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There are seven consecutive natural numbers. Find the average of the numbers. Statement I: The second largest number is 62.5% more than the smallest number. Statement II: The largest number is 6 more than the smallest number.

1. The data in statement I alone is sufficient to answer, while the data in statement II alone is not sufficient to answer the question.
2. The data in statement II alone is sufficient to answer, while the data in statement I alone is not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data given in both statements I and II together are not sufficient to answer the question.

Correct answer: The data in statement I alone is sufficient to answer, while the data in statement II alone is not sufficient to answer the question.

Solution

Let the numbers be $n, n+1, n+2, n+3, n+4, n+5, n+6$. Statement I gives $n+5 = 1.625n$, which determines $n$ uniquely, so the average can be found. Statement II gives $n+6 = n+6$, which is always true and does not determine the numbers.

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