Logical Reasoning

Direction Tests

Suppose someone asks you about an address. How will you tell that person? You will use the words like straight, right, left, turn, north, east, west, south, back etc. What are all these? These are some of the direction senses and terms used to locate an object or a location. In logical reasoning, we are given some problems based on the direction and the distance between them. The real question arises as to how to find the correct solution for these direction reasoning problems? Let us get started to learn more of the direction reasoning.

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Direction Reasoning

We all know that there are four main directions – East, West, North and South. Also, we are well aware of the four cardinal directions – South East, South West, North East, and North West. We are going to use all these eight directions to solve our direction reasoning problem.

We assume that in our front the direction is North, behind us, is South. To our left is West and to the right is East. Also, we know that the sun rises in the East and sets in the West. When a person faces the sun, then in his / her front is East and behind him/her is West. To the left will be North and in his/her right is South.

direction reasoning

Assumptions Related to Direction Reasoning

  • The main direction change undergoes a 90° change in direction. For instance, there is a 90° change from East to North / South.
  • The change is only 45° change in cardinal direction. For example, there is a 45° change in North to North – East or North to North – West.
  • The direction of the right turn is always clockwise.
  • The direction of the left turn is always anti-clockwise.
  • The problem on the distance covered or the minimal distance between two points in direction reasoning is solved by using the concept of Pythagoras theorem.
  • All these distances are along straight lines and between specified points.

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Pythagoras Theorem

The concept of Pythagoras theorem is highly applicable in direction reasoning problem. In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

direction reasoning

i.e., c2 = a2 + b2.

Left – Right Movements

Let us understand the various clock-wise and anti-clockwise turns in direction reasoning.

  • A person facing towards North, on taking left turn will face towards West.
  • On taking a right turn the person will face towards East if he was facing towards North earlier.
  • A person facing towards South, on taking left turn will face towards East.
  • On taking a right turn, the person will face West if he was facing towards South earlier.
  • A person facing towards East, on taking left turn will face towards North.
  • On taking a right turn, the person will face South if he was facing towards East earlier.
  • A person facing towards West, on taking left turn will face towards South.
  • On taking a right turn, the person will face North if he was facing towards West earlier.
  • A person facing towards North – West, on taking left turn will face towards South – West.
  • On taking a right turn, the person will face North – East if he was facing towards North – West earlier.
  • A person facing towards North – East, on taking left turn will face towards North – West.
  • On taking a right turn, the person will face South – East if he was facing towards North – East earlier.
  • A person facing towards South – East, on taking left turn will face towards North – East.
  • On taking a right turn, the person will face South – West if he was facing towards South – East earlier.
  • A person facing towards South – West, on taking left turn will face towards South – East.
  • On taking a right turn, the person will face North – West if he was facing towards South – West earlier.

The above result can be summarized as

Original Direction Direction after taking a turn
Right Turn Left Turn
North East West
East South North
West North South
South West East
North-East South-East North-West
North-West North-East South-West
South-East South-West North-East
South-West North-West South-East

Important Facts Related to Direction Reasoning

  • At the time of sunrise, if a person is facing East, his / her shadow will be towards West direction.
  • If a person is facing towards North at the time of sunrise, his / her shadow will be towards West (i.e., his / her left).
  • At the time of sunrise, if a person is facing South, his / her shadow will be towards his / her right (i.e., towards West).
  • If a person is facing towards North at the time of Sunset, his / her shadow will be towards his / her right.
  • At 12:00 noon, the sun rays are vertically downward, so no shadow will be formed at that time.

Solved Example for You

Problem: A person starts walking towards North for about 4 km and reaches a point P. From point P, he takes a left turn and walks for 2 km to reach a point Q. From Q, he again takes a left turn and walks for 6 km and reaches a point R. How far and in which direction is the point R from the starting point?

Solution: Let us first draw a rough sketch of the above reasoning direction problem.

 

direction reasoning

Joining the starting point O to the endpoint R and drawing a perpendicular on QR at Q’.

In a right angled triangle OQ’R, We have OQ’ = PQ = 2 km, and Q’R = QR – QQ’ = 6 – 4 = 2 km.

So, OR2 = 22 + 22 = 4 + 4 = 8.

or, OR = √8 = 2√2 km.

R is in the South-West direction from the starting point O.

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