GATE CE 2022 Set 2 — Question 10
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General Aptitude → Quantitative Aptitude → 2D & 3D Patterns
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Question
An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing east.The ant first turns anticlockwise at P, and then does the following two steps in sequence exactly FIVE times before halting.
1.moves forward for 10 cm.
2.turns clockwise.
The pattern made by the trace left behind by the ant isCorrect answer
(C) [figure] SQ = QT = TR = RP = PS = 10 cm
Solution
1.Initial State: The ant is at point P, facing East ().
2.First Turn: It turns anticlockwise. Its new heading is (North of East).
3.Iterative Movement: It repeats the following sequence 5 times:
- Move forward 10 cm.
- Turn clockwise.
5.Calculation: Here, the turning angle is . We can find by setting , which gives .
6.Conclusion: A star polygon is a regular 5-pointed star (pentagram). The total angle turned is , which completes two full rotations (), closing the figure. Option (C) correctly represents this 5-pointed star pattern with 5 segments of 10 cm each.
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