The area of a square is equal to that of a circle. What is the circumference of the circle? (1) The diagonal of the square is x inches. (2) The side of the square is y inches.
A
Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
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B
Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
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C
Both statements together are sufficient, but neither statement alone is sufficient.
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D
Statement (1) and (2) alone are sufficient.
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Solution
The correct option is D Statement (1) and (2) alone are sufficient. Given: πr2=a2 (where r = radius of circle; a = side of square) ⇒r=a√π Hence, to find the circumference of circle, one should know 'a' the side of square. (1) ⇒Side of square=diagonal√2 ∴ Statement (1) alone is sufficient. Also, as stated above, statement (2) alone is sufficient.