Paper IPaper I · General Mental Ability

Verbal Reasoning

Number and letter series, analogy, classification, coding and decoding, blood relations, and direction sense

CAPF wiki•4 min read•15 sections

At a glance

PaperPaper ISubjectGMASyllabusGeneral Mental Ability: logical reasoningImportanceHigh

GMAReasoningSeriesAnalogyCoding DecodingBlood RelationsDirection SensePaper 1

Verbal reasoning rewards pattern spotting more than calculation. Each sub-type has a small set of recurring patterns; once you can name the pattern, the answer is usually immediate.

The sub-types and their core method

Sub-type	What to look for
Number series	Constant difference, constant ratio, squares, cubes, alternating rules
Letter series	Position shift in the alphabet (A=1 ... Z=26), forward or backward steps
Analogy	The relation in A : B, applied to C : ?
Classification (odd one out)	The shared property that all but one item have
Coding and decoding	Letter shift, reversal, position-number, or symbol substitution
Blood relations	Build a small family tree; track generation and gender
Direction sense	Draw a rough map; track turns and net displacement

Alphabet positions (worth memorising in blocks of five)

A=1, B=2, C=3, D=4, E=5; F=6 ... J=10; K=11 ... O=15; P=16 ... T=20; U=21 ... Z=26. The 13th letter is M, the 14th is N (the EJOTY trick: E=5, J=10, O=15, T=20, Y=25 mark every fifth letter).

Worked examples

Example 1: Number series

Find the next term: 2, 6, 12, 20, 30, ?

Differences are 4, 6, 8, 10, so the next difference is 12. 30 + 12 = 42. (These are n(n+1): 1.2, 2.3, 3.4, ... so the sixth is 6.7 = 42.)

Example 2: Number series with squares

Find the next term: 1, 4, 9, 16, 25, ?

These are 1², 2², 3², 4², 5², so the next is 6² = 36.

Example 3: Letter series

Find the next term: B, D, G, K, ?

Positions 2, 4, 7, 11. Differences 2, 3, 4, so the next gap is 5: 11 + 5 = 16, which is P.

Example 4: Coding and decoding

If CAT is coded as DBU, how is DOG coded?

Each letter shifts forward by one (C to D, A to B, T to U). D to E, O to P, G to H, so DOG becomes EPH.

Example 5: Analogy

Doctor : Hospital :: Teacher : ?

A doctor works in a hospital; a teacher works in a school. Answer: School.

Example 6: Blood relations

Pointing to a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man?

"The only daughter of my mother" is the woman herself. So the man's mother is the woman. The woman is his mother.

Example 7: Direction sense

A soldier walks 5 km north, turns east and walks 4 km, then turns south and walks 5 km. How far is he from the start, and in which direction?

The 5 km north and 5 km south cancel. He is left 4 km east of the start. Distance = 4 km, direction = east.

Example 8: Classification

Which is the odd one out: 3, 5, 11, 15, 17?

All are prime except 15 (which is 3 times 5). Answer: 15.

Shortcut tips

For number series, always write the differences first; if they are not constant, check ratios, then squares or cubes, then an alternating two-rule pattern.
For letter series, convert to position numbers; the pattern is usually obvious in numbers.
In coding, test the simplest hypothesis first: a fixed forward or backward shift. If that fails, try reversal or position-number coding.
In blood relations, "only daughter of my mother" is "myself" if the speaker is female; "only son of my father" is "myself" if male. Resolve these phrases before drawing the tree.
In direction problems, opposite legs (north and south, east and west) subtract; use the right-angle distance (Pythagoras) only when both axes have a net displacement.

Practice questions

Find the next term: 3, 6, 11, 18, 27, ?
Find the next term: 5, 10, 20, 40, ?
Find the next letter: A, C, F, J, ?
If RED is coded 18-5-4 (position numbers), code the word SUN.
If FACE is coded as GBDF, decode HBSE.
Pen : Write :: Knife : ?
Find the odd one out: 8, 27, 64, 100, 125.
A woman introduces a man as "the son of the brother of my mother." How is the man related to the woman?
A man walks 3 km east, then 4 km north. How far is he from the start?
Find the missing term: AZ, BY, CX, ?

Answer key

Reveal the answer key and full worked solutions

Differences 3, 5, 7, 9, next 11; 27 + 11 = 38.
Each term doubles; 40 times 2 = 80.
Positions 1, 3, 6, 10 (differences 2, 3, 4); next gap 5; 10 + 5 = 15 = O.
S=19, U=21, N=14, so 19-21-14.
Each letter shifted back by one: H to G, B to A, S to R, E to D, giving GARD. (Forward shift in coding means backward shift to decode.)
A pen is used to write; a knife is used to cut. Answer: Cut.
8, 27, 64, 125 are cubes (2³, 3³, 4³, 5³); 100 is not a cube. Answer: 100.
The brother of her mother is her maternal uncle; his son is her cousin. Answer: cousin.
√(3² + 4²) = √(9 + 16) = √(25) = 5 km.
First letters A, B, C go forward; second letters Z, Y, X go backward; next is DW.