Question

What is the radius of the circle?
I. Ratio of its area to circumference is $> 7$.
II. Diameter of the circle is $\leq 32$.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both the statement I and statement II are needed to answer the question.
• D. If the question cannot be answered even with the help of both the statements.

Hint:

Translate verbal conditions into algebraic expressions, then isolate the variable to see what range it satisfies.

Answer 1

The Correct Option is A

Let the radius be $r$. Area of the circle $= \pi r^2$
Circumference of the circle $= 2\pi r$
\[ \frac{\text{Area}}{\text{Circumference}} = \frac{\pi r^2}{2\pi r} = \frac{r}{2} \Rightarrow \frac{r}{2}>7 \Rightarrow r>14 \] So, from statement I alone, we get that $r>14$, which is a sufficient answer. Statement II: Diameter $\leq 32 \Rightarrow r \leq 16$ This only provides an upper bound, not an exact or narrow enough value to determine $r$. So it's not sufficient. Thus, only statement I is sufficient.