Ranking

1. What ranking questions measure

Ranking is the placement of persons or objects according to an explicit rule: position in a queue, height, age, marks, speed or another comparable attribute. CSAT questions may ask for a total, an individual’s position, the number between two persons, or whether the information is sufficient. Unlike a full seating-arrangement puzzle, a basic ranking problem often concerns a single ordered line rather than several simultaneous spatial relationships.

First identify the direction and meaning of the order. Rank 1 normally indicates the highest performance in an examination, but first from the left only indicates a location. In a height problem, decide whether the sequence runs from tallest to shortest or the reverse. Write this convention beside the diagram. Changing conventions halfway through a solution is a frequent source of avoidable errors.

Ranking draws on logical reasoning and analytical ability within the CSAT syllabus. Because the paper is qualifying, the practical objective is reliable accuracy under time pressure. Simple ranking problems can be economical to solve, but familiarity should not lead to automatic formula use. Every formula depends on assumptions about the same group, consistent endpoints, distinct positions and whether the arrangement changes.

• Linear position: seventh from the left or ninth from the back.
• Comparative order: A is older than B but younger than C.
• Transformation: two persons exchange places or someone joins the queue.

2. Opposite-end ranks and counting between persons

Let N be the total number of persons, L a person’s position from the left and R the same person’s position from the right. Then N = L + R − 1. The subtraction removes the double counting of that person. For example, someone who is ninth from the left and fourteenth from the right belongs to a row of 22 persons. Rearranging gives R = N − L + 1.

The safest approach for two persons is to convert both positions to the same endpoint. In a row of 30, A is eighth from the left and B is eleventh from the right. B is therefore twentieth from the left. The number between them is |20 − 8| − 1 = 11. The absolute difference handles either relative order; subtracting one excludes the endpoint persons.

Opposite-end descriptions do not by themselves tell you which person stands farther left. If A is Lth from the left and B is Rth from the right, B’s left position is N − R + 1. Thus, the number between them is |N + 1 − L − R| − 1, provided A and B occupy distinct positions. Deriving their positions is generally safer than memorising this expression.

A useful distinction is that rank includes the person, whereas the number ahead does not. If six persons stand ahead of A, A is seventh from that end. Similarly, if four stand behind A, A is fifth from the opposite end.

3. Exchanges, arrivals and departures

When two persons exchange places, each takes the other’s original position. The total remains unchanged unless the question separately mentions an arrival or departure. Record the initial positions first, then the final positions. Do not transfer a person’s original numerical rank to the new location merely because the person’s name remains the same.

Suppose A is seventh from the left and B is tenth from the right. After they exchange places, A becomes nineteenth from the left. B’s original position was therefore nineteenth from the left. Since B was also tenth from the right, the row contained 19 + 10 − 1 = 28 persons. B now occupies A’s original position, so B becomes twenty-second from the right.

For arrivals and departures, count changes on the relevant side. If A is twelfth from the front and three persons ahead leave, A becomes ninth. If two persons then join ahead, A becomes eleventh. Persons joining behind A increase the total but do not change A’s rank from the front. They do, however, change the rank from the back.

When two persons move independently, update both positions before counting the persons between them. A statement such as ‘moves three places forward’ normally reduces the front rank by three. Nevertheless, inspect the wording carefully: moving ahead of three persons and moving to the third position are different operations.

4. Comparative ranking and incomplete information

Comparative questions are best represented by a chain. Define A > B to mean that A is taller than B. If A > B and B > C, then A > C by transitivity. However, if A > B and A > C, the relative order of B and C remains unknown. Both B > C and C > B may satisfy the statements.

Distinguish direct comparison from adjacency. ‘B is shorter than A’ allows other persons between them. ‘B is immediately below A in the height order’ does not. Similarly, ‘only two persons are taller than A’ fixes A as third tallest if heights are distinct. ‘At least two persons are taller than A’ provides only a bound: A is third or lower.

In data-sufficiency questions, a plausible order is not enough. The target answer must remain the same across every arrangement satisfying the statements. To disprove uniqueness, construct two valid arrangements producing different answers. A complete order need not be known: the tallest person can be uniquely identified even when several middle positions remain unresolved.

Ties require special care. In competition ranking, results may be numbered 1, 2, 2, 4; in dense ranking they may be 1, 2, 2, 3. Neither pattern is an ordinary sequence of unique queue positions. Unless the question specifies the ranking convention or resolves ties, do not infer group size from performance ranks using the opposite-end formula.

5. An efficient examination method

Read the final question before doing detailed work: identify whether the target is a rank, total, gap or sufficiency judgement. Next mark the endpoints and write only the relevant information. For numerical row questions, converting everything to positions from the left or front usually makes the calculation transparent. For comparative questions, use a chain and keep unresolved branches visibly separate.

Check three conditions before selecting an option. Every position must lie between 1 and N; distinct persons cannot occupy the same position unless a tie is explicitly permitted; and the proposed answer must satisfy the original statements. If conversion puts two supposedly distinct persons in the same place, revisit the interpretation rather than reporting a negative number between them.

Do not assume that a missing total can always be recovered. If A is fifth from the left and B is seventh from the right, the group size remains unknown without another link. Even a stated gap can allow two totals when the relative order is unspecified. Test both possible orders, reject impossible positions and retain all feasible solutions.

• Draw a short numbered line rather than a decorative diagram.
• Treat ‘immediately’, ‘only’, ‘at least’ and ‘at most’ as decisive constraints.
• Use answer options to check a result, not to replace missing evidence.

Previous year questions

No UPSC question has been asked directly on this micro-topic yet. Use the practice questions below.

Practice questions