Difficulty: Easy
Correct Answer: At point A
Explanation:
Introduction / Context:
This direction sense question is based on movements along four diagonal directions: north east, south east, south west and north west. The pattern of directions suggests that the person is tracing out a closed geometric figure, and the task is to identify the final position relative to the starting point. Understanding symmetry and cancelling of movements is crucial here, and this type of reasoning appears frequently in aptitude tests to check visualisation skills.
Given Data / Assumptions:
Concept / Approach:
Each diagonal direction can be split into a pair of perpendicular components, one north south and one east west. For example, north east contains equal parts north and east, while south west contains equal parts south and west. Because all segments have the same length, their horizontal and vertical components can cancel neatly. The key insight is that moving once in each of the four diagonal directions with equal distance creates a closed loop and brings the person back to the starting point, similar to walking around a square or diamond shape.
Step-by-Step Solution:
Step 1: Consider the first move of 100 m towards north east. This can be thought of as some amount north and the same amount east.Step 2: The second move is 100 m towards south east. This has the same east component as the first move but a south component equal in magnitude to the previous north component.Step 3: After these two moves, the north and south components cancel each other, leaving only an effective movement towards the east.Step 4: The third move is 100 m towards south west. This adds a west component and a south component which begin to cancel out the remaining east and the upcoming north west movement.Step 5: The final move of 100 m in the north west direction has equal north and west components, effectively cancelling the residual south and east components from the earlier legs.Step 6: Because the distances and diagonal angles are symmetric, the total north south displacement and the total east west displacement both become zero. Therefore, Ram returns to the original starting point A.
Verification / Alternative check:
A simple way to visualise this is to imagine a square or a rhombus. Starting from one corner, moving 100 m north east, then 100 m south east, then 100 m south west, and finally 100 m north west corresponds to moving all around the four sides of a closed figure and coming back to the starting corner. This geometric picture provides a quick mental verification without explicit component calculations.
Why Other Options Are Wrong:
Options A (West) and D (East) suggest that there is a net horizontal shift, which would only happen if the diagonal moves were not balanced. Option B (Southwest) implies a net diagonal movement, again ignoring the symmetry. Only option C correctly states that Ram is at point A, meaning his net displacement is zero after completing the four moves of equal length and symmetric directions.
Common Pitfalls:
Candidates often treat diagonal moves as if they were purely horizontal or vertical, which leads to incorrect cumulative results. Another mistake is to stop tracking after two or three moves, without noticing that the fourth move completes the loop. When diagonal directions appear in a symmetric pattern with equal distances, it is usually a hint that the path closes back on itself. Keeping an eye on symmetry is a powerful shortcut in many direction sense problems.
Final Answer:
After completing all four diagonal movements, Ram returns to his starting point, so he is exactly at point A and not displaced in any direction.
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