Identify the figure from among the given options which when put in place of the question mark (?) will logically complete the series.

- (a)

- (b)

- (c)

- (d)

Answer
Why
Correct — C. Two counters advance across the four given frames, and a third thing alternates.
Rule: the polygon gains a side each step, the arrows go up by one, and their direction alternates out, in, out, in.
The frames run triangle with 2 arrows, square with 3, pentagon with 4, hexagon with 5. So the fifth frame needs a seven-sided figure carrying six arrows.
The arrows on the triangle and the pentagon point away from the shape; those on the square and the hexagon point into it. Frame five is therefore an outward frame.
Option (c) is a heptagon ringed by six arrows, every one of them pointing outwards.
Why the others are wrong
- (a)A hexagon with six outward arrows. The arrows are right, but the shape repeats the fourth frame instead of gaining its side.
- (b)An octagon with five inward arrows — two faults at once: a shape that jumps two sides and an arrow count and direction held over from frame four.
- (d)An octagon with six outward arrows. The arrows are right, but eight sides is one more than the run 3, 4, 5, 6 calls for.
Concept
Read a polygon figure series on two clocks, a side count and a decoration count. Note the number of sides in each frame, then the number and direction of the decorations, and only then open the options.
Here the sides run 3, 4, 5, 6 and the arrows run 2, 3, 4, 5, so the arrows always number one fewer than the sides, while the direction alternates outward and inward.
Two independent rules point at the same answer here, which is a useful check: if the shape rule and the arrow rule disagreed, one of them would have been read wrongly.
Key facts
- The four given frames hold a triangle, a square, a pentagon and a hexagon.
- They carry 2, 3, 4 and 5 arrows, one fewer than the number of sides in every frame.
- The arrows point outward in frames 1 and 3 and inward in frames 2 and 4, so frame 5 points outward.
Study next
Common traps
- Fixing the shape and taking the first seven-sided option without checking the arrows
- Carrying the fourth frame's inward arrows into the answer
- Miscounting a heptagon as a hexagon in a small drawing — count vertices, not sides
The figure-series stem appears under several wordings across shifts; 9 Sep 2024, 12:30, Reasoning Q.8 carries one of them.
Related PYQs
No directly related past PYQ was found.