BPSC 71st CCE Prelims General Studies · Question 4 of 150

Correct — A, EAST. Track the direction Ram faces, one instruction at a time, remembering that on the compass rose the cardinal points run clockwise North (0 degrees), East (90), South (180), West (270). Ram starts facing NORTH. A right turn is a quarter turn clockwise, so North becomes EAST. He goes right again, a second quarter turn clockwise, so East becomes SOUTH. He then goes to the left, a quarter turn anticlockwise, and from South that brings him back to EAST. Now do it the faster way as a check, because the step-by-step method is where candidates lose their place. Score a right turn as plus 90 degrees and a left turn as minus 90, and simply add: plus 90, plus 90, minus 90 gives plus 90 in total. Ram began at 0 degrees, which is North, so he ends at 90 degrees, which is East. The two methods agree, and the algebraic one has the advantage that it cannot be derailed by miscounting the sequence. One more thing is worth noticing about the wording, because it settles what is being asked: the stem supplies no distances at all, only turns. Nothing about Ram's position relative to his starting point can therefore be calculated, so 'in which direction Ram is now' can only mean the direction he is now heading. (If you did assume the four legs were of equal length, the net displacement would work out at two units due east of his starting point, so both readings land on East here — but only the heading reading is answerable from what the paper actually gives you.)

• (b)SOUTH — This is exactly where Ram faces after the second right turn — North to East to South — and it is the answer of a candidate who stops one instruction early. The stem's phrasing invites it: 'turns right, then goes right again and then goes to left' packs three separate turns into one comma-spliced clause, and the last of the three is the one most easily read as part of the sentence's trailing-off rather than as a fresh instruction. Count the turns before you compute anything: there are three.
• (c)NORTH — The starting direction, and it is reached by a specific misreading rather than by carelessness: treating 'then goes right again' as continuing along the same eastward road rather than as a second turn. On that reading Ram faces East after one right turn, stays East, and then the final left takes him from East to North. It is also the answer of anyone who assumes that two rights and a left must roughly cancel out. They do not — the net is a single quarter turn clockwise.
• (d)WEST — The mirror-image answer, produced by interchanging left and right. Score a right turn as anticlockwise and a left as clockwise and you get North to West to South to West. The same option also catches the candidate who gets only the last turn the wrong way round, since from South a clockwise turn gives West. Both versions of the error come from picturing the compass rose as something you stand in front of and look at, instead of something you are standing on and walking across.

Direction-sense questions are rotation problems wearing a walking costume. The apparatus is the compass rose: four cardinal points 90 degrees apart, running clockwise North at 0 degrees, East at 90, South at 180 and West at 270, with the four intercardinal points inserted between them at North-east 45, South-east 135, South-west 225 and North-west 315. A right turn is plus 90 degrees, a left turn is minus 90, an about-turn is 180, and every heading is taken modulo 360, so 405 degrees is simply 45. Two rules cover the whole family. First, turns are always measured from the walker's own current heading and never from the printed page — a person facing South has East on his left and West on his right, the exact reverse of how the page looks. Second, heading and displacement are different questions and need different data: the heading after any number of turns needs only the turns, while the displacement from the starting point needs the distances as well, obtained by adding the north-south legs and the east-west legs separately and, if the straight-line distance is wanted, applying Pythagoras to the two totals. A stem that gives no distances can only be asking about heading, and a stem that asks 'how far and in which direction from the start' must be giving them.

Two methods, and the discipline is to run one and check with the other. The step method: facing North, right takes him to East, right again to South, left back to East. The algebraic method: right is plus 90 and left is minus 90, so the turns total plus 90, and North at 0 degrees plus 90 degrees is East at 90 degrees. The algebraic method is worth building as a habit, because it survives four or five turns without your having to hold a picture in your head. The single thing that discriminates in this item is how you read 'then goes right again'. Each of the four options corresponds to one precise reading of the stem, which is unusually clean design for a BPSC reasoning item and is why it is worth studying rather than merely answering. EAST is all three turns applied correctly. SOUTH is the final left dropped. NORTH is 'right again' read as continuing east rather than as a second turn. WEST is left and right interchanged. Note that none of the four wrong answers is random — so guessing pays nothing here, and under instruction 9 of the booklet a wrong guess costs a third of a mark. One practical habit prevents the mirror error that produces West more reliably than any amount of visualising: draw a small compass in the margin with North up, put an arrow on it for Ram's current heading, and physically rotate the page or your pen a quarter turn for each instruction. The mistake almost every candidate makes at least once is judging left and right from the page, where left always looks like West, instead of from the walker, for whom left is whatever lies a quarter turn anticlockwise from wherever he happens to be facing.

• On the compass rose the cardinal points sit 90 degrees apart and run clockwise: North 0 degrees, East 90, South 180, West 270. The eight-point rose adds North-east 45, South-east 135, South-west 225 and North-west 315.
• A right turn is plus 90 degrees, a left turn is minus 90 and an about-turn is 180; the final heading is the starting heading plus the sum of all the signed turns, reduced modulo 360.
• For this question the sum is plus 90 (right), plus 90 (right), minus 90 (left) = plus 90. Starting from North at 0 degrees, the final heading is 90 degrees, which is East.
• Heading and displacement are separate quantities. Heading needs only the turns; displacement needs the distances too, added separately along the north-south and east-west axes with Pythagoras giving the straight-line distance. This stem supplies no distances, so only the heading can be asked.
• Turns are always relative to the walker's own facing, never to the page. Reading them off the page — as though looking at the compass rose from the far side — interchanges left and right and converts every answer into its mirror image, which is precisely how option (d) is reached.

• Reading left and right off the page instead of from the walker, which reverses the moment he is facing South and produces the mirror answer
• Stopping after the second turn and answering South, because the three turns are packed into a single clause
• Assuming that two rights and a left cancel out and answering with the starting direction

BPSC keeps its direction item purely rotational — a short sequence of turns, no distances, no diagram, and a one-word cardinal answer — and puts one in the opening reasoning block in most cycles. UPSC set the harder version in GS Paper-I until 2010, where distances always came with the turns and the question asked for the straight-line displacement, as in its 2000 item on a person walking 3 km east and then turning left twice, or else reframed the problem by rotating the map itself, as in 2010 when south-east was made to become north. Since 2011 the type has lived in CSAT Paper-II. A candidate who can do the UPSC displacement version answers the BPSC version in five seconds; the reverse does not hold.

• practice — not a real PYQ

  A man walks 5 km towards the south, then turns left and walks 3 km, then turns left again and walks 5 km. In which direction is he now from his starting point?

  • (a)East
  • (b)West
  • (c)North
  • (d)South

  Answer(a) East — the 5 km southward leg and the 5 km northward leg cancel, leaving him 3 km due east of where he began. Note that his final heading is north while his displacement is east, which is why the two questions must never be confused.

• practice — not a real PYQ

  A person facing West turns 45 degrees clockwise, then turns 180 degrees anticlockwise, and finally turns 270 degrees clockwise. Which direction is the person facing now?

  • (a)North-east
  • (b)South-east
  • (c)North-west
  • (d)South-west

  Answer(a) North-east — West is 270 degrees; 270 plus 45 is 315 (north-west), minus 180 is 135 (south-east), plus 270 is 405, which reduced modulo 360 is 45 degrees, that is north-east.