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

Step 1: Set up the numbers.
Let the 7 consecutive whole numbers be n-3, n-2, n-1, n, n+1, n+2, n+3, where n is the middle number.
Step 2: Check statement II alone.
Sum of the 7 numbers = 7n, since all the offsets cancel out around the middle term. Statement II tells us the sum is 105, so 7n = 105, which gives n = 15. This is one clean equation with one unknown, so statement II alone fixes the middle number uniquely. Statement II alone is sufficient.
Step 3: Check statement I alone.
Statement I gives the product of the 7 numbers as 702800. To test whether this pins down a middle number, try nearby blocks of 7 consecutive whole numbers: 4x5x6x7x8x9x10 = 604800 and 5x6x7x8x9x10x11 = 1663200. The value 702800 falls strictly between these two products, so there is no set of 7 consecutive whole numbers whose product equals exactly 702800. Since the product in statement I does not correspond to any real block of consecutive whole numbers, it cannot be used to fix a unique middle number. Statement I alone is not sufficient.
Step 4: Combine and conclude.
Statement II alone gives a unique, consistent answer (middle number = 15), while statement I alone gives no valid answer at all. So statement II alone is sufficient, matching option 2. Note: the official SNAP 2010 answer key did not publish an answer for this question; this solution works out the correct choice independently using the standard consecutive-number sum property.