Difficulty: Medium
Correct Answer: Statement II alone is sufficient to answer the question.
Explanation:
Introduction / Context:
Data Sufficiency problems test whether the given pieces of information are enough to answer the question uniquely, not to compute the value by lengthy calculation. Here we have seven consecutive whole numbers and are asked to identify the middle number (the 4th number when they are in increasing order).
Given Data / Assumptions:
Concept / Approach:
The sum of seven consecutive numbers equals 7 * middle. The product is complicated and usually not practical for determining n in a DS setting unless it matches a very specific known product (which is rare).
Step-by-Step Solution:
From Statement II: sum = 105 = 7 * middle ⇒ middle = 105 / 7 = 15.Therefore Statement II alone directly determines the middle number.From Statement I: knowing only the product 702800 does not readily identify a unique set of seven consecutive integers; factoring does not easily map to a unique consecutive block, and in fact no standard consecutive 7-number block yields this product in a neat way for quick deduction.
Verification / Alternative check:
Using Statement II, the sequence is 12, 13, 14, 15, 16, 17, 18. This is consistent and unique.
Why Other Options Are Wrong:
Statement I alone is not sufficient because the product information does not isolate a unique middle quickly and reliably. Both-together is unnecessary because Statement II already suffices; claiming insufficiency is also wrong since II gives an exact middle.
Common Pitfalls:
Confusing “compute” with “determine sufficiency,” and attempting to factor a large product instead of noticing the simple sum-to-middle relation.
Final Answer:
Statement II alone is sufficient.
Discussion & Comments