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Reasoning · Verbal Reasoning

7 Part2 worked examples8 practice questions

In a puzzle question a number of short clues are given about some people or things — who is good at what, who is taller than whom, who does which job, who came on which day — and then 3–5 questions are asked on those clues. There is no formula; only pure logic works.

Every puzzle has exactly one answer, because enough clues are given to leave no second solution. Your job is to put the clues into a table and eliminate: strike off an option the moment a clue rules it out, and when only one option is left in a place, that one is certain.

This chapter has five kinds of puzzles: (1) classification — who is good in which game / subject (a table); (2) order and comparison — orders of height, age, weight; (3) matching — names, professions, colours, cities; (4) order of days — who came on which day; (5) family — the professions and relations of six members. Each is taught from the very beginning.

How to use this chapter

  1. Read — the idea first, then the method.
  2. Study the solved example — the clues are above and the solution is open step by step; ask why each clue is used the way it is.
  3. Try it yourself — put the clues into a table on paper, then choose an option. If stuck take the hint; open the solution last.
  4. Know the level — each question is marked Basic, Standard or Advanced.
NoteThe clues of each puzzle stand right above its questions and all the questions of one puzzle are on the same clues. The questions you get right are remembered in this browser.
1

Foundation — tables and elimination

The tools of every puzzle

The four-step method for solving puzzles, using ✓ and ✗ in a table and rules for reading the clues.

What a puzzle is and how to solve it

Read → table → eliminate → answer

The four-step method for puzzles and the rules for handling clues.

The clues of a puzzle are really a list of facts. Each fact either fixes something (“Ram is the doctor”), rules something out (“Shyam is not the engineer”) or narrows the choices (“the lawyer is either Ram or Shyam”). Using these three we reach the solution.

The four-step method
1. Read all the clues once2. Draw a table (people × features)3. Fill ✓ for sure facts, ✗ for ruled-out ones and keep eliminating4. Read the answer to the question from the table

Five rules for handling clues

  1. Each clue says exactly what is written — no more, no less. “Ram is taller than Shyam” does not mean nobody stands between them.
  2. One person — one value — unless said otherwise, each person has a single value in each category (one profession, one colour) and no two persons share the same value.
  3. When one is certain, the rest are struck off — once a ✓ appears in a row, the other cells of that row and column become ✗.
  4. The last option left is certain — if only one uncancelled cell is left in a row or column, that cell is ✓.
  5. Re-read the clues — after a new certain fact, an old clue gives new information.

Below is a classification puzzle: who is good in which game. The clues are above; the solution builds the table of games and shows the answer.

Read the information below:

  1. Seema, Indu and Tarun score well in Music and Geography.
  2. Seema and Nitin score well in Music, Geography and Science.
  3. Tarun scores well in Science and Maths.
Example 1 · Basic
Who scores well in all of Geography, Science and Maths?
Solution, step by step
  1. 1Making the table — Seema: Music, Geography, Science; Indu: Music, Geography; Tarun: Music, Geography, Science, Maths; Nitin: Music, Geography, Science.
  2. 2Look at the columns for Geography, Science, Maths: the person with a ✓ in all three is the one.
  3. 3Only Tarun is good in all three.
Answer Tarun
In each statement every person named gets a ✓ for every game named.

Read the information below:

  1. Bindu, Ravi and Bhavna score well in Maths and Drawing.
  2. Seema, Bindu and Bhavna score well in Maths and History.
  3. Seema and Ravi score well in Maths and Drawing.
  4. Ravi and Bhavna score well in Maths, Drawing and Science.
BasicTry it yourself first
Who scores well in all of Maths, Science and History?

Read the information below:

  1. Sunil scores well in Drawing and English.
  2. Deepa and Harsh score well in History, Drawing and English.
  3. Dinesh, Sunil and Deepa score well in History, English and Music.
  4. Sunil and Harsh score well in History, Drawing and English.
BasicTry it yourself first
Who is good in History and Drawing but not in Music?

Read the information below:

  1. Meena and Indu are good in Hockey, Badminton and Football.
  2. Meena, Mahesh and Indu are good in Badminton and Volleyball.
  3. Nitin is good in Hockey and Volleyball.
  4. Mahesh is good in Hockey, Badminton and Volleyball.
BasicTry it yourself first
In how many games is Meena good?

The matching table — ✓ and ✗

When names, professions, colours must be matched

The table of people and features, what to do in the table for each kind of clue, and a full example of elimination.

When each person has a profession, colour or city, put the persons in the rows and the features in the columns. Let us watch a tiny puzzle with three persons and three professions. Clues: (1) Seema is the teacher. (2) Ravi is not the doctor.

DoctorTeacherPilot
Ravi✗✗✓
Seema✗✓✗
Tina✓✗✗
  1. Clue (1): ✓ at Seema–teacher; the rest of Seema's row and the rest of the teacher column become ✗.
  2. Clue (2): ✗ at Ravi–doctor.
  3. Now in Ravi's row doctor is ✗ and teacher is ✗, so pilot is ✓ (the last left).
  4. For Tina only doctor is left: ✓.

What each kind of clue does in the table

Kind of clueExampleWhat to do
Direct (sure)Ram is the doctorPut ✓; the rest of the row and column ✗
NegativeRam is not the engineer✗ in that cell
One of twoThe lawyer is Ram or ShyamAll others ✗ in the lawyer column
Linking (two features)The doctor likes redBoth columns belong to one person: when one is known, so is the other
Reverse linkThe doctor does not like redThe two columns belong to different persons: when one is known, he/she is ✗ in the other
TrickWhen there are more than two categories (profession + colour + city), use the person's row as the link each time: “doctor → Ravi” and “Ravi → red” give “doctor → red” by themselves.

4 friends — Dinesh, Yash, Ravi, Tarun — each have a different profession and favourite colour (no two share the same). Read the clues below and answer the questions.

  1. Ravi does not like white
  2. The doctor is either Ravi or Tarun
  3. The person who likes orange is either Dinesh or Yash
  4. The engineer likes white
  5. The doctor does not like pink
  6. Ravi is not the doctor
  7. The pilot is either Dinesh or Tarun
Example 2 · Basic
On the basis of the clues: Who is the person who likes pink?
Solution, step by step
  1. 1Read the clues in order and cut down the possibilities each time:
  2. 2Clue 2: doctor can only be Ravi or Tarun.
  3. 3Clue 3: orange (colour) can only be Dinesh or Yash.
  4. 4Clue 6: doctor → Tarun.
  5. 5Clue 7: pilot → Dinesh.
  6. 6By elimination: engineer → Yash.
  7. 7By elimination: farmer → Ravi.
  8. 8Clue 4: white (colour) → Yash.
  9. 9By elimination: orange (colour) → Dinesh.
  10. 10Clue 5: pink (colour) → Ravi.
  11. 11By elimination: black (colour) → Tarun.
  12. 12Solved table — Dinesh: pilot, orange; Yash: engineer, white; Ravi: farmer, pink; Tarun: doctor, black.
  13. 13So the answer is Ravi.
Answer Ravi
Options already cut were not reconsidered; each clue made something sure or narrower.
BasicTry it yourself first
On the basis of the clues: Which colour does Dinesh like?
BasicTry it yourself first
On the basis of the clues: What is Dinesh's profession?

4 friends — Dinesh, Om, Meena, Vikas — each have a different profession and favourite colour (no two share the same). Read the clues below and answer the questions.

  1. Meena does not like pink
  2. The reporter is either Meena or Vikas
  3. The person who likes yellow is either Dinesh or Om
  4. The doctor likes orange
  5. Dinesh is not the doctor
  6. Vikas is the engineer
BasicTry it yourself first
On the basis of the clues: Which colour does Dinesh like?
BasicTry it yourself first
On the basis of the clues: Who is the reporter?
BasicTry it yourself first
On the basis of the clues: Who is the person who likes pink?
2

Classification, order and comparison

Ticks in a table and signs of inequality

Who is good in which game (a table), orders of height, age and weight (signs of inequality) and unnecessary or insufficient clues.

Classification — who is good in what

From statements to a table, from the table to answers

Making a ✓ table from statements like “A and B are good in hockey and cricket” and questions like ‘in all three’, ‘but not in’, ‘in how many’.

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Order and comparison — taller, older, heavier

Turn each statement into “>” and build a chain

Turning comparison statements about height, age, weight, marks or salary into a chain of inequality signs to find the order.

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Unnecessary statements and ‘cannot be determined’

Which statement is spare, when there is no answer

A statement that follows from the others is unnecessary; and when two orders are possible the answer cannot be determined.

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3

Matching and schedule puzzles

Name × profession × colour × city, and who on which day

Puzzles matching several categories with each other and puzzles about the order of days.

Matching names, professions, colours and cities

Several features per person, all different

Matching the professions, favourite colours and cities of four or five friends: using each clue in the table and building links.

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Order-of-days puzzles

Who came on which day — before, after, the very next day

Puzzles about several people coming on different days: clues like ‘before’, ‘exactly one day before’, ‘a gap of so many days’ and ‘not on this day’.

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4

Family puzzles

Six members, their relations and professions

Matching professions and colours in a family of grandparents, parents and two children using clues about relations.

The structure of the family and its relations

Who can be what to whom

The structure of a six-member family, sex and generation, and the table of possible pairs for each relation.

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Solving family puzzles

Relation + sex + generation + colour

Puzzles with clues of relation, sex, generation and colour, narrowing the possible members of each profession.

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5

Strategy guide

Recognising the type and common traps

The order of recognising the kind of puzzle, picking the right tool and the common mistakes.

Spot the kind, pick the tool

A tool for every puzzle

The kind of puzzle from the look of the question and the right tool for it.

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Common traps

The mistakes that keep happening

The commonest ways of losing marks in puzzles.

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6

Mixed practice

All kinds mixed — first spot the kind

Puzzles of every kind in three levels.

Basic practice

Four people, few clues

Tables of games, chains of order, small matching, order of days and family puzzles.

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Standard practice

Five people, links and pairs

Puzzles of five people, unnecessary statements, pairs of days and family relations.

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Advanced practice

Three categories, six days, professions with relations

Matching puzzles with three categories, six-day puzzles and family puzzles with colours.

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7

Revision — cards

Flip each card and test yourself

Think of the answer yourself first, then flip.

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