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GATE 2023 EC – Question 10

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

A 100 cm × 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm × 1 cm.

The total number of creases visible when the sheet is unfolded is ________.

  1. 32
  2. 5
  3. 31
  4. 63

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Show answer and explanation

Correct answer: (C) 31

Explanation

Each fold halves the 32 cm side, so after 5 folds it is $32/2^5=1$ cm. The number of creases after $n$ folds of this type is $2^n-1$, so $2^5-1=31$.