Direction Sense MCQs for UPSC Prelims

62 practice questions on Direction Sense from the Logical Reasoning section of the UPSC Prelims syllabus. 62 come with a written explanation and 14 are actual previous year questions. Try the sample set below - the answer stays hidden until you ask for it.

25 Easy 30 Medium 7 Hard 14 from past papers

Sample questions

Q1
Previous year question medium

A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point?

  1. A An angle less than 45° South of East
  2. B An angle less than 45° North of East
  3. C An angle more than 45° South of East
  4. D An angle more than 45° North of East
Show answer and explanation

Correct answer: B - An angle less than 45° North of East

Take the start as origin, East = +x, North = +y. North 12 km -> (0, 12); South 6 km -> (0, 6); East 8 km -> (8, 6). Her final position is 8 km east and 6 km north of the start, so she lies in the North-East quadrant. The angle above the East axis is arctan(6/8) = arctan(0.75) which is about 36.87°, less than 45°. So she is at an angle less than 45° North of East. Since she is north of the start, the 'South of East' options are ruled out, and because the angle is under 45°, 'more than 45°' is wrong.

Q2
Previous year question medium

A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?

  1. A North-West
  2. B West
  3. C South
  4. D South-West
Show answer and explanation

Correct answer: C - South

Test the option South. Start at the house at origin facing South: walk 100 m to (0, -100); turn left (now facing East) and walk 100 m to (100, -100); turn left again (now facing North) and walk 300 m to (100, 200); turn right (now facing East) and walk 100 m to (200, 200). The office is 200 m East and 200 m North of the house, which is exactly North-East. Starting in any other given direction rotates this whole path, placing the office in a direction other than North-East (for example, starting West puts the office in the South-West). So the initial direction is South.

Q3
Previous year question medium

A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house?

  1. A 20 km
  2. B 25 km
  3. C 30 km
  4. D 35 km
Show answer and explanation

Correct answer: B - 25 km

Place the house at the origin with East = +x and North = +y. Drive 10 km South -> (0, -10). Facing South, a left turn faces East; drive 20 km -> (20, -10). Facing East, a left turn faces North; drive 40 km -> (20, 30). Facing North, a right turn faces East; drive 5 km -> (25, 30). Facing East, a right turn faces South; drive 30 km -> (25, 0). The bank is at (25, 0) and the house at (0, 0); they share the same y-coordinate, so the straight-line distance is simply 25 km. The other options come from mishandling one of the turns or adding the wrong leg lengths.

Q4
Previous year question medium

There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?

  1. A 20 km
  2. B 25 km
  3. C 31 km
  4. D 37 km
Show answer and explanation

Correct answer: C - 31 km

Place A at the origin (0, 0). A is 6 km south of B, so B = (0, 6). A is 10 km west of C, so C = (10, 0). C is 6 km north of D, so D = (10, -6). D is 5 km east of E, so E = (5, -6). F is 9 km west of B, so F = (-9, 6). F is 12 km north of G, so G = (-9, -6). The available roads are AB, AC, CD, DE, BF, EG and FG. One route from D to F is D-C-A-B-F = 6 + 10 + 6 + 9 = 31 km. The other route D-E-G-F = 5 + 14 + 12 = 31 km (EG runs from (5, -6) to (-9, -6), a distance of 14 km). Either way the distance covered is 31 km. The official UPSC key confirms option (c).

Q5
Previous year question medium

The houses of A and B face each other on a road going north-south, A's being on the western side. A comes out of his house, turns left, travels 5 km, turns right, travels 5 km to the front of D's house. B does exactly the same and reaches the front of C's house. In this context, which one of the following statements is correct?

  1. A C and D live on the same street.
  2. B C's house faces south.
  3. C The houses of C and D are less than 20 km apart.
  4. D None of the above
Show answer and explanation

Correct answer: C - The houses of C and D are less than 20 km apart.

A is on the western side facing east. Stepping out, A's left is north; he goes 5 km north, turns right (east) and goes 5 km, reaching D's house, which lies northeast of A. B is on the eastern side facing west. Stepping out, B's left is south; he goes 5 km south, turns right (west) and goes 5 km, reaching C's house, which lies southwest of B. D ends up 5 km east of the road and 5 km north; C ends up 5 km west of the road and 5 km south. The straight-line distance between C and D works out to less than 20 km, so option (c) is correct.

Q6
Previous year question medium

A person X was driving in a place where all roads ran either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other in a parallel. He started at the intersection of two roads, drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point, if the same route is not repeated?

  1. A 3 km east, then 2 km south
  2. B 3 km east, then 1 km north
  3. C 1 km north, then 2 km west
  4. D 3 km south, then 1 km north
Show answer and explanation

Correct answer: B - 3 km east, then 1 km north

Take the start as origin (0,0), with north = +y, east = +x. After 3 km north: (0,3). After 3 km west: (-3,3). After 4 km south: (-3,-1). To return to (0,0) he must move +3 in x (east) and +1 in y (north). Option (b) '3 km east, then 1 km north' takes him from (-3,-1) to (0,-1) to (0,0), reaching the start. None of the other options end at (0,0): (a) ends at (0,-3), (c) ends at (-5,0), (d) ends at (-3,-3).

Q7
Previous year question medium

Consider the Question and two Statements given below in respect of three cities P, Q and R in a State : Question : How far is city P from city Q? Statement-1 : City Q is 18 km from city R. Statement-2 : City P is 43 km from city R. Which one of the following is correct in respect of the Question and the Statements?

  1. A Statement-1 alone is sufficient to answer the Question
  2. B Statement-2 alone is sufficient to answer the Question
  3. C Both Statement-1 and Statement-2 are sufficient to answer the Question
  4. D Both Statement-1 and Statement-2 are not sufficient to answer the Question
Show answer and explanation

Correct answer: D - Both Statement-1 and Statement-2 are not sufficient to answer the Question

Knowing Q is 18 km from R and P is 43 km from R does not pin down P-to-Q, because the three cities need not be collinear; P and Q could lie at many angles around R, giving a range of P-Q distances (anywhere from 25 km if in line on the same side up to 61 km if opposite, and other values off the line). Neither statement alone gives any P-Q link, and even together they leave the distance undetermined, so both statements are not sufficient.

Q8
Previous year question medium

There are six villages A, B, C, D, E and F. F is 1 km to the west of D. B is 1 km to the east of E. A is 2 km to the north of E. C is 1 km to the east of A. D is 1 km to the south of A. Which three villages are in a line?

  1. A A, C, B
  2. B A, D, E
  3. C C, B, F
  4. D E, B, D
Show answer and explanation

Correct answer: B - A, D, E

Place E at the origin (0,0). B is 1 km east of E, so B is at (1,0). A is 2 km north of E, so A is at (0,2). C is 1 km east of A, so C is at (1,2). D is 1 km south of A, so D is at (0,1). F is 1 km west of D, so F is at (-1,1). Villages A (0,2), D (0,1) and E (0,0) all share x = 0, so they lie on the same vertical (north-south) line. Hence A, D, E are in a line.

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