Chapter 3 of 4

Analytical Aptitude

In the GATE Civil syllabus under General Aptitude · 5 parts

Syllogism · Analogy · Statement & Conclusions / Courses of Action · Number Series · Puzzles

CIVILGYAN TEST SERIES · civilgyantests.com — free study notes for civil engineering exams

📑 Contents (30 sections)

Part 1 of 5

Syllogism

Last reviewed 22 Sept 2026 · 5 min read

The four forms

Form	Statement	What it allows
A (universal affirmative)	All A are B	every A is inside B; B may be bigger
E (universal negative)	No A is B	the circles do not touch
I (particular affirmative)	Some A are B	the circles overlap; they may also coincide
O (particular negative)	Some A are not B	part of A lies outside B

RememberThe one rule

A conclusion is valid only if it holds in every diagram the statements allow. One legal diagram in which it fails is enough to reject it. So the work is not to draw a diagram, but to draw the diagram that commits to the least — and then to try to break the conclusion.

Drawing the least-committed diagram

All A are B: A wholly inside B. (Do not make them equal unless forced.)
No A is B: two separate circles.
Some A are B: two overlapping circles — and remember that "some" does not deny "all".
Some A are not B: A overlapping B with a part of A clearly outside.

Then read the conclusion and ask: can I redraw this, still obeying the statements, so that the conclusion becomes false? If yes, it does not follow.

Conversions that are always safe

All A are B → Some B are A (and Some A are B).
No A is B → No B is A, and Some A are not B.
Some A are B → Some B are A.
Some A are not B → nothing about B and A in reverse.

Possibility conclusions

Modern papers ask about possibility: "All A being C is a possibility." Such a conclusion is true when at least one legal diagram contains it — the mirror image of the main rule. So:

A definite conclusion needs every diagram.
A possibility conclusion needs one diagram.

Either-or (complementary pairs)

When neither conclusion follows alone, but together they cover every case and overlap in none, the answer is either I or II follows. The pair must:

have the same subject and predicate, and
be of the forms (Some A are B, No A is B) or (All A are B, Some A are not B).

Worked examples

Worked ExampleExample 1 — the basic test

Statements: All pens are books. All books are tables. Conclusions: I. All pens are tables. II. Some tables are pens.

Solution. Pens inside books inside tables, in every legal drawing → I follows. From "all pens are tables", some tables are pens → II follows. Both follow.

Worked ExampleExample 2 — a middle term that does not connect

Statements: Some cats are dogs. Some dogs are rats. Conclusions: I. Some cats are rats. II. No cat is a rat.

Solution. Cats and rats may overlap, or may not — both drawings are legal, so neither conclusion follows on its own. But the two together cover every case and overlap in none → either I or II follows.

Worked ExampleExample 3 — a negative statement

Statements: All fruits are sweet. No sweet thing is bitter. Conclusions: I. No fruit is bitter. II. Some bitter things are fruits.

Solution. Fruits lie inside sweet, which is separate from bitter → I follows in every drawing; II contradicts it → only I follows.

Worked ExampleExample 4 — "some" does not mean "not all"

Statements: Some books are pens. All pens are red. Conclusions: I. Some books are red. II. All books are red.

Solution. The books that are pens are red → I follows. II fails in the drawing where other books lie outside red → only I follows.

Worked ExampleExample 5 — possibility

Statements: All roses are flowers. Some flowers are red. Conclusion: All roses being red is a possibility.

Solution. A legal drawing exists with every rose inside the red region → the possibility holds.

Worked ExampleExample 6 — a trap with "only"

Statement: Only boys can play. Conclusion: All who play are boys.

Solution. "Only A are B" means all B are A → the conclusion follows. Note it does not mean that all boys play.

Worked ExampleExample 7 — three statements

Statements: All A are B. No B is C. Some C are D. Conclusions: I. No A is C. II. Some D are not B.

Solution. A inside B, and B separate from C → I follows. The C's that are D lie outside B, so some D are not B → II follows. Both follow.

Worked ExampleExample 8 — reverse syllogism

Which set of statements makes "Some pens are papers" definitely true? (a) All pens are books, all books are papers (b) Some pens are books, some books are papers

Solution. (a) — pens inside books inside papers forces the overlap. In (b) the middle term connects nothing.

Part 2 of 5

Analogy

Last reviewed 22 Sept 2026 · 6 min read

What the question is really asking

An analogy gives one pair whose members are related in a definite way, and asks for another pair related in exactly the same way. The safest method never looks at the options first:

Say the relationship aloud in a full sentence, using both words: "A pen is the tool a writer works with."
Put the first word of each option into that same sentence.
Only one option will fit in the same direction and at the same level.

Exam TipDirection matters

"Doctor : Patient" is not the same as "Patient : Doctor". If the first pair runs cause → effect, the answer must run cause → effect too, never the reverse.

The relationships that appear again and again

Type	Example	The sentence to say
Synonym	Huge : Enormous	"Huge means the same as enormous"
Antonym	Ancient : Modern	"Ancient is the opposite of modern"
Worker and tool	Carpenter : Chisel	"A carpenter works with a chisel"
Worker and workplace	Teacher : School	"A teacher works in a school"
Part and whole	Petal : Flower	"A petal is a part of a flower"
Individual and class	Sparrow : Bird	"A sparrow is a kind of bird"
Raw material and product	Wheat : Bread	"Bread is made from wheat"
Cause and effect	Virus : Disease	"A virus causes disease"
Unit and measure	Metre : Length	"A metre measures length"
Instrument and measurement	Thermometer : Temperature	"A thermometer measures temperature"
Animal and young one	Cow : Calf	"A calf is the young of a cow"
Study and subject	Ornithology : Birds	"Ornithology is the study of birds"
Symbol and thing	Dove : Peace	"A dove is the symbol of peace"
Degree or intensity	Warm : Hot	"Warm is a milder form of hot"

Number analogies

Look for one rule that turns the first number into the second: a constant difference, a ratio, a power, a cube or square with an adjustment, or a digit operation.

Common patterns: $n \to n^{2}$ ; $n \to n^{3}$ ; $n \to n^{2} + 1$ ; $n \to n (n + 1)$ ; sum or product of the digits; the next prime; reverse of the number.

Letter analogies

Number the alphabet $A = 1$ to $Z = 26$ and compare positions. Typical rules: a fixed forward or backward shift, opposite letters (the EJOTY trick: $A \leftrightarrow Z$ , $B \leftrightarrow Y$ , and in general the pair sums to 27), the same shift applied to each letter of a group, or reversing the letters.

RememberTwo alphabet facts worth memorising

Opposite pairs add to 27: $A (1) + Z (26)$ , $C (3) + X (24)$ , $M (13) + N (14)$ .
EJOTY: E=5, J=10, O=15, T=20, Y=25 — lets you place any letter in two steps.

Part 3 of 5

Statement & Conclusions / Courses of Action

Last reviewed 22 Sept 2026 · 5 min read

The only question being asked

"Does this conclusion follow from the statement?" means: reading only the statement, and nothing you happen to know about the world, is the conclusion necessarily true?

Three tests dispose of most options:

Is it stated or forced? If the statement leaves it open, it does not follow.
Is it too strong? Words such as all, never, only, always, must usually go beyond a statement that was modest.
Is it too wide? A statement about one city does not support a conclusion about the country.

Exam TipThe restatement trap

An option that merely repeats the statement in other words is not a conclusion — it adds nothing. Exam keys treat such options as not following, unless the paper's own instructions say otherwise.

Conclusion, inference, assumption

Term	Where it sits	Test
Conclusion	after the statement	must be true if the statement is true
Inference	after the statement	probably true, drawn from it
Assumption	before the statement	taken for granted by the writer

An assumption is what the speaker must already believe for their sentence to make sense; a conclusion is what a reader may take away from it. Confusing the two is the commonest error in the whole topic.

Courses of action

A course of action is a step suggested to deal with a problem in the statement. It follows only if it passes all three tests:

Relevance — it addresses the problem actually stated.
Practicality — it can be done by the body that would have to do it.
Proportion — it is not an extreme step where a mild one would do, and not a mild one where the statement describes an emergency.

Actions that are punitive for their own sake, or that ban an activity wholesale, are usually rejected; actions that inform, regulate, repair or investigate are usually accepted.

Worked examples

Worked ExampleExample 1 — too strong

Statement: Most of the students in the class passed the examination. Conclusion: All the students studied hard.

Solution. "Most" does not give "all", and studying hard is nowhere in the statement → does not follow.

Worked ExampleExample 2 — forced

Statement: All the trains from this station run to the east. Conclusion: No train from this station runs to the west.

Solution. Forced by the statement → follows.

Worked ExampleExample 3 — too wide

Statement: The sale of electric scooters in Delhi rose 40% last year. Conclusion: Electric scooters are becoming popular across India.

Solution. One city does not settle a country → does not follow.

Worked ExampleExample 4 — two conclusions

Statement: The company has decided to raise the salaries of its workers from next month. Conclusions: I. The workers were dissatisfied with their salaries. II. The company can afford the rise.

Solution. I is a guess about the reason → does not follow. II is implied by the decision to make it → only II follows.

Worked ExampleExample 5 — an assumption, not a conclusion

Statement: "Use our detergent for whiter clothes" — an advertisement. Which is an assumption? (a) People want whiter clothes. (b) The detergent is cheap.

Solution. (a) — the advertisement makes no sense unless whiteness is wanted. Price is not taken for granted anywhere.

Worked ExampleExample 6 — a course of action

Statement: A large number of road accidents on the highway occur at night at one particular curve. Courses: I. The curve should be re-designed and lit. II. The highway should be closed at night.

Solution. I is relevant, practical and proportionate → follows. II is disproportionate → only I follows.

Worked ExampleExample 7 — both follow

Statement: A sudden outbreak of a water-borne disease has been reported in a locality. Courses: I. The water supply of the locality should be tested at once. II. Residents should be advised to boil drinking water until further notice.

Solution. Both are relevant, practical and immediate → both follow.

Worked ExampleExample 8 — neither follows

Statement: Many students of the school scored poorly in mathematics this year. Courses: I. The mathematics teacher should be dismissed. II. Mathematics should be removed from the syllabus.

Solution. I is punitive before any enquiry; II is absurd → neither follows. (A remedial class would have followed.)

Part 4 of 5

Number Series

Last reviewed 22 Sept 2026 · 5 min read

A working order

Do these in order and stop at the first that works:

First differences. Constant → arithmetic. Growing → take the second differences; constant there means a quadratic pattern (often $n^{2}$ based).
Ratios. Constant → geometric. Nearly constant → multiply-and-add.
Squares, cubes and their neighbours: $n^{2}$ , $n^{2} \pm 1$ , $n^{3}$ , $n^{3} \pm n$ .
Primes (2, 3, 5, 7, 11, 13, 17, 19, 23, 29) or their squares.
Alternating: two patterns interleaved — look at terms 1, 3, 5 and 2, 4, 6 separately.
Mixed operation: $\times 2 + 1$ , $\times 3 - 2$ , $+ 1 \times 2$ repeated.
Digit rules: sum of the digits added, digits reversed, digits multiplied.

Exam TipTwo seconds well spent

Before anything, notice whether the series grows slowly (differences — think arithmetic or squares) or explodes (ratios — think geometric, cubes or factorials). That single judgement removes half the possibilities.

The three question types

Type	What is asked	Method
Next term	continue the series	find the rule, apply it once more
Missing term	fill a gap in the middle	find the rule from the terms around the gap, then verify on the rest
Wrong term	one term breaks the rule	find the rule from the majority, then name the term that does not obey

In a wrong term question the answer is the term to be removed, not its correct replacement — read what the options represent.

Patterns worth recognising on sight

$2, 6, 12, 20, 30 \dots$ → $n (n + 1)$
$1, 4, 9, 16, 25 \dots$ → $n^{2}$ ; $2, 5, 10, 17, 26 \dots$ → $n^{2} + 1$
$1, 8, 27, 64 \dots$ → $n^{3}$ ; $0, 7, 26, 63 \dots$ → $n^{3} - 1$
$1, 1, 2, 3, 5, 8 \dots$ → Fibonacci (each term is the sum of the two before)
$1, 2, 6, 24, 120 \dots$ → factorials
$4, 9, 25, 49, 121 \dots$ → squares of primes
Differences that are themselves $2, 4, 6, 8$ or $1, 2, 3, 4$ → a quadratic rule

Part 5 of 5

Puzzles

Last reviewed 22 Sept 2026 · 6 min read

Every matching puzzle is a grid

Five people, five cities, five subjects — that is two grids, or one table with three columns. Draw the table before reading the clues a second time.

Rows: the fixed set that never changes — usually the people, or the floors 1 to 7.
Columns: each attribute to be matched.
Fill a cell only when a clue forces it; write a small ✗ in a cell a clue forbids.
Re-read the clue list from the top every time a new cell is filled: clues that were useless often become decisive.

Exam TipThe order that saves time

Definite clues ("C lives on floor 3") → relative clues ("A lives two floors above B") → negative clues ("D does not teach physics"). A negative clue is worth little at the start and a great deal at the end.

Floor and stack puzzles

Seven floors, seven people: number the floors with 1 at the bottom and say so on your paper. Then:

"A lives above B" means A's number is larger.
"Exactly two people live between A and B" means their numbers differ by 3.
"A lives immediately above B" means $A = B + 1$ .
The topmost and bottommost floors are the most constrained — clues about them are usually the ones to use first.

The same layout handles boxes stacked one on another and books piled on a shelf.

Scheduling puzzles

Days of the week, months, or dates in a month. Write the days in order along the top and mark what is fixed. Watch for two traps: a week that runs Monday to Sunday versus Sunday to Saturday, and clues that talk about "the day before" a day that is itself unknown.

Carrying two cases

When a clue allows two placements, start Case 1 and Case 2 side by side. Continue both until a later clue contradicts one. Deciding early which case "feels right" is the commonest reason a puzzle takes twenty minutes instead of four.

A worked puzzle

Five friends — Amit, Bina, Chetan, Deepa and Esha — live on five floors of a building (1 at the bottom to 5 at the top). Each likes a different colour: red, blue, green, white, yellow.

Chetan lives on floor 4.
The one who likes red lives immediately below Chetan.
Amit lives on the topmost floor.
Bina does not live on floor 1.
The one who likes blue lives on floor 1.
Deepa likes green.
Esha does not like white.

Worked ExampleSolving it clue by clue

From 1 and 3: Chetan is on 4, Amit on 5. Floors 1, 2 and 3 are left for Bina, Deepa and Esha; by 4, Bina is on 2 or 3.

From 2: the red-lover is on floor 3. From 5: the blue-lover is on floor 1. From 6: Deepa likes green, so Deepa is not on floor 1 or 3 → Deepa is on floor 2, so Bina is on 3 and Esha on 1.

So Bina (floor 3) likes red and Esha (floor 1) likes blue. By 7 Esha does not like white, which is consistent. White and yellow are left for Amit and Chetan, and no clue separates them — the puzzle fixes the floors and three colours, and leaves white and yellow undetermined.

Floor	Person	Colour
5	Amit	white or yellow
4	Chetan	white or yellow
3	Bina	red
2	Deepa	green
1	Esha	blue

A real exam set would add an eighth clue, such as "Chetan does not like yellow", which finishes the grid at once. Noticing what is not determined is itself a skill: several questions ask exactly that.

Worked examples

Worked ExampleExample 1 — floors and a gap

In a seven-floor building, P lives on floor 2 and exactly three people live between P and Q. Where does Q live?

Solution. Their floor numbers differ by 4 → Q is on floor 6 (floor $- 2$ does not exist).

Worked ExampleExample 2 — immediately above

R lives immediately above S, and S lives on floor 3 of six. Who lives on floor 4?

Solution. R.

Worked ExampleExample 3 — a negative clue at the right time

Four people A, B, C, D take four subjects: maths, physics, chemistry, biology. A does not take maths or physics. B takes chemistry. C does not take biology. What does A take?

Solution. A takes chemistry or biology; chemistry is B's, so A takes biology. Then C takes maths or physics, and D takes the other.

Worked ExampleExample 4 — days

A meeting is on a day between Tuesday and Friday, but not on Wednesday. Which day is it?

Solution. Between Tuesday and Friday means Wednesday or Thursday; not Wednesday → Thursday.

Worked ExampleExample 5 — two cases

In a row of five boxes, box P is somewhere above box Q, and exactly one box lies between them. Box Q is not at the bottom. List the possible positions of P and Q.

Solution. Q at 2 → P at 4; Q at 3 → P at 5. Two cases survive, and neither can be ruled out without another clue.

Frequently tested points

Draw the grid first; fill only what a clue forces, and mark ✗ for what it forbids.
Use definite clues, then relative, then negative.
In floor puzzles, state which end is floor 1 on your own paper.
"Exactly $k$ between" means the numbers differ by $k + 1$ .
Carry two cases side by side rather than guessing.
Re-read the clue list after every new entry.

Common MistakeCommon mistakes

Filling a cell on a hunch and building the rest of the grid on it.
Reading "above" as a bigger number in one puzzle and a smaller one in the next — fix the convention once.
Treating "between A and B" as an order.
Abandoning a case too early, or forgetting to finish the second one.
Missing that the puzzle genuinely leaves something open.

Revision SummaryChapter summary

Matching puzzles are grids: rows for the fixed set, columns for each attribute.
Clues are used in order — definite, relative, then negative.
Floor and box puzzles need an explicit numbering convention before anything else.
When a clue allows two placements, both are carried until one is contradicted.
Recognising what the clues do not determine is part of the answer, not a failure.

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