Logical Problems

What you need to understand

Each clue is a link: one person stands above another in the trait being described.

A chain of clues that reaches from one person to the next in an unbroken line fixes the order of everyone in it.

If two people are never linked, directly or through a chain, nothing can be concluded about their relative order.

A superlative question, such as who is tallest, always refers to one end of the chain.

The direction of the chain matters: reading it backwards gives the opposite answer.

How to work through these questions

List the people and draw an arrow from the greater to the lesser for each clue.

Join the arrows into chains wherever two clues share a person.

Identify the chain that contains the people named in the question.

Read that chain from one end to the other and take the position you need.

If the question asks about two people who are not in the same chain, the answer is that the relationship is undetermined.

Mistakes that cost marks

Reading the chain in the wrong direction when the question asks for a superlative.
Assuming two people are ordered when no chain connects them.
Answering with the person standing next to the one asked about rather than the end of the chain.
Losing track of a person who appears in more than one clue.
Treating a clue that compares two isolated people as though it ordered the whole group.

Worked example

Amit is taller than Bela. Bela is taller than Chetan. Chetan is taller than Divya. Who is the shortest?

Draw an arrow from the taller to the shorter for each clue.
The three clues form one chain: Amit, then Bela, then Chetan, then Divya.
The question asks for the shortest, which is the end of the chain where everyone else is above.
Reading the chain from top to bottom, Divya is last, so Divya is the shortest.

Answer: Divya

Practice questions with answers

A few Logical Problems questions with the full solution shown, so you can see how the method is applied before you attempt the timed set.

Question 1

Study the clues and answer the question. Hari scored more than Esha Esha scored more than Isha Divya scored more than Hari Lata scored more than Divya Who is the highest score?

A Lata
B Divya
C Hari
D Esha

Answer: Option A — with explanation

The clues form one chain: Lata scored more than Divya scored more than Hari scored more than Esha scored more than Isha. Reading it end to end, Lata is first and Isha is last, so Lata is the highest score. Common mistakes - picked the middle of the chain: Hari - stopped one place short in the chain: Divya - read the chain from the wrong end: Esha

Question 2

Study the clues and answer the question. Chetan faster than Gita Gita faster than Farhan Farhan faster than Amit Lata faster than Chetan Who is exactly in the middle of the group?

A Chetan
B Gita
C Lata
D Farhan

Answer: Option B — with explanation

The clues form one chain: Lata faster than Chetan faster than Gita faster than Farhan faster than Amit. There are five people, so the one in the middle is third in the chain, which is Gita. Common mistakes - picked the top of the chain instead of the middle: Lata - stopped one place above the middle: Chetan - stopped one place below the middle: Farhan

Question 3

Study the clues and answer the question. Divya older than Isha Chetan older than Hari Isha older than Amit Which person is definitely above Isha?

A Hari
B Chetan
C Amit
D Divya

Answer: Option D — with explanation

The clues Divya older than Isha and Isha older than Amit put Divya above Isha, and Amit below. Chetan and Hari are only ranked against each other, so nothing is known about where they sit. Only Divya is definitely above Isha. Common mistakes - belongs to the other pair in the clues: Chetan - belongs to the other pair in the clues: Hari - is below in the chain, not above it: Amit

Question 4

Study the clues and answer the question. Esha older than Chetan Divya older than Farhan Chetan older than Bela Farhan older than Esha Who is the oldest?

A Farhan
B Divya
C Chetan
D Esha

Answer: Option B — with explanation

The clues form one chain: Divya older than Farhan older than Esha older than Chetan older than Bela. Reading it end to end, Divya is first and Bela is last, so Divya is the oldest. Common mistakes - read the chain from the wrong end: Chetan - picked the middle of the chain: Esha - stopped one place short in the chain: Farhan

Question 5

Study the clues and answer the question. Gita faster than Esha Kiran faster than Amit Farhan faster than Gita Amit faster than Farhan Who is exactly in the middle of the group?

A Kiran
B Gita
C Amit
D Farhan

Answer: Option D — with explanation

The clues form one chain: Kiran faster than Amit faster than Farhan faster than Gita faster than Esha. There are five people, so the one in the middle is third in the chain, which is Farhan. Common mistakes - stopped one place above the middle: Amit - stopped one place below the middle: Gita - picked the top of the chain instead of the middle: Kiran

Frequently asked questions

How do I solve a ranking puzzle?

Turn every clue into an arrow pointing from the greater to the lesser, then join the arrows into chains. Once the chain is drawn, the question is only about reading a position off it.

What if some people are never compared with each other?

Then their relative order is genuinely unknown, and a question asking about it would have no answer. Questions are written so that the people you are asked about always sit in the same chain.

How do I avoid reading the chain backwards?

Decide before you start which end means most and which means least, then state it to yourself. A question about the tallest wants the top of the chain, and a question about the shortest wants the bottom.

What if two clues contradict each other?

That cannot happen in a well-formed question. If your chain contains a loop, you have misread a clue, so go back to the clues rather than trusting the diagram.

Do these puzzles always have five people?

The number varies, but four or five is most common. The method is identical whatever the size of the group; only the length of the chain changes.