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: The largest of five different integers is 8 and least is 2. What is the average of these integers ?<br><br>Statement-I: The sum of all the 5 integers is a multiple of 5<br><br>Statement-II: The number of odd integers is odd<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 cannot be answered even by using both the Statements together

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

Let the distinct integers be 2, a, b, c, 8. The sum S = 10 + a + b + c. To maximize/minimize, a,b,c are chosen from \{3,4,5,6,7\}. The minimum possible sum is 10+3+4+5=22 and maximum is 10+5+6+7=28. Statement I says S is a multiple of 5. The only multiple of 5 between 22 and 28 is 25. Average = \frac{25}{5} = 5. Thus, Statement I alone is sufficient.

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