How many gift boxes were sold on Monday? Consider the following statements: I. The number of gift boxes sold on Monday was 10 percent more than the number of boxes sold on the previous day, that is, Sunday. II. Every third visitor to the shop purchased exactly one box, and there were 1500 visitors to the shop on Sunday.

Introduction / Context:
This data sufficiency question combines percentage increase with visitor based sales information. The objective is to find out how many gift boxes were sold on Monday. Two statements relate Monday sales to Sunday sales and relate Sunday sales to the number of visitors. The core skill is to see whether we can convert these into a unique numeric value and which statements are required for that.

Given Data / Assumptions:

• Statement I: Monday sales in gift boxes were 10 percent more than Sunday sales.
• Statement II: On Sunday, every third visitor purchased exactly one box and there were 1500 visitors.
• All visitors are counted once, and every third visitor means one out of every three visitors bought one box, with no other sales on Sunday.

Concept / Approach:
Let S be the number of boxes sold on Sunday and M be the number of boxes sold on Monday. Statement I relates M to S via a percentage increase. Statement II allows us to calculate S from visitor data. To decide sufficiency, we check whether S and M can be uniquely determined from each statement alone or only from their combination.

Step-by-Step Solution:
Step 1: From statement II, there are 1500 visitors on Sunday and every third visitor buys one box. That means one box for every three visitors, so S = 1500 divided by 3. Step 2: Compute S. Since 1500 divided by 3 is 500, Sunday sales equal 500 gift boxes. Step 3: Using statement II alone, we know S but we do not know M. No information is given about Monday sales in this statement, so II alone is not sufficient. Step 4: From statement I, Monday sales are 10 percent more than Sunday sales. In algebraic form, M = S + 10 percent of S = 1.10 * S. Step 5: Using statement I alone, we have only the relation between M and S. Without a numerical value for S, M remains undetermined. Therefore statement I alone is also not sufficient. Step 6: Combine statements I and II. From statement II we have S = 500. Substituting into M = 1.10 * S gives M = 1.10 * 500 = 550. Now Monday sales are uniquely fixed at 550 gift boxes. Step 7: Since neither statement alone yields M but the combination does, both statements together are necessary to answer the question.

Verification / Alternative check:
To verify, imagine varying S while still satisfying statement I. For any positive S, statement I allows a corresponding M equal to 1.10 * S. Without statement II, there are infinitely many possible pairs (S, M). With statement II alone, S is fixed at 500, but M can still vary because the link to Monday is missing. Only when both pieces of information are used does the pair (S, M) become fixed as (500, 550).

Why Other Options Are Wrong:
Option A is wrong because statement I alone does not give any numeric base for Sunday sales. Option B is wrong because statement II alone does not mention Monday. Option C, which suggests that either I or II alone is sufficient, is clearly incorrect. Option E claims that even both statements together are not sufficient, which contradicts the clear computation of 550 boxes for Monday. Only option D correctly recognises that both statements together are necessary and sufficient.

Common Pitfalls:
Learners may confuse the phrase every third visitor with one third of all visitors, but here the interpretation gives the same result as long as the total is divisible by three. Another common oversight is to treat a percentage relation as if it alone fixes both quantities, ignoring the need for an absolute reference value. Careful separation of relative statements from absolute numerical statements helps to avoid these mistakes.

Final Answer:
The data in both statements I and II together are necessary to answer the question, so the correct option is D.