Difficulty: Medium
Correct Answer: 9 km North
Explanation:
Introduction / Context:
This question describes the trip of a marketing executive who makes several turns while walking fixed distances in different directions. The goal is to determine his final position relative to his starting point. Direction sense problems of this type are common in verbal reasoning and test the ability to translate word descriptions into a mental or drawn map and then compute net displacement.
Given Data / Assumptions:
Concept / Approach:
We treat the movements as vectors on a coordinate plane. Let the starting point be (0, 0). Moving north increases the y coordinate, moving south decreases it, moving east increases the x coordinate, and moving west decreases it. By adding each movement step by step, we obtain the final coordinates and then interpret the net displacement as a distance and direction from the origin.
Step-by-Step Solution:
Take the starting point as (0, 0).
Walking 2 km north leads to position (0, 2).
Turning west and walking 6 km leads to position (-6, 2).
Turning north and walking 7 km leads to position (-6, 9).
From facing north, a right turn means facing east; walking 6 km east leads to position (0, 9).
Final coordinates relative to the origin: (0, 9).
Thus, the executive is 9 km directly north of his starting point.
Verification / Alternative check:
We can also reason verbally. The 6 km west and 6 km east movements cancel each other out, leaving no net east west displacement. The north movements are 2 km and 7 km, for a total of 9 km north, with no southward movement to cancel them. Hence he must be 9 km north of his starting position.
Why Other Options Are Wrong:
Option A: 5 km North underestimates the total northward displacement.
Options C and D mention south, which is opposite to the actual direction.
Option E: None of these is incorrect because 9 km North is explicitly available in the options as the correct answer.
Common Pitfalls:
Common mistakes include misinterpreting a right turn from north as west instead of east, or failing to notice that opposite horizontal displacements cancel out. Another frequent issue is to add distances without regard to direction. Carefully tracking net north south and east west movements avoids these errors.
Final Answer:
The marketing executive is 9 km North of his starting position.
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