How many New Year greeting cards were sold this year in your shop? Statement I: Last year, 2935 cards were sold. Statement II: The number of cards sold this year was 1.2 times the number of cards sold last year.

Introduction / Context:
This data sufficiency question is about sales comparison between two years. We are asked to find how many New Year greeting cards were sold in a shop this year. One statement gives last year's sales figure, and the other statement gives this year's sales as a multiple of last year's figure. We must determine which combination of statements allows us to compute this year's sales uniquely.

Given Data / Assumptions:

• We want the exact number of cards sold this year.
• Statement I: Last year, 2935 cards were sold.
• Statement II: This year's sales were 1.2 times last year's sales.
• Sales numbers are whole numbers and 1.2 means 120 percent, that is, 1.2 times.

Concept / Approach:
The underlying concept is simple percentage based growth: this_year_sales = last_year_sales * 1.2 We first check each statement alone: one provides a numeric base, the other gives a multiplicative factor, but neither alone is enough for a complete calculation. Both together provide a solvable equation for this year's sales. Data sufficiency requires that we recognise this and identify the minimum set of statements needed to determine the value.

Step-by-Step Solution:
Step 1: From statement I, last year's number of cards sold was 2935. This is a numeric value but does not directly tell us this year's figure. Step 2: Statement I alone is not sufficient because we are not told whether this year's sales are equal to, greater than or less than last year's sales. Step 3: From statement II, this year's sales are 1.2 times last year's sales. However, statement II alone does not provide the numerical value of last year's sales, so we cannot compute a number for this year. Step 4: Statement II alone is therefore also insufficient. Step 5: Combining both statements, we have last_year_sales = 2935 and this_year_sales = 1.2 * last_year_sales. Step 6: Substitute last_year_sales into the formula: this_year_sales = 1.2 * 2935. Step 7: Compute the product. One way is to note that 1.2 = 6 / 5, so this_year_sales = (6 / 5) * 2935. Step 8: First compute 2935 * 6 = 17610. Step 9: Then divide by 5: 17610 / 5 = 3522. Step 10: Therefore, this year the shop sold 3522 New Year greeting cards.

Verification / Alternative check:
Another way to compute is to break 1.2 into 1 + 0.2. So 1.2 * 2935 = 2935 + 0.2 * 2935. Compute 0.2 * 2935, which is 2935 / 5 = 587. Now add 2935 and 587 to get 3522. This matches the earlier calculation, confirming our result. Because we obtain a unique integer value for this year's sales, the combination of statements is sufficient.

Why Other Options Are Wrong:
Option a is wrong because last year's sales alone do not tell us about this year's change. Option b is wrong because knowing the factor 1.2 without last year's numerical value does not permit computation of this year's sales. Option c is wrong because neither statement alone is sufficient. Option e is wrong because we clearly obtain a unique number when using both statements together.

Common Pitfalls:
Some students may misinterpret 1.2 times as an increase of 1.2 percent rather than 120 percent. It is important to recognise that 1.2 times a quantity is equivalent to 120 percent of that quantity, representing a 20 percent increase over the original. Others might make arithmetic mistakes when multiplying or dividing by 5. To avoid such errors, one can use multiple methods to check the calculation, such as the fraction method and the decomposition into 1 plus 0.2.

Final Answer:
This year, 3522 New Year greeting cards were sold in the shop. Correct option: The data in both statements I and II together are sufficient to answer the question.