Q travels towards East. M travels towards North. S and T travel in opposite directions. T travels towards right of Q. Which of the following is definitely true?

Correct: D, M and S travel in the same direction. The chain has only two links and it runs in one direction, so do it in order and do not draw more than a cross on the page.

Link 1: fix T. The stem says T travels towards the right of Q, and Q is travelling East. In a direction-sense question 'the right of' a moving person means that person's own right hand, not the right-hand side of the page, so you turn ninety degrees clockwise from the direction Q faces. Clockwise from East is South. T therefore travels South.

Link 2: fix S. S and T travel in opposite directions, and the opposite of South is North. S therefore travels North.

Now compare. M is given as travelling North and S has just been shown to travel North, so M and S travel in the same direction, which is option (d). Test the other three against the same two deductions and each fails on a fact you have already established: (a) claims M and S are opposite when they are identical; (b) puts S in the West when S is in the North; (c) puts T in the North when T is in the South, and in fact North is the one direction T certainly does not take, since T and S are opposites and S holds the North.

Notice how little of the stem is load-bearing. Q's direction is used once, only to define T's, and is then finished with; M's direction is never derived at all, it is simply given so that there is something to compare S against. No distances are stated anywhere, so nothing here needs coordinates or a Pythagoras step: this is a pure bearing question, and the answer is fully determined, which is what the words 'definitely true' in the stem are checking. Both independent derivations reached D with full confidence, and the reasoning above is closed: there is no reading of the stem on which S and M part company, once 'right of Q' is taken in its standard sense.

Why the others are wrong

• (a)
  M and S travel in the opposite directions: The exact inverse of the truth, and it is the option you land on if you drop a negation somewhere in the chain: most often by making S the opposite of M rather than the opposite of T. The stem never relates S to M; it relates S to T, and M's direction is supplied separately. Once T is South, S is North, and North is also where M is going, so 'opposite' is precisely wrong.
• (b)
  S travels towards West: This is the answer to the question as it would read if 'the right of Q' meant the right-hand side of a map. With North at the top of the page, the right-hand side is the East, so that reading makes T travel East, S travel West and option (b) true. It is a manufactured trap, and a good one, because the misreading is silent: nothing later in the question contradicts it. The convention that closes it is that a direction described relative to a person who is moving is taken from that person's own facing; a question that meant the compass East would have said East.
• (c)
  T travels towards North: T travels South, not North, so this reverses the very first deduction. It is produced either by turning anticlockwise instead of clockwise: treating Q's right as North rather than South, or by correctly working out that somebody goes North and then attaching that to T instead of to S. Keeping the two apart is easy if you write the chain down as Q → T → S rather than trying to hold it in your head, because T and S must always end up on opposite arms of the cross.

Every direction-sense question rests on the same compass convention: North at the top, South at the bottom, East to the right and West to the left, with North-East, South-East, South-West and North-West on the diagonals. Two operations act on that cross. A right turn is ninety degrees clockwise and a left turn is ninety degrees anticlockwise, both measured from the direction the person is currently facing, which gives the cycle North → East → South → West → North for successive right turns and the same cycle read backwards for left turns. 'Opposite' is a half turn, so the pairs are North with South, East with West, North-East with South-West and North-West with South-East. The one idea that separates a careless solver from a careful one is that these turns are relative to the traveller, not to the sheet of paper: when a question says T goes to the right of Q, it is asking you to stand where Q stands and face where Q faces. Only when a question names a compass point: 'to the east of': is the frame absolute. Where a problem also gives distances, the same cross becomes a coordinate grid and the shortest distance from start to finish is found with Pythagoras; where it gives none, as here, the whole problem is a chain of turns and the answer is a bearing.

Key facts

• A right turn is 90 degrees clockwise from the direction faced: facing North the right is East, facing East the right is South, facing South the right is West, facing West the right is North
• A left turn is 90 degrees anticlockwise: facing North the left is West, facing East the left is North, facing South the left is East, facing West the left is South
• Opposite directions are half turns: North with South, East with West, North-East with South-West, North-West with South-East
• The chain here is exactly two steps: Q = East fixes T = South (right of East), and T = South fixes S = North (opposite of South); M = North is given, so M and S coincide
• Directions given relative to a moving person are taken from that person's own facing; only a named compass point such as 'to the east of' is absolute: reading 'right of Q' as the right-hand side of the map is what generates option (b)
• The question states no distances at all, so no coordinate or Pythagoras step is needed; the answer is a bearing, not a displacement

Common traps

• Taking 'the right of Q' as the right-hand side of the map, which turns South into East and makes the wrong option look right
• Turning anticlockwise for a right turn, which reverses South and North throughout the chain
• Relating S to M instead of to T: the stem links S only to T, and M is given independently

• practice, not a real PYQ

  A person is walking towards the West. He turns to his right and then turns to his right again. In which direction is he walking now?

  • (a)North
  • (b)East
  • (c)South
  • (d)West
  Answer(b) East: a right turn from West faces him North, and a second right turn faces him East; two right turns always reverse the original direction.
• practice, not a real PYQ

  X travels towards South. Y travels towards the left of X. Z travels in the direction opposite to Y. Which of the following is true?

  • (a)Y travels towards West
  • (b)Z travels towards West
  • (c)Z travels towards North
  • (d)Y travels towards North
  Answer(b) Z travels towards West: the left of South is East, so Y travels East, and the direction opposite to East is West.