Question

The figure below shows a circle divided into 3 equal parts. The shaded region corresponds to $(\frac{2}{3}{)}^{\text{rd}}$ of the circle. If the unshaded region corresponds to $(\frac{a}{3}{)}^{\text{rd}}$ of the circle, then the value of $a$ is

• A. 1
• B. 2
• C. 3
• D. $\frac{1}{3}$

Answer 1

The correct option is A 1

Since the entire circle is divided into 3 equal parts, each part corresponds to $(\frac{1}{3}{)}^{\text{rd}}$ of the circle.
Since there are two shaded parts, the shaded region corresponds to$(\frac{2}{3}{)}^{\text{rd}}$ of the circle.
Since there is only one part which is unshaded, it corresponds to $(\frac{1}{3}{)}^{\text{rd}}$ of the circle.
i.e., $\frac{a}{3}=\frac{1}{3}$
$\therefore a=1$