Each of the following questions consists of five figures marked A, B, C, D and…

2024

Each of the following questions consists of five figures marked A, B, C, D and E called the Problem Figures followed by five other figures marked 1, 2, 3, 4 and 5 called the Answer Figures. Select a figure from amongst the Answer Figures which will continue the same series as established by the five Problem Figures. Problem Figures : Answer Figures:

(A) (B) (C) (D) (E) (1) (2) (3) (4) (5)

  1. A.

    1

  2. B.

    2

  3. C.

    3

  4. D.

    4

  5. E.

    5

Attempted by 24 students.

Show answer & explanation

Correct answer: E

In figure-series items built on a square boundary, three symbols occupy fixed points around the perimeter (the four corners and the four edge-midpoints, eight slots in all). Across the run of problem figures, exactly one symbol moves per step, in a repeating 2-3-4 anticlockwise cycle: the symbol at the anticlockwise-end of the current three-symbol cluster moves 2 slots anticlockwise, then the symbol at the clockwise-end of that cluster moves 3 slots anticlockwise, then the remaining (middle) symbol moves 4 slots anticlockwise -- after which the three symbols form a new consecutive cluster and the 2-3-4 cycle restarts with the anticlockwise-end/clockwise-end/middle roles reassigned from that new cluster.

  1. Number the eight boundary slots clockwise starting at the top-left corner: 1 = top-left corner, 2 = top-middle, 3 = top-right corner, 4 = right-middle, 5 = bottom-right corner, 6 = bottom-middle, 7 = bottom-left corner, 8 = left-middle.

  2. In Problem Figure A the star, the equals-sign and the cross sit at slots 2, 3 and 4 -- three consecutive slots. Within this cluster the star is the anticlockwise-end, the cross is the clockwise-end, and the equals-sign is the middle symbol.

  3. Step A to B: the anticlockwise-end symbol (star) moves 2 slots anticlockwise, from 2 to 8; the cross and the equals-sign do not move. This reproduces Figure B (equals-sign at 3, cross at 4, star at 8).

  4. Step B to C: the clockwise-end symbol from the same cluster (cross) moves 3 slots anticlockwise, from 4 to 1. This reproduces Figure C (cross at 1, equals-sign at 3, star at 8).

  5. Step C to D: the middle symbol (equals-sign) moves 4 slots anticlockwise, from 3 to 7. This reproduces Figure D (cross at 1, star at 8, equals-sign at 7). The three symbols now sit at slots 7, 8 and 1 -- a new consecutive cluster -- so the roles reset: the equals-sign (7) becomes the new anticlockwise-end, the cross (1) the new clockwise-end, and the star (8) the new middle symbol.

  6. Step D to E: the new anticlockwise-end symbol (equals-sign) moves 2 slots anticlockwise, from 7 to 5. This reproduces Figure E (cross at 1, star at 8, equals-sign at 5), the last given problem figure.

  7. Step E to the missing figure: within the same reassigned cluster it is now the clockwise-end symbol's (cross) turn to move 3 slots anticlockwise, from 1 to 6 (1 to 8 to 7 to 6). The star and the equals-sign are not due to move on this step, so they stay at 8 and 5.

  8. This places the cross at the bottom-middle edge (6), the star at the left-edge midpoint (8) and the equals-sign at the bottom-right corner (5) -- exactly the arrangement shown in Answer Figure 5.

Checking the remaining answer figures against the same rule rules them out: the figures with the cross still at the right-edge midpoint or at the bottom-left corner have not advanced it the required 3 slots anticlockwise from Figure E's top-left position; the figures that relocate the star instead of the cross, or move the star in addition to the cross, break the one-symbol-per-step rule already established across Figures A to E. Answer Figure 5 is the only arrangement consistent with the pattern.

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