Equal sized circular regions are shaded in a square sheet of paper of 1 cm…

GATE · 2022 · AE · General AptitudeGATE · 2022 · GE · General AptitudeGATE · 2022 · ME · Set 2 · General Aptitude

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.

What is the ratio of the areas of unshaded regions of case M to that of case N?

Two square outlines labelled case M and case N. Case M contains four equal shaded circles in a two-by-two arrangement, touching neighbouring circles and square edges. Case N contains nine equal shaded circles in a three-by-three arrangement, similarly touching neighbours and square edges. Shading is gray patterned fill. The stem gives the square side length as 1 cm; no dimensions are printed inside the diagrams.
  1. A.

    2 : 3

  2. B.

    1 : 1

  3. C.

    3 : 2

  4. D.

    2 : 1

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