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Order & Ranking

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medium importance~1-2 Q in Tier 111 formulas⚡ 6 shortcuts4 subtopics
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Ordering and comparison chains

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⏱ 5 min read🧩 6 question types🎯 12 practice Q
The idea in one minute

These questions give scattered comparisons such as 'A is taller than B'. Write each clue as a short arrow. Join the arrows into one chain, then read the seat that is asked. Words like 'shorter', 'younger' and 'below' point the arrow the other way, so turn them around first.

01

Write each clue as an arrow

Use one arrow for one clue. Point it towards the taller, older or higher person.

  • "A is taller than B" becomes A > B.
  • "C is shorter than B" becomes B > C.
  • "D scored less than C" becomes C > D.

Rule: Always put the bigger, older or higher person on the left. Turn 'shorter', 'younger', 'less' and 'below' around before you write.

02

Join the arrows into a chain

Clues that share a person join together. A > B and B > D make A > B > D.

Example: "A is taller than B. C is taller than D and shorter than B. E is shorter than D." Write A > B, B > C > D and D > E. The chain is A > B > C > D > E. The second tallest is B.

03

Read the seat

Read the chain from the left end.

  • Tallest: the first person.
  • Shortest: the last person.
  • Second tallest: the second person from the left.

The middle seat of five people is the third one.

04

When the full order is not known

Some clues leave two people unranked. For example, A > B and C > D say nothing about A against C. So the whole order is open.

But the answer may still be fixed. If only one person can stand first, that person is the tallest, even when other seats stay open.

Tip: Fix the seat that is asked. You do not always need the full order.

05

Marks, ages and objects

Marks, ages, heights and weights all work alike. Use the same arrows for all of them.

Objects in a stack work alike too. "The red box is above the blue box" is an arrow pointing up. Write the stack from the top down and read it like a chain. "Third from the top" is the third person in the chain.

06

Words that fix a place

Some words fix a place more tightly than a simple "taller than".

  • "Immediately above B" means directly next to B, with no one between.
  • "Between B and D" means somewhere in the middle. It does not say the exact seat.

Use "immediately" clues first. They join two people into one block.

Watch: Read the clue again if you find two possible orders. A full puzzle has one order only.

07

A slow example

Read the clues once, then write the arrows. "Ann is older than Ben. Cara is younger than Ben. Dev is older than Ann." Arrows: Ann > Ben, Ben > Cara, Dev > Ann. Chain: Dev > Ann > Ben > Cara. The youngest is Cara. The second oldest is Ann.

Example: Ask a different question of the same chain. Who is older than Ben but younger than Dev? Only Ann fits. Reading the chain answers every version of the question.

08

Facing pairs

Two people who face each other have opposite left and right. The left hand of one is the right hand of the other. Draw the two arrows first.

09

Question types you will see

Each type: how to recognise it, the method step by step, and one question to try.

Type 1very common2 practice Q

Height or size chain

How to spot it:

Clues use 'taller than', 'bigger than' or 'heavier than'. The tallest, shortest or one seat is asked.

Method

  1. Write each clue as an arrow with the taller person first.

  2. Join clues that share a person.

  3. Read the chain from the left.

Why it works:

Clues that share a person always join into a single line.

Try this

A is taller than B. C is taller than D and shorter than B. E is shorter than D. Who is the second tallest?

Show solution

  1. Arrows: A > B, B > C > D, D > E.

  2. Chain: A > B > C > D > E.

  3. The second person from the left is B.

Answer

B

Type 2very common2 practice Q

Marks and scores

How to spot it:

Clues use 'scored more than' or 'scored less than'. The highest, lowest or an exact seat is asked.

Method

  1. Write each clue as an arrow towards the higher score.

  2. Turn 'less than' around.

  3. Join the arrows and read the chain.

Why it works:

'Scored more' works exactly like 'taller'.

Try this

Kiran scored more than Lata but less than Manu. Neeta scored less than Lata. Om scored more than Manu. Who scored the second highest?

Show solution

  1. Arrows: Manu > Kiran > Lata, Lata > Neeta, Om > Manu.

  2. Chain: Om > Manu > Kiran > Lata > Neeta.

  3. The second person from the left is Manu.

Answer

Manu

Type 3very common2 practice Q

Ages with 'younger' and 'older'

How to spot it:

Clues use 'older than' and 'younger than' about three to six people.

Method

  1. Put the older person on the left in every arrow.

  2. Turn each 'younger than' clue around.

  3. Join and count from the left.

Why it works:

Turning every clue to the same direction stops sign slips.

Try this

Rita is younger than Sita. Tina is older than Sita. Uma is younger than Rita. Vani is older than Tina. Who is the third oldest?

Show solution

  1. Arrows: Sita > Rita, Tina > Sita, Rita > Uma, Vani > Tina.

  2. Chain: Vani > Tina > Sita > Rita > Uma.

  3. The third person from the left is Sita.

Answer

Sita

Type 4common2 practice Q

Stacked books and boxes

How to spot it:

Books, boxes or subjects are described as above or below. A seat from the top or the bottom is asked.

Method

  1. Turn each 'below' clue into an 'above' clue.

  2. Write the stack from the top down as a chain.

  3. Count from the asked end.

Why it works:

'Above' is just the arrow pointing up.

Try this

Five books are in a stack. Maths is above Science. History is below Science. Art is above Maths but below English. Which book is in the middle?

Show solution

  1. Arrows: Maths above Science, Science above History, English above Art above Maths.

  2. Stack from the top: English, Art, Maths, Science, History.

  3. The middle (third) book is Maths.

Answer

Maths

Type 5common

The seat is fixed but the order is not

How to spot it:

Some pairs are never compared, but the question asks only for the tallest, shortest or one seat.

Method

  1. Draw the arrows you have.

  2. Check who has nobody above them. If only one person, that is the first seat.

  3. Ignore the pairs that are never compared.

Why it works:

A seat can be fixed even when the whole order is open.

Try this

P is taller than Q. Q is taller than R. S is taller than P. T is shorter than S. Who is the tallest?

Show solution

  1. Arrows: S > P > Q > R and S > T.

  2. T is below S, but T is not compared with P, Q or R.

  3. Nobody is above S.

Answer

S

Type 6occasional

Clues with 'immediately' and 'between'

How to spot it:

Clues say 'immediately above' or 'between'. An exact rank is asked.

Method

  1. Join 'immediately' pairs into one block first.

  2. Place the other people above or below the block.

  3. Fit each 'between' clue into the gap.

Why it works:

An 'immediately' pair is a fixed block, and the other clues only place things around it.

Try this

Five students are ranked by marks. A is ranked immediately above B. C is ranked above A. D is ranked below B. E is ranked between B and D. Who is ranked 4th?

Show solution

  1. A and B form a block: A, B. C is above the block.

  2. D is below B, and E is between B and D.

  3. Order: C, A, B, E, D. Rank 4 is E.

Answer

E

10

Shortcuts that save time

⚡ Write two symbols for each clue

Turn each sentence into two letters with a sign, such as S < V. Keep the sign pointing the same way all through. The reversed words then become easy to see.

Example

Sunil is younger than Vijay. Vijay is younger than Wasim. Who is the oldest?

Show solution

  1. Arrows: Vijay > Sunil, Wasim > Vijay.

  2. Chain: Wasim > Vijay > Sunil.

Answer

Wasim

⚡ Start from the person named most often

The person who appears in the most clues is the best starting point. Build the chain outwards from that person and it forms in one pass.

Example

A is taller than B. B is taller than D. C is taller than A. Who is the tallest?

Show solution

  1. B appears twice. Chain B > D.

  2. A is above B: A > B > D.

  3. C is above A: C > A > B > D.

Answer

C

11

Mistakes to avoid

Where most students lose marks on this subtopic.

Mistake 01

Answering from part of the chain before using every clue.

Use all the clues, then read the chain.

Mistake 02

Reading 'younger than' or 'less than' in the surface direction.

Turn every clue so the bigger, older or higher person is on the left.

Mistake 03

Ignoring the word 'immediately'.

It means directly next to. It can change who is second or third.

Mistake 04

Accepting two possible orders.

A full puzzle has exactly one order. Read the clues again.

Mistake 05

Building the whole order when the seat is already fixed.

Check whether only one person can fill the seat asked.

12

Quick revision

Read this the night before the exam.

  • Every clue is an arrow towards the bigger, older or higher person.

  • Join clues that share a person into one chain.

  • Turn 'shorter', 'younger', 'less' and 'below' around first.

  • Read the chain: tallest is the first, shortest is the last.

  • A seat can be fixed even if the whole order is open.

  • 'Immediately' means next to. 'Between' means somewhere inside.

13

Practice: 12 questions

Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.

Topic test · 12 questions

Suggested time 9 min · wrong answers go to your mistake notebook automatically.

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