The problem figures below change by a fixed rule. Which option figure continues the series?

Answer & explanation
Correct answer: option 4
The correct answer is Option (4) →
From each figure to the next, the half-shaded circle turns 90° anticlockwise each time. So the next figure has the half-shaded circle with the shaded half towards the bottom-left.

Why the other options are incorrect
Option (1) — Incorrect. The half-shaded circle has turned 90° clockwise instead of anticlockwise.
Option (2) — Incorrect. The half-shaded circle has not turned at all since the last figure.
Option (3) — Incorrect. The half-shaded circle has turned 45° instead of 90°.