Question

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.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Statement (1) and (2) alone are sufficient.

Answer 1

The correct option is D Statement (1) and (2) alone are sufficient.

Given: $\pi r^2=a^2$
(where r = radius of circle; a = side of square)
$\Rightarrow r=\frac{a}{\sqrt{\pi }}$
Hence, to find the circumference of circle, one should know 'a' the side of square.
(1) $\Rightarrow \text{Side of square}=\frac{diagonal}{\sqrt{2}}$
$\therefore$ Statement (1) alone is sufficient.
Also, as stated above, statement (2) alone is sufficient.