Select the figure from among the given options that can replace the question mark (?) in the following series.

- (a)

- (b)

- (c)

- (d)

Answer
Why
Correct — A. Each frame is a face built from three parts, and each part runs on its own cycle.
Rule: the eyebrows alternate between cups and arches; the shaded half of each eye turns a quarter-turn clockwise every step; the mouth's opening turns a quarter-turn anticlockwise every step.
Eyebrows: cups, arches, cups, arches — so frame 5 takes cups.
Eye shading: bottom, then left, then top, then right. That is a whole turn in four steps, so frame 5 returns to the bottom.
Mouth: opening downward, then rightward, then upward, then leftward. Another whole turn, so frame 5 opens downward again.
Option (a) shows cup eyebrows, eyes shaded across the bottom and a downward-opening mouth — the frame-1 state, which is where a four-step cycle lands at step five.
Why the others are wrong
- (b)Option (b) draws arch eyebrows, which belong to the even frames, and a mouth opening upward, which is the frame-3 mouth. Only its eyes are right.
- (c)Option (c) keeps the cup eyebrows but shades its eyes across the top and opens its mouth leftward — the frame-3 eyes and the frame-4 mouth held over.
- (d)Option (d) gets the cup eyebrows and the downward mouth right, but shades its eyes on the left, which is the frame-2 state rather than the bottom.
Concept
A series of face-like figures is solved part by part. Split the picture into its elements — eyebrows, eyes, mouth — and track each element across all four given frames before you look at the options.
The parts here move at different rates. The eyebrows have a period of two: cup, arch, cup, arch. The eye shading and the mouth each have a period of four, turning a quarter-circle per step, and they turn in opposite senses.
Four steps is a whole revolution for both of the slower parts, so the fifth figure repeats the first exactly. Seeing that ends the question without predicting anything new.
The options are pictures, so nothing can be read from the option text. Describe each option to yourself in the same three-part vocabulary you used on the series, then compare the descriptions rather than the drawings.
Key facts
- The eyebrows are cups in frames 1 and 3 and arches in frames 2 and 4.
- The shaded half of each eye runs bottom, left, top, right across the four frames.
- The mouth's opening runs downward, rightward, upward, leftward across the four frames.
- An element on a four-step cycle returns to its starting state at the fifth figure.
Study next
Common traps
- Matching an option on a single element, usually the eyebrows, and stopping there.
- Reading the eye shading as a rotation of the whole eye instead of the shaded half.
- Missing that a four-step cycle brings the fifth figure back to the first.
Check each element of every option against your prediction before choosing. The wrong pictures here are built by leaving one part, or two, at an earlier step of the cycle rather than by drawing something new.
Related PYQs
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