BPSC 69th CCE Prelims General Studies · Question 142 of 144

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.

• (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.

Solve it by writing a chain, not by holding four travellers in mind at once. Ask which statement can be resolved with no prior work: 'T travels towards right of Q' can, because Q's direction is given outright. That yields T = South. Then ask which statement now becomes resolvable: 'S and T travel in opposite directions' does, and yields S = North. At that point every traveller has a direction and the options can be read off. The discriminating fact for the whole item is the single conversion right-of-East = South; get that one step right and all four options fall into place, get it wrong in the clockwise sense and you produce option (c), get it wrong in the frame-of-reference sense and you produce option (b). It is also worth registering what 'definitely true' is for. In many items of this family some travellers are left partly free — 'S travels either North or East' — and then an option can be possibly true without being definitely true. Here nothing is free: two given directions plus two relations pin all four travellers, so 'definitely' costs you nothing extra. But the habit of asking whether a conclusion is forced or merely available is the habit that saves marks on the harder version of this question.

• 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

• 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

BPSC keeps a block of reasoning inside the General Studies paper and returns to direction sense almost every year, usually in one of two shapes: a single traveller making a sequence of turns, as in the 71st CCE paper's item on Ram going North and then turning right, right and left; or, as here, several named travellers whose directions are defined against one another and a 'which is definitely true' stem. UPSC set the same material in General Studies Paper I through the 1990s and up to 2000, generally with distances attached so that the answer was a length rather than a bearing; since the CSAT was introduced in 2011 this material has sat in the qualifying Paper II.

• 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.