divisible by (a+b) if and only if n is an odd positive integer. Since 327+173=500, Statement I (n is odd) is sufficient to definitively answer "Yes". Statement II (n is a positive integer) is insufficient because if n is even, it will not be divisible.

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