Question Bank • QB_GA_ADV_129 MSQ • 2 Marks

Section 8: General Aptitude

Analytical & Spatial Aptitude

Subtopic: Logic Deduction & Pattern Recognition

Question Statement:

A farm surveyor starts from base station $O$ and walks along the following path: 1. $40\text{ m}$ due North to point $A$ 2. Turns right and walks $30\text{ m}$ due East to point $B$ 3. Turns right and walks $80\text{ m}$ due South to point $C$ 4. Turns right and walks $30\text{ m}$ due West to point $D$ Which of the following statements is/are TRUE regarding the surveyor's final position $D$ relative to base station $O$?

Options:

  • (A) The surveyor is exactly $40\text{ m}$ away from base station $O$.
  • (B) The final position $D$ lies directly South of base station $O$.
  • (C) The total distance walked by the surveyor along the path is $180\text{ m}$.
  • (D) The final position $D$ lies directly West of point $C$.

Answer Key:

A, B, C, D

Step-by-Step Solution & Explanation

**Method 1: Cartesian Coordinate Tracking** Let $O = (0, 0)$: 1. North $40\text{ m} \implies A = (0, 40)$ 2. East $30\text{ m} \implies B = (30, 40)$ 3. South $80\text{ m} \implies C = (30, 40 - 80) = (30, -40)$ 4. West $30\text{ m} \implies D = (30 - 30, -40) = (0, -40)$ Verification: - (A) Distance from $O(0,0)$ to $D(0, -40) = \sqrt{0^2 + (-40)^2} = 40\text{ m}$. True. - (B) $D(0, -40)$ lies on the negative y-axis, directly South of $O(0,0)$. True. - (C) Total path length $= 40 + 30 + 80 + 30 = 180\text{ m}$. True. - (D) $C = (30, -40)$ and $D = (0, -40)$ share the same y-coordinate, so $D$ is directly West of $C$. True. All four statements **A**, **B**, **C**, and **D** are correct.
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