Directions : Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. Read both the statements and Give answer (a) if the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question; Give answer (b) if the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question; Give answer (c) if the data either in Statement I or in Statement II alone are sufficient to answer the question; Give answer (d) if the data even in both Statements I and II together are not sufficient to answer the question; Give answer (e) if the data in both Statements I and II together are necessary to answer the question. What is the total cost of painting the inner surface of an open box at the rate of 50 paise per 100 sq. cm? I. The box is made of wood 3 cm thick. II. The external dimensions of the box are 50 cm, 40 cm and 23 cm.

### Concept & Logic To find the cost of painting the *inner* surface of a rectangular box, we first need to calculate its inner surface area. To derive inner dimensions from outer dimensions, the thickness of the box material must be subtracted. $$Inner\ Length = External\ Length - 2(Thickness)$$ ### Step-by-Step Solution Given: The rate of painting is provided in the question stem. 1. Evaluate Statement I alone: Provides only the thickness of the wood ($3\text{ cm}$). Without overall dimensions, inner surface area cannot be calculated. 2. Evaluate Statement II alone: Provides external dimensions only. Without knowing the thickness of the wood, we cannot determine the inner dimensions. 3. Combine Statements I and II: Using the external dimensions (II) and the thickness (I), we can determine the internal dimensions. For an open box (no lid), Inner Length = $50 - 2(3) = 44\text{ cm}$, Inner Width = $40 - 2(3) = 34\text{ cm}$, Inner Height = $23 - 3 = 20\text{ cm}$ (only one thickness subtracted for height since top is open). With inner dimensions, we can find the inner surface area and compute the final cost. ### Exam Strategy & Shortcut Identify the dependencies: Cost requires Inner Area. Inner Area requires Inner Dimensions. Inner Dimensions require External Dimensions AND Material Thickness. Therefore, both pieces of information are strictly required. ### Common Pitfall Forgetting that for an open box, you only subtract the thickness *once* from the external height, as there is no top lid contributing to thickness. While not strictly necessary to solve a Data Sufficiency question, this error ruins standard calculation problems. ### Final Answer Therefore, the correct answer is **if the data in both Statements I and II together are necessary to answer the question**.