Question:
If the number of square units in the area of a circle is 'A' and the number of linear units in the circumference is 'C', what is the radius of the circle?
I) $A > C + 3$
II) $A/C = 3/2$
If the number of square units in the area of a circle is 'A' and the number of linear units in the circumference is 'C', what is the radius of the circle?
I) $A > C + 3$
II) $A/C = 3/2$
I) $A > C + 3$
II) $A/C = 3/2$
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The ratio of area to circumference of a circle is always $r/2$.
Updated On: Jun 26, 2026
- Statement I alone is sufficient
- Statement II alone is sufficient
- Statements I and II together are sufficient
- Statements I and II together are not sufficient
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The Correct Option is B
Solution and Explanation
Step 1: Concept
$A = \pi r^2$ and $C = 2\pi r$.
Step 2: Analysis of Statement I
$\pi r^2 > 2\pi r + 3$. This is an inequality and provides a range of values for 'r', not a unique value. Not sufficient.
Step 3: Analysis of Statement II
$A / C = 3/2$.
$\frac{\pi r^2}{2\pi r} = \frac{3}{2}$
$\frac{r}{2} = \frac{3}{2} \Rightarrow r = 3$.
Statement II alone provides a unique value for the radius. Sufficient.
Step 4: Conclusion
Statement II alone is sufficient, so the answer is (2). Final Answer: (2)
$A = \pi r^2$ and $C = 2\pi r$.
Step 2: Analysis of Statement I
$\pi r^2 > 2\pi r + 3$. This is an inequality and provides a range of values for 'r', not a unique value. Not sufficient.
Step 3: Analysis of Statement II
$A / C = 3/2$.
$\frac{\pi r^2}{2\pi r} = \frac{3}{2}$
$\frac{r}{2} = \frac{3}{2} \Rightarrow r = 3$.
Statement II alone provides a unique value for the radius. Sufficient.
Step 4: Conclusion
Statement II alone is sufficient, so the answer is (2). Final Answer: (2)
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