What is the perimeter of the square? a) The area of the square is 16 b) The…
2024
What is the perimeter of the square?
a) The area of the square is 16
b) The diagonal of the square is 4√2
- A.
Statement A alone is sufficient
- B.
Statement B alone is sufficient
- C.
Both statements are required
- D.
Either of statement A or B is sufficient
Show answer & explanation
Correct answer: D
Concept: For a square, Area = side2, Diagonal = side × √2, and Perimeter = 4 × side. In a Data Sufficiency question, a statement is sufficient on its own if it lets you compute the required quantity (here, the perimeter) uniquely, without needing the other statement.
Statement A gives Area = 16, so side2 = 16, giving side = 4. Perimeter = 4 × 4 = 16. Statement A alone is sufficient.
Statement B gives Diagonal = 4√2, so side × √2 = 4√2, giving side = 4. Perimeter = 4 × 4 = 16. Statement B alone is sufficient.
Cross-check: Both statements independently give the same side length (4) and the same perimeter (16), confirming the calculation is consistent. Since each statement alone already answers the question, the correct choice is that either statement A or B alone is sufficient.