2024 · Q67
A question is given followed by two statements I and II. Consider the Question and the Statements and mark the correct option.
Question: The largest of five different integers is 8 and least is 2. What is the average of these integers?
Statement IThe sum of all the 5 integers is a multiple of 5
Statement IIThe number of odd integers is odd Which one of the following is correct in respect of the above Question and the Statements?
Elementary MathematicsStatistics
- AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone
- BThe Question can be answered by using either Statement alone
- CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
- DThe Question cannot be answered even by using both the Statements together
Explanation
The five distinct integers lie in [2,8]. Statement I: the three middle values (from {3,…7}) must sum to a multiple of 5; the possibilities {3,5,7} and {4,5,6} both give total 25, so the average is uniquely 5. Statement II (odd count of odds) admits averages like 4.6, 5, 5.4. Only statement I alone suffices — option A.