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Discussion :: Analytical Reasoning

  1. Determine the number of rectangles and hexagons in the given figure.

  2. A.
    30, 5
    B.
    32, 3
    C.
    28, 5
    D.
    30, 3

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    Answer : Option A

    Explanation :

    The figure may be labelled as shown.

    Rectangles:

    The simplest rectangles are CVSR, VETS, RSWM and STKW i.e. 4 in number.

    The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e. 4 in number.

    The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e. 4 in number.

    The rectangles composed of four components each are CEKM, AVSP,PSWO, VGHS and SHIW i.e. 5 in number.

    The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e. 4 in number.

    The rectangles composed of six components each are ACMO and EGIK i.e. 2 in number.

    The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e. 4 in number.

    The rectangles composed of ten components each are AEKO and CGIM i.e. 2 in number.

    AGIO is the only rectangle having sixteen components.

    Total number of rectangles in the given figure

    = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.

    Hexagons:

    The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP.

    So, there are 5 hexagons in the given figure.


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