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GATE 2024 EC – Question 10

General Aptitude · Spatial Aptitude: Spatial Reasoning and Visualization · 2 marks · Multiple choice

Two identical sheets A and B, of dimensions 24 cm × 16 cm, can be folded into half using two distinct operations, FO1 or FO2.

In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge.

If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is

  1. 14:11
  2. 11:14
  3. 18:11
  4. 11:18

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Show answer and explanation

Correct answer: (A) 14:11

Explanation

FO1 halves the 16 cm side each time: 24 × 16 → 24 × 8 → 24 × 4, with perimeter $2(24+4)=56$ cm. FO2 halves the 24 cm side each time: 24 × 16 → 12 × 16 → 6 × 16, with perimeter $2(6+16)=44$ cm. The ratio is $56:44=14:11$.