Brief Theory Overview

Figure-series questions test the ability to identify visual patterns, movements, and logical progressions among geometric shapes. Typically, a sequence of five or six figures is given; the candidate must pick the figure that continues the established rule. The rule may be based on rotation, addition/deletion of elements, change in size or orientation, alternation of shading, or a combination of these. The key is to isolate the simplest transformation that links every consecutive pair, then apply it one step forward to the answer choices.

While practising, always:

1. Number the positions (1-5) and write the observed change (e.g., “clockwise 90°”, “+1 side”, “invert shading”).
2. Look for composite patterns—two independent rules running in parallel (e.g., outer shape rotates while inner shape increases sides).
3. Eliminate options that violate any single step of the chain; the remaining option is almost always correct.
   Remember, railway exams favour speed—never spend more than 45 s on a single figure-series item. Use the shortcuts given at the end to decide quickly.

Practice Set – 25 MCQs

Directions: In each question, five figures marked (1), (2), (3), (4) and (5) continue a definite series. Which figure from the answer choices (a), (b), (c), (d) should come next in place of the question mark?

Easy (Q 1-8)

1. A square rotates 45° clockwise in every step.

   • (a) Square 45° rotated
   • (b) Square 90° rotated
   • (c) Square 135° rotated
   • (d) Square 180° rotated
   Answer

   Correct: Option a. The next clockwise 45° turn after four steps (total 180°) brings it to 225°; only option a matches.

2. One extra dot is added inside the circle each time.

   • (a) 5 dots
   • (b) 6 dots
   • (c) 7 dots
   • (d) 8 dots
   Answer

   Correct: Option b. Series: 2,3,4,5 → next 6 dots.

3. An arrow flips vertically every alternate step.

   • (a) Arrow up
   • (b) Arrow down
   • (c) Arrow right
   • (d) Arrow left
   Answer

   Correct: Option a. Step 5 is up (flip of step 4 down).

4. Number of sides increases by 1 each figure.

   • (a) Hexagon
   • (b) Heptagon
   • (c) Octagon
   • (d) Nonagon
   Answer

   Correct: Option b. 3,4,5,6 → next 7 sides.

5. Shading moves one sector clockwise.

   • (a) Sector 1
   • (b) Sector 2
   • (c) Sector 3
   • (d) Sector 4
   Answer

   Correct: Option c. After 4 steps, sector 3 is shaded.

6. A small line disappears from the right end each step.

   • (a) 1 line
   • (b) 2 lines
   • (c) 3 lines
   • (d) 0 lines
   Answer

   Correct: Option d. All 4 lines gone → 0.

7. Triangle alternates between pointing up and down.

   • (a) Up
   • (b) Down
   • (c) Left
   • (d) Right
   Answer

   Correct: Option a. Step 5 is up.

8. A cross symbol moves one corner clockwise.

   • (a) Top-left
   • (b) Top-right
   • (c) Bottom-right
   • (d) Bottom-left
   Answer

   Correct: Option b. After 4 moves, top-right.

Medium (Q 9-17)

9. Outer shape rotates 90° clockwise; inner shape rotates 90° anticlockwise.

   • (a) Outer right, inner left
   • (b) Outer down, inner up
   • (c) Outer left, inner right
   • (d) Outer up, inner down
   Answer

   Correct: Option c. Both continue their respective rotations.

10. One petal gets shaded every step clockwise; total 5 petals.

    • (a) 2 shaded
    • (b) 3 shaded
    • (c) 4 shaded
    • (d) 5 shaded
    Answer

    Correct: Option c. 1,2,3,4 → next 4 shaded.

11. Figure is mirrored across vertical axis every step.

    • (a) Original
    • (b) Mirror
    • (c) 180° rotate
    • (d) Same as step 1
    Answer

    Correct: Option b. Odd steps are mirrored.

12. Number of intersection points increases by 2.

    • (a) 8
    • (b) 10
    • (c) 12
    • (d) 14
    Answer

    Correct: Option b. 2,4,6,8 → next 10.

13. A small circle inside a square moves diagonally top-left → bottom-right → top-right → bottom-left → centre; next?

    • (a) Top-left
    • (b) Top-right
    • (c) Bottom-left
    • (d) Centre
    Answer

    Correct: Option a. Cycle repeats; next top-left.

14. Alternately add 2 lines vertical then 2 horizontal.

    • (a) 3 V, 2 H
    • (b) 2 V, 3 H
    • (c) 4 V, 2 H
    • (d) 2 V, 4 H
    Answer

    Correct: Option c. Step 5 adds 2 V → 4 V, 2 H.

15. Size doubles every second step.

    • (a) Same
    • (b) Double
    • (c) Triple
    • (d) Half
    Answer

    Correct: Option b. Steps 1,3,5 double; step 5 is double of step 3.

16. Arrow rotates 45° clockwise and colour reverses every step.

    • (a) Black 45°
    • (b) White 90°
    • (c) Black 135°
    • (d) White 135°
    Answer

    Correct: Option d. Step 4 white 90° → step 5 white 135°.

17. Two independent shapes: square→pentagon→hexagon; circle stays. Next?

    • (a) Hexagon+circle
    • (b) Heptagon+circle
    • (c) Octagon+circle
    • (d) Pentagon+circle
    Answer

    Correct: Option b. 4,5,6 → next 7 sides.

Hard (Q 18-25)

18. Composite: outer shape sides +1 every two steps; inner dots −1 every step; next after 4 steps?

    • (a) Hexagon 2 dots
    • (b) Hexagon 1 dot
    • (c) Heptagon 2 dots
    • (d) Heptagon 1 dot
    Answer

    Correct: Option b. Step 5: sides 6 (hexagon), dots 1.

19. A 3-step cycle: rotate 90°, add line, mirror; repeat. Next after 5 steps?

    • (a) Rotate 90°
    • (b) Add line
    • (c) Mirror
    • (d) Same as step 2
    Answer

    Correct: Option b. Step 6 is second occurrence of “add line”.

20. Fibonacci-based number of elements: 1,1,2,3,5 → next?

    • (a) 6
    • (b) 7
    • (c) 8
    • (d) 9
    Answer

    Correct: Option c. 5+3=8.

21. Figure divides into 2 identical parts every alternate step; next undivided?

    • (a) Divided
    • (b) Undivided
    • (c) Tripled
    • (d) Quartered
    Answer

    Correct: Option b. Step 5 is undivided.

22. Angle of inclination follows prime numbers: 2°,3°,5°,7° → next?

    • (a) 9°
    • (b) 11°
    • (c) 13°
    • (d) 15°
    Answer

    Correct: Option b. Next prime 11°.

23. Shading follows binary toggle: 000 001 010 011 100 → next?

    • (a) 101
    • (b) 110
    • (c) 111
    • (d) 000
    Answer

    Correct: Option a. Binary count 5 → 101.

24. Nested squares increase both in number and rotate 18° cumulative.

    • (a) 4 squares 72°
    • (b) 5 squares 90°
    • (c) 5 squares 72°
    • (d) 4 squares 90°
    Answer

    Correct: Option b. 5 squares, 18°×5=90°.

25. Alternating reflection across x-axis then y-axis; next after 4 reflections?

    • (a) Original
    • (b) 180° rotate
    • (c) Mirror across x
    • (d) Mirror across y
    Answer

    Correct: Option b. 4 reflections (x then y twice) equivalent to 180° rotation.

Quick Shortcuts & Tips

1. 45-sec rule: If you can’t spot the rule in 15 s, skip and mark for review; figure-series rarely requires lengthy calculation.
2. Twin-track check: Always ask “Is there a second independent pattern?”—railway loves dual rules.
3. Eliminate outliers: Remove options that break even one observed transformation; usually only one survives.
4. Corner tracker: For moving symbols, mentally number corners 1-4; modulo-4 arithmetic gives next position instantly.
5. Prime & Fibonacci flags: Sudden jumps in count/angle often follow prime or Fibonacci sequences—memorise first 10 of each.
6. Mirror vs rotate: Two mirrors (X then Y) = 180° rotate; saves mental flipping.
7. Practice with folded paper: Physically rotate your rough sheet to mimic shape rotation—visually faster than imagination alone.