Question

A rectangular paper of 20 cm×8 cm20\text{ cm} \times 8\text{ cm} is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. The perimeter of the final folded sheet (in cm) is

Choose one option
Official answer and solution
Official answer
A
From
Official GATE 2024 answer key

Solution

At each of the 3 folds, identify the current longer edge of the rectangular sheet and halve that dimension.

Each fold is made along the line of symmetry perpendicular to the current long edge of the sheet, which halves the longer dimension at each step:

  1. Initial dimensions: 20 cm×8 cm20\text{ cm} \times 8\text{ cm} (long edge =20 cm= 20\text{ cm}).
  2. After 1st fold: Halving the 20 cm20\text{ cm} edge gives 10 cm×8 cm10\text{ cm} \times 8\text{ cm} (long edge is still 10 cm10\text{ cm}).
  3. After 2nd fold: Halving the 10 cm10\text{ cm} edge gives 5 cm×8 cm5\text{ cm} \times 8\text{ cm} (now the long edge is 8 cm8\text{ cm}!).
  4. After 3rd fold: Halving the current long edge (8 cm8\text{ cm}) gives 5 cm×4 cm5\text{ cm} \times 4\text{ cm}.

Therefore, the perimeter of the final 5 cm×4 cm5\text{ cm} \times 4\text{ cm} folded sheet is:

Perimeter=2×(5+4)=18 cm\text{Perimeter} = 2 \times (5 + 4) = 18\text{ cm}
Final answer

Option (A)

Common trap

Halving the original 20 cm edge all three times to get 2.5 cm by 8 cm (perimeter 21 cm), overlooking that after the second fold the 8 cm edge becomes the longer edge.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper
GATE 2024 Computer Science and Information Technology - Set 1 (CS1)
Question
9 of 65
Section
General Aptitude

Report an error in this question

GATE questions are the work of the organising institutes. This site is independent and is not affiliated with them.