Question

What are the dimensions of a certain rectangle?
(I) The perimeter of the rectangle is 14.
(II) The diagonal of the rectangle is 5.

• A. Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
• B. Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Answer 1

Answer: (C)

Both statements together are sufficient, but neither statement alone is sufficient.

(I) $\Rightarrow 2x+2y=14$ or $x+y=17$
(II) $\Rightarrow x^2+y^2=4$
We can find the dimensions of certain rectangle using both equation. Therefore, we need both the statements to find the value of x and y.