GATE ECE 2023 | GA | Question: 10

Question

A $100 \mathrm{~cm} \times 32 \mathrm{~cm}$ 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 $100 \mathrm{~cm} \times 1 \mathrm{~cm}$.

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

• A. $32$
• B. $5$
• C. $31$
• D. $63$

Comments

video solution

https://www.youtube.com/watch?v=4PLOWLI_3t0&t=2s

Answer 1

$1$ fold divides the sheet into to parts $2$ parts with $1$ crease in between.

$2$ folds divides the sheet into $4$ parts with $3$ creases.

$5$ folds will divides the sheet into $32$ parts with $31$ creases.

Hence answer will be Option $C$ $31$

Comments

Alternate method:

$1^{st}$ fold $\rightarrow$ $1$ new crease $= 2^{0} $

$2^{nd}$ fold $\rightarrow$ $2$ new creases $= 2^{1} $

$3^{rd}$ fold $\rightarrow$ $4$ new creases $= 2^{2} $

$4^{th}$ fold $\rightarrow$ $8$ new creases $= 2^{3} $

$5^{th}$ fold $\rightarrow$ $16$ new creases $= 2^{4} $

So, total creases after $5$ folds $= 2^{0} + 2^{1} + 2^{2} + 2^{3} + 2^{4} = 2^{5} - 1 = 31$

Answer 2

folds       crease total

1

Answer 3

fold  crease total  cm length

1            1          100:16

2            3          100:8

3            7          100:4

4            15        100:2

5            31        100:1          

ans is c 31