Logical Word Problems

In this lesson, you will learn how to solve logical word problems — questions that combine verbal reasoning with logical thinking. These appear regularly in CEM 11+ exams and test your ability to draw conclusions from written information.

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What Are Logical Word Problems?

Logical word problems give you a set of statements or clues and ask you to work out something based on those clues. You must use logic — not guessing — to find the correct answer.

These questions might involve:

• Ordering (who is tallest, who came first, etc.)
• Matching (who owns what, who lives where)
• True/false deduction (what MUST be true based on the statements)
• Conditional reasoning (if A happens, then B happens)

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Why CEM Tests Logical Reasoning

CEM exams test your ability to think carefully and systematically. Logical word problems are excellent for this because:

• They cannot be answered by learning vocabulary alone — you must reason.
• They test whether you can process information under time pressure.
• CEM exams interleave these with other question types, so you must switch between skills quickly.

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Step-by-Step Method

Step 1: Read All the Clues

Read every statement carefully. Do not start answering until you have read all the information.

Step 2: Identify What You Need to Find

What is the question asking? The tallest? The fastest? Who has what? Be clear about your goal.

Step 3: Organise the Information

Use a quick method to keep track:

• Lists — write names in order (tallest to shortest, first to last)
• Tables — draw a grid to match people to things
• Diagrams — use arrows to show relationships

Step 4: Work Through Logically

Do not jump to conclusions. Work through each clue one at a time.

Step 5: Check Your Answer

Re-read the clues and make sure your answer does not contradict any of them.

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Worked Example 1: Ordering

Question: Tom is taller than Sam. Sam is taller than Alex. Alex is taller than Ben. Who is the shortest?

Step-by-step:

1. Tom > Sam (Tom is taller).
2. Sam > Alex.
3. Alex > Ben.
4. Order: Tom > Sam > Alex > Ben.
5. Answer: Ben is the shortest.

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Worked Example 2: Matching

Question: Three children — Amy, Ben, and Clara — each have a different pet: a cat, a dog, and a fish. Amy does not have a cat. Ben does not have a dog. Clara has a cat. Who has the dog?

Step-by-step:

Child	Cat	Dog	Fish
Amy	No	?	?
Ben	?	No	?
Clara	Yes	No	No

1. Clara has a cat, so Clara does not have a dog or fish.
2. Amy does not have a cat. Ben does not have a dog.
3. Since Clara has the cat, the dog and fish go to Amy and Ben.
4. Ben does not have a dog, so Ben has the fish.
5. That means Amy has the dog.
6. Answer: Amy has the dog.

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Worked Example 3: Conditional Reasoning

Question: If it rains, Lily takes her umbrella. If Lily takes her umbrella, she walks to school. If she walks, she arrives late. It is raining today. What can you conclude?

Step-by-step:

1. It is raining -> Lily takes her umbrella.
2. Lily takes her umbrella -> she walks to school.
3. She walks -> she arrives late.
4. Following the chain: rain -> umbrella -> walk -> late.
5. Answer: Lily arrives late.

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Worked Example 4: True or False Deduction

Question: "All roses are flowers. Some flowers are red." Which statement MUST be true?

A) All roses are red. B) Some roses are red. C) All flowers are roses. D) All roses are flowers.