BPSC 71st CCE Prelims General Studies · Question 6 of 150

Correct — D, 16th. Take the two facts in the order the stem supplies them. Joginder stands 17th from the last in a class of 39, so counting from the beginning he is 39 - 17 + 1 = 23rd. The +1 is not decoration: Joginder is himself counted once in the 17 and once again in the 39, so plain subtraction discards him from one of the two runs and lands you one place short. Nitin is 7 ranks ahead of Joginder, and in a rank order 'ahead' means nearer the top, so you subtract: 23 - 7 = 16th from the beginning. A second route never converts Joginder at all. Nitin sits 7 places further from the last end than Joginder does, so Nitin is 17 + 7 = 24th from the last, and 39 - 24 + 1 = 16th from the beginning. That is the route the Commission itself set out on 31 October 2025 when it disposed of the objections filed against this item, and the fact that two independent routes land on the same number is the real safety net — an off-by-one slip almost never survives being made from both ends at once. Then close with the gap test: Joginder is 23rd, Nitin is 16th, and 23 - 16 = 7, exactly the separation the stem states. Notice how tightly the paper-setter has packed the choices — 15th, 16th, 17th and 18th, every one of them within two places of the truth. Nothing in this item rewards understanding the situation; the mark turns entirely on whether the 1 was added to the right number at the right moment, which is why writing the identity down before touching any arithmetic is worth more than speed.

• (a)17th — This is Joginder's own figure, 17, lifted straight off the page and re-labelled as Nitin's rank from the opposite end — the commonest failure on ranking items, because 17 is the only number in the stem that looks like a rank. Test it: if Nitin were 17th from the beginning, the gap to Joginder's 23rd would be 6 ranks, not the 7 the question specifies. It is also what you get by subtracting 7 from Nitin's from-the-last position, 24 - 7 = 17, which mixes the two reference ends inside a single calculation.
• (b)15th — The classic dropped +1, and two different careless routes deliver it. Either you compute Nitin as 24th from the last and then write 39 - 24 = 15 without restoring the 1, or you convert Joginder as 39 - 17 = 22 and take 22 - 7 = 15. Both count Nitin, or Joginder, out of one of the two runs. The gap test exposes it at once: 23 - 15 = 8 ranks, one more than the 7 stated, and 15 + 24 = 39 rather than the 40 that any two counts of the same student in a class of 39 must add to.
• (c)18th — This is 17 + 1 — the +1 correctly remembered but attached to the wrong number, applied to Joginder's printed rank instead of to the difference 39 - 24. It is also the answer of a candidate who converts Joginder properly to 23rd and then subtracts 5 instead of 7. Either way the gap test kills it: 23 - 18 = 5 ranks between the two, well short of the stated 7, and 18 + 24 = 42, which no pair of end-counts in a 39-strong class can produce.

Every ranking and row-position question in an Indian state-service paper rests on one identity: for n people standing in a single ordered line, a person's position from the front plus that same person's position from the back equals n + 1. The extra 1 exists because the person is counted once in each of the two runs, so the two counts overlap by exactly one place — the same inclusive-counting effect that makes a fence of 10 posts have 9 gaps. Rearranged, position from the front = n - position from the back + 1, which converts any count given from one end into a count from the other. Three standard variants are built on it, and BPSC has used all three across cycles. First, one person and one end-count, asking for the other end-count: apply the identity directly. Second, one person and both end-counts, asking for the class strength: n = a + b - 1, subtracting the double count instead of adding it. Third, the version on this paper — two people, a stated separation, and a single end-count — where you convert once, then move along the line by the stated gap. The direction of that move is fixed by language, not by arithmetic: 'ahead of', 'above', 'better than' and 'senior to' all mean a smaller rank number, while 'behind', 'below' and 'after' mean a larger one. Everything else in the topic is bookkeeping.

Reason in three fixed steps and this class of question stops being risky. Step one, label which end every number is anchored to. Here 17 is anchored to the last and the answer is wanted from the beginning, so exactly one conversion is needed — do it once, in writing, and never carry both frames of reference in your head at the same time. Step two, fix the direction of the move: 7 ranks ahead is 7 fewer, so 23 - 7 = 16, not 23 + 7. Step three, verify by the gap, because a ranking answer is uniquely testable: subtract your answer from the other person's rank and the difference must reproduce the stated separation. That single test discriminates completely here — 16th gives 7, 17th gives 6, 18th gives 5 and 15th gives 8, so only one option can survive. The reason the trap bites is arithmetic pressure rather than confusion: at 150 questions in 120 minutes the candidate has about 48 seconds per item and every wrong tick costs one-third of a mark, so the instinct is to do 39 - 17 mentally, get 22, and move on. That single dropped 1 propagates straight through to option (b). The discriminating fact worth memorising is therefore not a method but a number — in a class of 39, any student's two end-counts must add to 40. Check that sum before you commit and the whole family of off-by-one distractors becomes unpickable.

• For n people in one ordered line, position from the front + position from the back = n + 1, because the person is counted once in each of the two runs; with n = 39 every student's pair of end-counts must add to exactly 40, and that single sum is enough to audit any answer on this item.
• Joginder is 17th from the last, so from the beginning he is 39 - 17 + 1 = 23rd, and the check 17 + 23 = 40 confirms the conversion; the bare subtraction 39 - 17 = 22 is the one-place error that seeds option (b).
• Nitin is 7 ranks ahead, so 23 - 7 = 16th from the beginning; equivalently 17 + 7 = 24th from the last and then 39 - 24 + 1 = 16th, with 24 + 16 = 40 again. The Commission's own disposal of the objections to this question on 31 October 2025 takes that second route.
• The gap test discriminates all four options at a glance: 16th leaves a separation of 23 - 16 = 7, while 17th leaves 6, 18th leaves 5 and 15th leaves 8, and only 7 matches the stem — every distractor is an arithmetic slip of one or two places, not a misreading.
• Companion identity for the other standard variant: a person a-th from the front and b-th from the back stands in a line of a + b - 1 people, so 15th and 20th means 34 people rather than 35 — note that the correction is subtracted here and added in the conversion identity.
• Exam arithmetic that drives the error rate: the 71st CCE prelims paper carries 150 questions in 120 minutes, about 48 seconds each, with +1 for a correct answer and, under the booklet's own instruction 9, -1/3 for a wrong one, so a guessed off-by-one costs a third of a mark rather than nothing.

• Dropping the +1 when converting a rank from one end to the other, which shifts the answer by exactly one place and produces option (b)
• Reading 'ahead' as further from the beginning and adding where you should subtract — 'ahead', 'above' and 'senior to' all mean a smaller rank number
• Reading '7 ranks ahead' as '7 people standing in between', which would put the gap at 8 places instead of 7
• Re-using a number printed in the stem as if it were the answer — 17 is Joginder's count from the last end and belongs to no part of Nitin's answer

BPSC puts a compact reasoning block at the very top of the General Studies paper — questions 1 to 10 of the 71st CCE prelims covered odd-one-out, coding, blood relations, ranking, ages and a number grid — and asks each as a bare, self-contained one-liner worth one mark against a 48-second average and a one-third-mark penalty. UPSC has not set a naked ranking sum in the General Studies paper since 2011, when mental ability moved to Prelims Paper-II, which has been merely qualifying at 33 per cent since 2015 and contributes nothing to the merit list. Before that split the same skill did appear in the GS paper, but dressed as a multi-clue ordering puzzle — seven swimmers finishing a race, seven men in a queue — in which the counting identity is only the final step after the order has been deduced. Practise both shapes: BPSC tests the identity itself, UPSC tested the deduction that hands you the identity.

• practice — not a real PYQ

  In a row of 40 students, Ravi is 12th from the left end. What is his position from the right end?

  • (a)28th
  • (b)29th
  • (c)27th
  • (d)30th

  Answer(b) 29th — the two end-counts must add to 40 + 1 = 41, so 41 - 12 = 29. Answering 28th is the same dropped +1 that produces option (b) in the BPSC question.

• practice — not a real PYQ

  In a queue, Sunita is 15th from the front and 20th from the back. How many people are standing in the queue?

  • (a)33
  • (b)34
  • (c)35
  • (d)36

  Answer(b) 34 — here the identity runs the other way: n = a + b - 1 = 15 + 20 - 1 = 34, because Sunita has been counted once in each run. Answering 35 adds the counts without removing the double count.