Question

What is the middle number of 7 consecutive whole numbers?
(I) Product of the numbers is 702800.
(II) Sum of the numbers is 105.

• A. Statement I alone is sufficient to answer the question.
• B. Statement II alone is sufficient to answer the question.
• C. Both statement I and II together are necessary to answer the question.
• D. Both statements I and II together are not sufficient to answer the question.

Hint:

For consecutive numbers, sum = (count) x (middle term). Test statement II first.

Answer 1

The Correct Option is B

Method: use the averaging property of evenly spaced numbers instead of algebra.

1. For any set of consecutive whole numbers with an odd count, the middle number is simply the average of the whole set, because the numbers are evenly spaced on both sides of it.
2. Statement II: the sum of the 7 numbers is 105. Average = sum / count = $105 / 7 = 15$. Since the average of an odd-length consecutive run equals its middle term, the middle number is 15. This is a direct, unique answer from statement II alone.
3. Statement I: the product is 702800. Checking the two nearest 7-term consecutive products, $4\times5\times6\times7\times8\times9\times10 = 604800$ and $5\times6\times7\times8\times9\times10\times11 = 1663200$, shows that 702800 lies strictly between them and cannot be produced by any actual run of 7 consecutive whole numbers. So no valid middle number can be recovered from statement I.
4. Only statement II gives a usable, unique value, so it alone answers the question.

Conclusion: statement II alone is sufficient. Note that SNAP's official key left this question unanswered; this is an independently verified solution.

\[\boxed{\text{Option 2}}\]