Reasoning: series, codes and relationships
Spot the rule, then apply it: differences or ratios for number series, alphabet positions for letters and codes, and a family tree for blood relations.
Worked example: number series
Find the next term: 4, 9, 19, 39, 79, ?
- Differences: 9 − 4 = 5, 19 − 9 = 10, 39 − 19 = 20, 79 − 39 = 40.
- The differences double each time, so the next difference is 80.
- 79 + 80 = 159.
- Check with the rule ×2 + 1: 4 × 2 + 1 = 9, 9 × 2 + 1 = 19, 19 × 2 + 1 = 39, 39 × 2 + 1 = 79, 79 × 2 + 1 = 159.
159. Shortcut: if the differences double (or triple), test ×2 + k (or ×3 + k) directly on the terms.
Worked example: letter series
Find the next term: AZ, CX, FU, JQ, ?
- Write positions: A 1, Z 26; C 3, X 24; F 6, U 21; J 10, Q 17.
- First letters: 1, 3, 6, 10 rise by 2, 3, 4, so the next is 10 + 5 = 15 = O.
- Second letters: 26, 24, 21, 17 fall by 2, 3, 4, so the next is 17 − 5 = 12 = L.
- Check: each pair adds to 27 (opposite letters), and O + L = 15 + 12 = 27.
OL. Shortcut: use EJOTY (5, 10, 15, 20, 25) to find any position fast, and test pairs for a sum of 27.
Worked example: coding-decoding
If TEACHER is coded as VGCEJGT, how is STUDENT coded?
- Compare letter by letter: T → V, E → G, A → C, C → E, H → J, E → G, R → T.
- Every letter moves 2 places forward (+2).
- Apply +2 to STUDENT: S → U, T → V, U → W, D → F, E → G, N → P, T → V.
UVWFGPV. Shortcut: check the first, second and last letters; if the shift is the same, apply it to all and verify once against the given pair.
Worked example: blood relations
Pointing to a girl in a photograph, Arun says, 'Her mother is the only daughter of my mother-in-law.' How is the girl related to Arun?
- Start from the end: Arun's mother-in-law is his wife's mother.
- Her only daughter is therefore Arun's wife.
- So the girl's mother is Arun's wife.
- The girl is the daughter of Arun and his wife.
Daughter. Shortcut: read backwards from 'my', replace each phrase with one relation, and sketch a small tree marking + for male and − for female.
NET gives 4-6 term series with one blank or wrong term, letter-shift codes, and one-line blood relations ('pointing to a photo…'). Types of reasoning appear as deductive vs inductive statement questions.
Typical MCQ: “Find the next term: 2, 6, 12, 20, 30, ?” 42. The differences are 4, 6, 8, 10, so add 12; or note the terms are n(n + 1).
Typical MCQ: “Is 'All metals conduct electricity; copper is a metal; so copper conducts electricity' inductive or deductive?” Deductive: it goes from a general rule to a particular case, so the conclusion is certain if the premises are true.
EJOTY gives 5-10-15-20-25. Opposite letters always add to 27. In blood relations, read backwards from 'my'.