Order & Ranking
🔒 Log in to trackOrdering and comparison chains
🔒 Log in to track'P is taller than Q but shorter than R… who is second tallest?' The constraints sort a small set — five people, five or six statements. The reliable method:
- Write each statement as an inequality fragment: 'P taller than Q' → P > Q.
- Chain all fragments into one ordering, or brute-force by hand when fragments branch.
- Read the answer from the final chain.
A complete CGL puzzle always has a unique chain. If two orderings satisfy your reading of the statements, you misread one — usually 'X is taller than Y' vs 'Y is taller than X', or a hidden 'immediately taller'. Note the special comparatives: 'immediately above' fixes adjacency; 'between A and B' fixes position, not just inequality.
Detailed notes
'Taller than, older than, scored more than': ranking from clues
These puzzles give scattered comparisons and ask for a slot: tallest, second oldest, least scorer. The method is always the same — merge the clues into one ordered line, then read it.
The chain-building routine.
- Write each clue as an arrow: 'A is taller than B' → A > B.
- Join arrows that share a head or tail into one long chain. A > B and B > D merges to A > B > D.
- Where the chain is under-determined (two people never compared), the answer is 'cannot be determined' — but check the question first: many slots are fixed even when the full order is not.
- Read the asked slot from the finished chain: tallest = left end, shortest = right end, second tallest = second from the left.
Marks and scores. 'Scored more' behaves exactly like 'taller'. Beware the reversed words: 'fewer than', 'younger than', 'less than' point the arrow the other way. Convert every clue into > arrows pointing at the better/bigger/older person before merging.
Under-determined traps. Five clues about four people can still leave a free pair: 'A > B, C > D' says nothing about A vs C. If the question asks for the tallest and only one candidate can possibly top the chain (everyone else has someone above them), the answer stands even without a total order. Rule: fix the slot, not necessarily the list.
Objects in columns and shelves. 'The red box is above the blue box' is a comparison with the arrow pointing up. Stack the chain top to bottom and read positions ('third from the top') exactly as you read 'second tallest'.
Facing pairs. Two people facing each other (like a north-facing and a south-facing person) have opposite left/right directions: the north-facing person's left is the south-facing person's right. Draw the two arrows before using any such clue.
Quick revision
- Every clue → an arrow toward the bigger/older/better; join arrows into one chain.
- Read the slot: tallest = chain head, Nth = Nth from the head.
- Reversed words (less, younger, fewer, shorter) flip the arrow — convert first.
- A slot is answerable when only one person can fill it, even if the whole order is open.
- Stacks: 'above' is the arrow; facing pairs have mirrored left/right.
Extraction habits that prevent wrong chains. Rewrite every clue as a two-symbol line before thinking: 'Sunil is younger than Vijay' → S < V. Keep the inequality signs pointing the same way throughout (bigger/older/higher on the left). Most wrong answers here come from reading a reversed sentence ('younger than', 'fewer than', 'below') in its surface direction — the rewrite step makes the reversal visible.
When options expose the shortcut. If two options share a person ('C' and 'C is second oldest'), the chain probably pins that person; test the slot directly: can anyone else occupy slot 2? If nobody can, stop building the chain and mark the answer — total order is a luxury, the slot is the requirement.
Types of questions asked
Every way this subtopic shows up in exams — how to recognise it, the formula or logic to use, and a solved example.
Type 1: Height/size chain to a slotvery common2 practice Q
'A is taller than B...' — find the tallest, shortest or an exact slot.
- Write each clue as an arrow toward the taller.
- Merge into one chain; read slot from the end.
- If a pair is never compared but only one person can top the chain, that person is the answer.
Why it works: 'taller than' is a total-order arrow; chains merge head to tail.
Example: A is taller than B; C is taller than A; D is shorter than B. Who is the shortest?
C > A > B > D → shortest = D.
Type 2: Marks rankingvery common2 practice Q
'Scored more/less than' clues; highest, lowest or Nth scorer is asked.
- Convert 'scored less' clues so all arrows point toward more marks.
- Merge; read the slot from the top end.
- Double-check nobody outside the chain could beat the head.
Why it works: scores order exactly like heights.
Example: A scored more than B; C scored less than D; B scored more than D. Who scored the least?
A > B > D > C → least = C.
Type 3: Age rankingcommon2 practice Q
'Older/younger than' clues about three to six people.
- Point every arrow at the older person.
- Merge and read: oldest at the head, youngest at the tail.
- Watch 'younger' — it reverses the sentence's surface order.
Why it works: ages are another total order.
Example: Rahul is older than Vijay; Sunil is younger than Vijay; Anil is older than Rahul. Who is the youngest?
Anil > Rahul > Vijay > Sunil → youngest = Sunil.
Type 4: Stacked objects and shelvescommon2 practice Q
Boxes/books/subjects with above-below clues; a slot from the top or bottom is asked.
- Treat 'above' as > pointing upward.
- Build the stack top to bottom on paper.
- Slots: Nth from the top = Nth of the list; from the bottom = mirror.
Why it works: vertical stacks obey the same order logic as lines.
Example: Civics is below Geography; History is below Economics but above Geography; Political Science is at the bottom. Which subject is third from the top?
Economics > History > Geography > Civics > Political Science → third = Geography.
Shortcut tricks
⚡ Longest-chain first
Find the person who appears in the most statements and build outwards from them. The chain assembles in one pass instead of three.
Example: Q. A > B; C > A; D > C but D < E. Order?
Sol. Chain the A–C–D–E spine: E > D > C > A > B — unique. Middle (third tallest) = C.
Start from the most-mentioned name; attach the rest one fragment at a time.
Where students lose marks
Answering from a partial chain before all statements are used.
Ignoring 'immediately' — adjacency changes 'second tallest' answers.
Accepting two possible orders without re-reading the statements.
Practice sets — 12 questions
Sets of 10, mixed across the question types above. Each answer comes with a step-by-step explanation.
Topic test · 12 questions
Suggested time 9 min · wrong answers go to your mistake notebook automatically.