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. Is a given rectangular block, a cube? I. At least 2 faces of the rectangular block are squares. II. The volume of the block is 64.

### Concept & Logic A rectangular block (cuboid) has dimensions $l$, $b$, and $h$. For it to be a cube, all three dimensions must be equal ($l = b = h$). ### Step-by-Step Solution 1. Evaluate Statement I alone: "At least 2 faces... are squares." In a cuboid, faces come in opposite pairs. If the base is a square, then $l = b$. However, the height $h$ could be any value (e.g., $2 \times 2 \times 10$). It is not necessarily a cube. Not sufficient. 2. Evaluate Statement II alone: "The volume... is 64." The volume is $l \times b \times h = 64$. This could be a cube ($4 \times 4 \times 4$) or a cuboid ($8 \times 4 \times 2$ or $16 \times 2 \times 2$). Not sufficient. 3. Combine Statements I and II: We know $l = b$ (two square faces) and $l \times b \times h = 64 \rightarrow l^2 \times h = 64$. - Case 1: If $l = 4$, then $16 \times h = 64 \rightarrow h = 4$. This is a cube ($4 \times 4 \times 4$). - Case 2: If $l = 2$, then $4 \times h = 64 \rightarrow h = 16$. This is a cuboid ($2 \times 2 \times 16$), not a cube. Since we can get a "Yes" (Case 1) and a "No" (Case 2), the data is still not sufficient. ### Exam Strategy & Shortcut For "Is it a [shape]?" questions, your goal is to find multiple distinct cases that fit the criteria. If you can create one case that IS the shape and one case that IS NOT, the statements are insufficient. ### Common Pitfall A frequent trap is stopping at the first logical set of numbers that works. Many test-takers see $l^2 \times h = 64$, immediately think of $4^2 \times 4 = 64$, and assume it must be a cube without testing other integers like $2^2 \times 16 = 64$. ### Final Answer Therefore, the correct answer is **if the data even in both Statements I and II together are not sufficient to answer the question**.