Mental Ability & Reasoning

Bihar Public Service Commission — Combined Competitive Examination | General Studies Paper I

1. Introduction to Mental Ability

Mental Ability (also called Reasoning or Logical Aptitude) tests a candidate's capacity to think logically, recognise patterns, and draw valid conclusions — without relying on subject-specific academic knowledge. In the BPSC CCE Preliminary Examination, reasoning questions are part of General Studies Paper I and typically account for 15–25 questions, making this one of the most score-determining areas of the paper.

Definition Mental Ability is the measure of a person's capacity for logical reasoning, pattern recognition, analytical thinking, and structured problem-solving under timed conditions. It is distinct from general knowledge — it tests how you think, not what you know.

The BPSC reasoning section draws from three broad categories:

Verbal Reasoning — problems expressed in words: analogies, classification, blood relations, syllogism, coding-decoding, direction sense.
Non-Verbal Reasoning — pattern recognition using figures and matrices (less frequent in BPSC but possible in some years).
Logical Deduction — drawing conclusions from given statements: Venn diagrams, syllogisms, seating arrangement puzzles.

General Approach to Every Reasoning Question

Read the question fully before looking at options.
Identify the question type immediately — each type has a fixed method.
Apply the method systematically, not by guesswork.
Eliminate obviously wrong options to improve selection odds.
If genuinely stuck after 40 seconds, mark and move on — return if time permits.

2. Series Completion

Series completion asks you to find the missing or next term in a sequence. The key is to identify the underlying rule. Always check four possibilities in order: (a) constant difference, (b) constant ratio, (c) squares or cubes, (d) differences that form their own pattern.

2.1 Number Series Patterns

Pattern Type	Example Series	Rule	Answer
Arithmetic Progression	3, 7, 11, 15, 19, ?	Add 4 each time	23
Geometric Progression	2, 4, 8, 16, 32, ?	Multiply by 2	64
Perfect Squares	1, 4, 9, 16, 25, ?	1², 2², 3², 4², 5²	36
Perfect Cubes	1, 8, 27, 64, 125, ?	1³, 2³, 3³, 4³, 5³	216
Increasing Differences	2, 3, 5, 8, 12, 17, ?	Differences: 1, 2, 3, 4, 5, then 6	23
Second-order Difference	1, 2, 5, 10, 17, 26, ?	Differences 1,3,5,7,9 form an AP of odd numbers	37
Alternating Sub-series	2, 5, 4, 10, 8, 20, 16, ?	Odd positions ×2; even positions ×2	40
Mixed Add Pattern	3, 6, 11, 18, 27, ?	Add 3, 5, 7, 9, 11 (successive odd numbers)	38

BPSC Important — Most Tested Number Patterns In recent BPSC Prelims, difference-based series and square/cube series appear most often. Memorise squares up to 25 (625) and cubes up to 12 (1728). A series like 2, 5, 10, 17, 26 — where differences are 3, 5, 7, 9 — is a classic BPSC-style question.

2.2 Letter Series

Letters are numbered A=1 through Z=26. Most letter series involve positional shifts. Treat the alphabet as a cycle when required (after Z comes A again).

Letter position values: A=1 B=2 C=3 D=4 E=5 F=6 G=7 H=8 I=9 J=10 K=11 L=12 M=13 N=14 O=15 P=16 Q=17 R=18 S=19 T=20 U=21 V=22 W=23 X=24 Y=25 Z=26 Common patterns: Skip 1: A, C, E, G, I, ? → K (every alternate letter) Gap of 3: A, D, G, J, M, ? → P (add 3 each time) Reverse: Z, X, V, T, R, ? → P (subtract 2) Pairs: AB, DE, GH, JK, ? → MN (skip 2, take 2)

2.3 Mixed Series

Mixed series combine numbers and letters, or follow two interleaved rules. Example: A2, C4, E6, G8, ? — letters jump by 2 (A, C, E, G, I) and numbers increase by 2 (2, 4, 6, 8, 10). Answer: I10.

Quick Tip — Series Solving Sequence Step 1: Write differences between consecutive terms. Step 2: If differences are constant → AP. Step 3: If differences multiply → GP. Step 4: If differences themselves form an AP → 2nd-order pattern. Step 5: Check squares and cubes. This 5-step approach covers 95% of BPSC series questions.

3. Analogy

Analogy questions present a pair of items with a specific relationship, then ask you to find a word/number/letter that has the same relationship with a new item. The format is: A : B :: C : ?

Definition An analogy is a relationship of similarity between two pairs of items. To solve it: (1) identify the relationship in the given pair, (2) apply exactly the same relationship to find the missing term.

3.1 Types of Word Analogies

Relationship Type	Example	Logic
Object : Workplace	Doctor : Hospital :: Teacher : School	Where the professional works
Object : Tool	Carpenter : Saw :: Painter : Brush	Tool used by the professional
Animal : Young one	Cat : Kitten :: Dog : Puppy	Name of the young of the animal
Animal : Sound	Lion : Roar :: Snake : Hiss	Sound made by the animal
Part : Whole	Page : Book :: Brick : Wall	The first item is a part of the second
Cause : Effect	Fire : Ash :: Rain : Flood	First causes the second
Object : Material	Shoe : Leather :: Window : Glass	What the object is made of
Singular : Plural	Tooth : Teeth :: Mouse : Mice	Irregular plural form
Word : Antonym	Day : Night :: Hot : Cold	Opposite meaning
Country : Capital	India : New Delhi :: Japan : Tokyo	Capital city of the country
Product : Source	Wool : Sheep :: Silk : Silkworm	Where the product comes from

3.2 Number Analogies

Example	Relationship	Answer
4 : 16 :: 5 : ?	Square of the number (4²=16)	25
3 : 27 :: 4 : ?	Cube of the number (3³=27)	64
8 : 4 :: 20 : ?	Half of the number	10
6 : 42 :: 8 : ?	Number × (Number+1): 6×7=42	72 (8×9)
5 : 30 :: 7 : ?	Number × 6	42

3.3 Letter Analogies

Example	Relationship	Answer
AC : EG :: IK : ?	Pairs with gap of 1; advance by 4	MO
ABCD : DCBA :: PQRS : ?	Reverse the order of letters	SRQP
BDF : CEG :: MOQ : ?	Each letter +1 in the pair	NPR

BPSC Important — Analogy Trap The most common mistake is picking a "related" word instead of the word with the exact same relationship. Example: Dog : Kennel :: Bird : ? — the answer is Nest (where it lives), NOT "cage" (where it is kept). Always state the relationship in a sentence before looking at options.

4. Classification / Odd One Out

Classification (Odd One Out) questions give four or five items, one of which does not belong to the same category as the rest. The key is identifying the common property shared by the majority and finding the exception.

Rule Find the property shared by all but one item. The item that does NOT share this property is the odd one out. Be careful — the common property might be subtle (e.g., all prime numbers, all mammals, all words with silent letters).

4.1 Word Classification Examples

Question	Odd One Out	Reason
Rose, Marigold, Jasmine, Tulip, Mango	Mango	All others are flowers; Mango is a fruit tree
Tiger, Lion, Leopard, Elephant, Cheetah	Elephant	All others are big cats (felidae); Elephant is not
Pen, Pencil, Eraser, Scale, Book	Book	All others are stationery items used for writing; Book is for reading
Patna, Mumbai, Kolkata, Delhi, London	London	All others are Indian cities; London is in the UK

4.2 Number Classification Examples

Question	Odd One Out	Reason
2, 3, 5, 7, 9, 11	9	All others are prime numbers; 9 = 3×3 (composite)
36, 49, 64, 81, 90	90	All others are perfect squares (6²,7²,8²,9²); 90 is not
3, 6, 9, 12, 16	16	All others are multiples of 3; 16 is not
1, 8, 27, 64, 100	100	All others are perfect cubes (1³,2³,3³,4³); 100 is not (it's 10²)

Key Point — Look for Multiple Valid Groupings Sometimes two answers seem valid. Choose the one where the common property is more specific and clear-cut. If 3 items share an obvious property and 1 does not, that 1 is the answer — do not overthink it. BPSC questions have a single intended answer.

5. Coding-Decoding

Coding-Decoding questions use a secret code to convert words, letters, or numbers into another form. Your job is to decode the rule and apply it to the new input.

5.1 Letter-Position Coding (A=1 to Z=26 type)

Rule: Replace each letter with its position number in the alphabet. A=1, B=2, C=3 ... Z=26 Example: If CAT is coded as 3-1-20, what is DOG coded as? D=4, O=15, G=7 Answer: 4-15-7

5.2 Letter Shift Coding

Each letter is shifted forward or backward by a fixed number of positions.

Forward shift by 1: A→B, B→C, C→D ... Z→A (wraps around) Forward shift by 2: A→C, B→D, C→E ... Y→A, Z→B Example: If PEN is coded as QFO (each letter +1), decode: P+1=Q, E+1=F, N+1=O → PEN = QFO ✓ Question: What is BOOK coded as (shift +2)? B→D, O→Q, O→Q, K→M Answer: DQQM

5.3 Mirror / Reversal Coding

Mirror coding pairs each letter with its mirror counterpart: A↔Z, B↔Y, C↔X, D↔W, E↔V, F↔U, G↔T, H↔S, I↔R, J↔Q K↔P, L↔O, M↔N Rule: A's mirror = Z (1+26=27), B's mirror = Y (2+25=27) Position of mirror letter = 27 - original position Example: If BPSC is coded in mirror: B(2)→Y(25), P(16)→K(11), S(19)→H(8), C(3)→X(24) Answer: YKHX

5.4 Word-Based Coding

The code for a word is derived from the word itself using a consistent rule applied to all words in the set.

Given Code	Rule Applied	Find Code For	Answer
ROAD → URDG	Each letter +3 (R+3=U, O+3=R, A+3=D, D+3=G)	KING	NLQJ
BOOK → CPPL	Each letter +1 (B+1=C, O+1=P, O+1=P, K+1=L)	EXAM	FYBN
FIRE → ERHI	Reverse the word then shift back? No — swap pairs: FI→IF, RE→ER? Check: F-I-R-E → E-R-I-H? Each letter -1	CODE	BNCD

5.5 Number Coding

Example: If 1=A, 2=B, 3=C ... decode 3-1-20 → C-A-T = CAT Mixed coding: If APPLE = 1-16-16-12-5 (each letter's position), find MANGO: M=13, A=1, N=14, G=7, O=15 → 13-1-14-7-15

BPSC Important — Systematic Approach to Coding Always verify your decoded rule by testing it against ALL the given examples, not just one. A rule that works for the first pair but fails on the second is wrong. Decode at least two pairs before applying to the question.

6. Blood Relations

Blood relation questions require you to determine how one person is related to another given a set of relational statements. The secret is to draw a simple family tree diagram — never solve blood relation questions purely in your head.

Key Terminology Paternal = Father's side | Maternal = Mother's side | Sibling = brother or sister | Spouse = husband or wife | In-law = relative by marriage

6.1 Common Family Relationships

Relationship	Meaning
Father's or Mother's son	Brother (if male sibling)
Father's brother	Uncle (Paternal)
Mother's brother	Uncle (Maternal / Mama)
Father's sister	Aunt (Bua)
Son's wife	Daughter-in-law
Wife's or Husband's brother	Brother-in-law
Son's son	Grandson
Father's father	Grandfather (Paternal)

6.2 Solved Examples

Problem Statement	Step-by-step Solution	Answer
A is the son of B. C is the daughter of B. How is A related to C?	Both A and C have the same parent B. A is male (son). C is female (daughter). Same parent = siblings.	A is the brother of C
Pointing to a man, a woman says, "His mother is the only daughter of my mother." How is the woman related to the man?	"Only daughter of my mother" = the woman herself. So the man's mother = the woman. The woman is his mother.	Mother
P is the brother of Q. R is the mother of P. S is the father of R. How is Q related to S?	Draw: S → R → P (and Q is P's sibling). S is R's father, R is Q's mother, so S is Q's maternal grandfather.	Grandson/Granddaughter of S
A + B means A is the son of B. A - B means A is the wife of B. If P + Q - R, who is R to P?	P + Q → P is son of Q. Q - R → Q is wife of R. So R is Q's husband and P's father. R is P's father.	Father
Introducing a girl, Ramesh says "She is the daughter of the only son of my grandfather." Who is the girl to Ramesh?	Only son of Ramesh's grandfather = Ramesh's father. Daughter of Ramesh's father = Ramesh's sister.	Sister

Key Method: Always Draw a Family Tree Use boxes or circles for people and arrows to show parent-child links. Mark M (male) and F (female) where indicated. Trace the path from person A to person B through the tree to find the relationship. This eliminates confusion in multi-step problems.

7. Direction Sense

Direction sense questions involve a person travelling in specified directions for given distances. You must find either the final direction faced, the total straight-line (displacement) distance from the start, or the direction of the person from the starting point.

Compass Directions North (N) is up on your diagram. South (S) is down. East (E) is right. West (W) is left. Intermediate: NE = between N and E, NW = between N and W, SE = between S and E, SW = between S and W.

7.1 Distance Calculation — Pythagoras Theorem

When a person travels in perpendicular directions, the straight-line distance from start to end is found using: Distance = √(horizontal² + vertical²)

Problem	Movements	Net Position	Displacement
Ravi walks 3 km North, then 4 km East. How far from start?	N: 3 km, E: 4 km	3 km up, 4 km right	√(3²+4²) = √25 = 5 km
Priya walks 5 km South, then 12 km West. Distance from start?	S: 5 km, W: 12 km	5 km down, 12 km left	√(5²+12²) = √169 = 13 km
Mohan walks 6 km East, 6 km North, 6 km West. Where is he relative to start?	E:6, N:6, W:6 → net E=0, N=6	6 km North of start	6 km, due North

BPSC Important — Common Mistake in Direction Questions Candidates confuse "which direction is the person facing?" with "in which direction is the person from the starting point?" These are different questions. Always re-read what is being asked before answering.

8. Ranking and Arrangement

Ranking questions involve ordering people or objects and finding a specific position. Arrangement questions place people or objects in a line or circle based on given conditions.

8.1 Key Formula: Rank from Top and Bottom

If a person's rank from the top is R(T) and from the bottom is R(B): Total number of people = R(T) + R(B) - 1 Example: Anita is 8th from the top and 15th from the bottom in a queue. Total = 8 + 15 - 1 = 22 people in the queue. Finding rank from opposite end: Rank from bottom = Total + 1 - Rank from top

8.2 Linear Arrangement

In a row of people, use given clues to fix positions. Start with the most definitive clues (person at the extreme left/right end, or someone adjacent to a fixed reference).

Problem	Given Information	Solution
5 friends sit in a row. A is to the left of B. C is at the extreme right. D is between A and B. E is to the left of A.	C is rightmost. B is left of C but right of D. A is between E and D.	Order: E – A – D – B – C
In a class of 40, Raju is 12th from the left. What is his position from the right?	Total = 40, Rank from left = 12	From right = 40 + 1 - 12 = 29th

8.3 Circular Arrangement

In circular arrangement, the positions are relative (no absolute left or right). Fix one person's position as reference and arrange others relative to that person. For circular tables, "to the right of A" means the person sitting clockwise of A.

Circular Arrangement Rule In circular arrangement of N people, the number of distinct arrangements = (N-1)! (one person is treated as fixed). In BPSC questions, you are usually given enough conditions to uniquely determine all positions.

9. Logical Venn Diagrams

Venn diagram questions ask you to represent relationships between groups visually (overlapping circles), or to use given Venn diagrams to answer quantitative questions using set theory.

Key Symbols A ∪ B = Union (all elements in A or B or both) | A ∩ B = Intersection (elements in both A and B) | A' = Complement of A (elements NOT in A)

Inclusion-Exclusion Principle: n(A ∪ B) = n(A) + n(B) - n(A ∩ B) For three sets: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C)

9.1 Worked Examples

Problem	Given	Find	Solution
Students studying Hindi and English	Total=50, Hindi=30, English=25, Both=10	Students studying only Hindi or only English (not both)	Only Hindi=30-10=20; Only English=25-10=15; Total=20+15=35
A town survey on TV and Newspaper	n(TV)=200, n(Newspaper)=150, n(TV∩Newspaper)=80, Total=400	How many read/watch neither?	n(TV∪News)=200+150-80=270; Neither=400-270=130

9.2 Venn Diagram Type Questions

A common BPSC question type shows three overlapping circles labelled (for example) "Doctors," "Lawyers," and "Politicians," with numbers in each region. Questions ask: How many are only doctors? How many are both lawyers and politicians but not doctors? Always assign a variable to each distinct region and use the given totals to solve.

BPSC Important — Venn Diagram with 3 Sets Label the 7 regions: only A, only B, only C, only A&B, only B&C, only A&C, and all three. Write the numbers given directly into these regions. Sum all seven regions to check against the total. This systematic labelling prevents errors.

10. Syllogism

Syllogism questions give two or more statements (premises) and ask which conclusions necessarily follow. The premises are assumed 100% true even if they contradict real-world knowledge.

Four Standard Propositions

Universal Affirmative (A): All A are B.
Universal Negative (E): No A is B.
Particular Affirmative (I): Some A are B.
Particular Negative (O): Some A are not B.

10.1 Quick Inference Rules

Premises	Valid Conclusion	Explanation
All A are B. All B are C.	All A are C.	Transitive: A is fully inside B, B is fully inside C.
All A are B. No B is C.	No A is C.	If A is fully in B, and B has nothing in common with C, then A has nothing in common with C.
All A are B. Some B are C.	Some A are C — NOT necessarily. This is the most common trap.	B may have two parts: the A part and a non-A part. C could only overlap the non-A part.
Some A are B. All B are C.	Some A are C. ✓	The A's that are also B must be in C, since all B are C.
No A is B. Some B are C.	Some C are not A. ✓	The B's that are also C have no overlap with A.

10.2 Solved Example

Statements: All cats are dogs. Some dogs are birds.
Conclusions: I. Some cats are birds. II. Some birds are dogs.

Analysis: Conclusion II follows directly from "Some dogs are birds" (convertible: Some birds are dogs). Conclusion I does NOT necessarily follow — the "some dogs" that are birds might be the non-cat dogs. Answer: Only Conclusion II follows.

Venn Diagram Method for Syllogism Draw circles for each category. Place them in the most conservative (maximum overlap possible) arrangement allowed by the statements. If a conclusion holds in ALL valid diagrams, it follows. If even one valid diagram disproves it, the conclusion does not follow.

11. Puzzle Types

Puzzles integrate multiple reasoning skills into a single problem. They test your ability to organise information systematically and avoid contradiction. BPSC papers occasionally include short 3–5 question puzzles (seating arrangement, comparison, scheduling).

11.1 Comparison Puzzles (Tallest/Heaviest/Oldest)

Given: A is taller than B. C is shorter than D. B is taller than C. D is shorter than A.

Arrange all in order: Compare overlapping pairs. A > D > B > C. Tallest: A. Shortest: C. B is third tallest.

Strategy for comparison puzzles: 1. List all given inequalities. 2. Build a chain by linking common elements. 3. Resolve ambiguities (where no direct comparison exists) by noting "cannot be determined."

11.2 Calendar Problems

Calendar problems ask: If 1st January 2020 is a Wednesday, what day is 1st March 2020?

Key facts: Ordinary year: 365 days = 52 weeks + 1 odd day Leap year: 366 days = 52 weeks + 2 odd days Months and their days: Jan=31, Feb=28(29), Mar=31, Apr=30, May=31, Jun=30, Jul=31, Aug=31, Sep=30, Oct=31, Nov=30, Dec=31 Day advance: Add up days from the reference date, divide by 7, remainder = number of days to advance the starting weekday. Example: Jan 1 = Wednesday. Days in Jan = 31. Days to Mar 1: Jan has 31 days → Feb 1 is 31 days after Jan 1 → 31÷7 = 4r3 → Wed+3 = Saturday (Feb 1) Feb 2020 has 29 days (2020 is a leap year) → 29÷7 = 4r1 → Sat+1 = Sunday (Mar 1) Answer: March 1, 2020 was a Sunday.

11.3 Seating Arrangement Puzzle Strategy

Draw the arrangement format (line / circle / table) on paper immediately.
Place people mentioned with definitive positions first (e.g., "at the extreme left end").
Use clues about adjacency and direction to fill remaining seats.
Check all remaining clues against your completed arrangement to verify.

BPSC Important — Matrix / Grid Puzzles Some BPSC puzzles present a 3×3 or 4×4 matrix with numbers and ask for the missing entry. Look for: row totals, column totals, diagonal patterns, or a rule connecting adjacent entries. Always check row AND column rules before committing to an answer.

12. Exam Strategy for Mental Ability

Mental ability questions reward systematic thinking over speed. With the right strategy, this section can be completed accurately within the allotted time.

Recommended Attempt Order (BPSC Prelims)

Start with Series and Analogy — fastest to solve; 20–30 seconds each if the rule is clear.
Attempt Classification next — usually quick if the common property is obvious.
Blood Relations and Direction Sense — requires a diagram but is methodical; 1–2 minutes each.
Syllogism and Venn Diagrams — medium difficulty; 1–2 minutes each.
Puzzles and Seating Arrangements — leave for last; may take 3–5 minutes; skip if stuck.

Question Type	Expected Time	Elimination Tips
Series Completion	20–45 sec	Eliminate options that don't match the rule even partially
Analogy	20–40 sec	State the relationship aloud; eliminate options with different relationship types
Odd One Out	20–40 sec	Find the property of 3 items; the 4th that lacks it is the answer
Coding-Decoding	45–90 sec	Verify the rule on given coded word before applying; wrong rule gives wrong answer
Blood Relations	60–90 sec	Draw a tree; never solve purely mentally for multi-step problems
Direction Sense	60–90 sec	Draw the movement diagram; calculate displacement only if asked
Ranking / Arrangement	60–90 sec	Use the rank formula; draw a line and place people systematically
Syllogism	60–90 sec	Use Venn circles on rough paper; test each conclusion independently
Complex Puzzles	3–5 min	If not solved in 2 min, skip and return; don't let puzzles eat into other attempts

BPSC Important — Negative Marking Awareness The BPSC CCE Prelims carries negative marking (typically 1/3 mark deducted per wrong answer). Do not guess randomly. Use elimination to narrow down to 2 options before committing. If you cannot narrow down past 3 options, skip the question rather than guess.

Practice Recommendation Solve at least 15–20 reasoning questions daily from previous BPSC Prelims papers and standard reasoning books. The pattern of questions in BPSC has been relatively consistent — mastering the 12 topic types covered in these notes is sufficient to score well in the mental ability section.

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