Select the alternative which represents three out of the five alternative…

2024

Select the alternative which represents three out of the five alternative figures which when fitted into each other would form a complete square.

  1. A.

    123

  2. B.

    235

  3. C.

    245

  4. D.

    145

Attempted by 4 students.

Show answer & explanation

Correct answer: C

In a figure-fitting (shape-construction) question, the target square is already divided into a fixed set of regions by straight cutting lines. Each of the five alternative figures must be checked against these regions by matching edge lengths, angles, and orientation (rotation is allowed, distortion is not); exactly three of the five figures will tile the square edge-to-edge with no gap or overlap, and the other two will fail to match any region.

Looking at the square in the figure: the region running along the full left edge is a single continuous strip bounded by one long straight edge and a zig-zag cut -- it matches figure (5)'s irregular multi-sided boundary. The upper region is bounded by two parallel horizontal edges (the square's top edge and one of the internal horizontal cut lines) -- this parallel-edge pattern matches figure (4), an isosceles trapezium. The remaining lower-right region is bounded by a vertical edge meeting a horizontal edge at right angles, exactly the right-trapezium shape of figure (2). Together, figures (2), (4) and (5) -- combination 245 -- reconstruct the square exactly, edge to edge.

Figures (1) and (3) are left over: figure (3) is a sharply concave, arrow-like shape with two acute points that has no matching edge anywhere along the square's cutting lines, and figure (1) has no edge that fits the right-angled vertical-horizontal corner of the lower-right region. So any group that includes figure (1) or figure (3) -- i.e. 123, 235, or 145 -- cannot complete the square, confirming that 245 is the only combination that works.

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