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GATE 2021 CE (CE2) – Question 6

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 2 marks · Multiple choice

From O, travel 3 units east and 4 south to P. Move northeast until reaching a point 6 units east of O, then northwest to Q, which is 8 units north of P. Find OQ.

  1. 3
  2. 4
  3. 5
  4. 6

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Show answer and explanation

Correct answer: (C) 5

Explanation

O is (0,0) and P is (3,−4). “A point 6 units east of O” means the intermediate point is (6,0), reached along a northeast direction. Q lies 8 units north of P, so Q=(3,4); the last leg from (6,0) to (3,4) is northwest. Therefore OQ=√(3²+4²)=**5 (C)**. Northeast and northwest name quadrants, not necessarily exact 45° bearings.