Question:
What is the radius of the circle?
I. Ratio of its area to circumference is $> 7$.
II. Diameter of the circle is $\leq 32$.
What is the radius of the circle?
I. Ratio of its area to circumference is $> 7$.
II. Diameter of the circle is $\leq 32$.
I. Ratio of its area to circumference is $> 7$.
II. Diameter of the circle is $\leq 32$.
Show Hint
Translate verbal conditions into algebraic expressions, then isolate the variable to see what range it satisfies.
Updated On: Mar 23, 2026
- If the question can be answered with the help of statement I alone.
- If the question can be answered with the help of statement II alone.
- If both the statement I and statement II are needed to answer the question.
- If the question cannot be answered even with the help of both the statements.
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The Correct Option is A
Solution and Explanation
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.
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.
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