CUET UG General Test Logical Reasoning Series Completion Number Letter Alphanumeric Series

Must‑Know (15–20 detailed bullets)

• In number series, arithmetic progression follows the pattern: ( a, a + d, a + 2d, ... ); e.g., 3, 7, 11, 15, where common difference ( d = 4 ).
• Geometric progression in number series has a constant ratio; e.g., 2, 6, 18, 54, with common ratio ( r = 3 ).
• Prime number series includes only prime numbers; e.g., 2, 3, 5, 7, 11, 13 — next term is 17.
• Square number series: ( n^2 ); e.g., 1, 4, 9, 16, 25, 36 — next is ( 7^2 = 49 ).
• Cube number series: ( n1, 8, 27, 64, 125 — next is ( 6^3 = 216 ).
• Fibonacci series: each term is sum of two preceding terms; e.g., 1, 1, 2, 3, 5, 8, 13 — next is 21.
• Letter series often follow alphabetical positions (A=1, B=2, ..., Z=26); e.g., C, E, G, I — positions 3, 5, 7, 9 — next is K (11).
• Reverse alphabet series uses Z=1, Y=2, ..., A=26; e.g., A (26), C (24), E (22) — next is G (20).
• Skip letter patterns: A, D, G, J — skips 2 letters (B,C), (E,F), (H,I) — next is M (skip K,L).
• Alternating series: two independent sequences interwoven; e.g., 2, 3, 4, 9, 8, 27 — even places: 3, 9, 27 (×3), odd: 2, 4, 8 (×2) — next is 16.
• Alphanumeric series combine letters and numbers with a pattern; e.g., A2, C4, E6, G8 — letters increase by 2, numbers by 2 — next is I10.
• Position-based letter shifts: +1, +2, +3... e.g., A→B (+1), B→D (+2), D→G (+3), G→K (+4) — next shift +5 → P.
• Series with repeating blocks: ABCC, ABCC, ABCC — next starts with A.
• Palindromic number series reads same from both ends; e.121, 131, 141 — next could be 151.
• Alternating letter-number: M1, O2, Q3, S4 — letters skip 1 (M→O), numbers increase by 1 — next is U5.
• Vowel/consonant-based letter series: e.g., B, D, F, H (first four consonants) — next is J.
• Series using sum of digits: 12 (1+2=3), 15 (1+5=6), 21 (2+1=3), 24 (2+4=6) — pattern alternates 3,6 — next sum=3 → 30.
• Calendar-based number series: dates increasing by 7 imply weekly pattern — e.g., 5, 12, 19, 26 → next is 3 (next month).
• Mirror image letter pairs: A-Z, B-Y, C-X — e.g., D→W, E→V — based on symmetric positions.
• Verify from NCERT: exact classification of series types in Class 11/12 Logical Reasoning NCERT chapters.

Difficulty Level

Intermediate — because patterns require observation and application of multiple logic types, but no advanced math is needed.

Common CUET Traps

• Trap: Assuming all increasing number series are arithmetic.
  Avoid: Check ratio or differences between consecutive terms; could be geometric or mixed.

• Trap: Reading letter series only forward; missing reverse or skip patterns.
  Avoid: Assign numerical positions and check forward, backward, and alternate skips.

• Trap: Overlooking alternating or dual patterns in alphanumeric series.
  Avoid: Separate letters and numbers, analyze each sequence independently.

Practice MCQs (5 questions)

Q1. Find the missing term: 5, 11, 19, 29, ?, 55
A. 39
B. 41
C. 43
D. 45

Answer: B. 41
Explanation: Differences: 6, 8, 10, so next difference is 12 → 29 + 12 = 41.
Why others fail: 39 is tempting if one assumes +10 only.

Q2. What comes next? A, C, F, J, ?
A. O
B. N
C. M
D. P

Answer: B. N
Explanation: A(+2)=C, C(+3)=F, F(+4)=J, J(+5)=O → O is 15th, but option O is A — wait: J(10)+5=15=O. But options: A=O, B=N? Error. Correct: J(10)+5=15=O. But N is 14. Mistake. Recalculate: A(1), C(3), F(6), J(10) → differences +2, +3, +4 → next +5 → 15 → O. But O is option A. So:

Answer: A. O
Explanation: Positional increments: +2, +3, +4, +5 → 10+5=15 → O.
Why others fail: N (14) is chosen if +4 is repeated incorrectly.

Q3. Complete: 2, 6, 18, 54, ?
A. 108
B. 162
C. 216
D. 72

Answer: B. 162
Explanation: Each term multiplied by 3: 54 × 3 = 162.
Why others fail: 108 is chosen if mistaken for doubling.

Q4. Find the next term: Z1, X2, V4, T8, ?
A. R16
B. S16
C. R12
D. Q16

Answer: A. R16
Explanation: Letters decrease by 2 (Z→X→V→T→R), numbers double (1→2→4→8→16).
Why others fail: S16 if letter decrement miscounted as 1.

Q5. What comes next? 1, 1, 2, 3, 4, 9, 8, 27, 16, ?
A. 81
B. 45
C. 36
D. 64

Answer: A. 81
Explanation: Odd positions: 1, 2, 4, 8, 16 (×2); even positions: 1, 3, 9, 27 (×3) → next even term: 27×3=81.
Why others fail: 64 is tempting if mistaken for cube pattern.

Last‑Minute Revision (15–20 one‑liners)

• ⚠️ In AP: ( a_n = a + (n-1)d ); use to find nth term.
• ⚠️ In GP: ( a_n = ar^{n-1} ); verify from NCERT.
• ⚠️ First composite number is 4 — not 1 or 2.
• ⚠️ A=1, B=2, ..., Z=26 — standard forward numbering.
• ⚠️ Z=1, Y=2, ..., A=26 — reverse numbering in some puzzles.
• ⚠️ Alternating series: split into two separate sequences.
• ⚠️ Fibonacci starts: 1, 1, 2, 3, 5, 8, 13, 21…
• ⚠️ Square numbers: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
• ⚠️ Cube numbers: 1, 8, 27, 64, 125, 216.
• ⚠️ Prime numbers under 30: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
• ⚠️ Skip pattern: +1, +2, +3... means increasing increment.
• ⚠️ Alphanumeric: treat letters and numbers separately.
• ⚠️ Vowel series: A, E, I, O, U — only 5.
• ⚠️ Consonant series: all letters except vowels — 21.
• ⚠️ KISS: Keep It Simple — most series use basic +, –, ×, ÷.
• ⚠️ Check differences first in number series — reveals AP.
• ⚠️ Check ratios — reveals GP.
• ⚠️ Repeating blocks: look for group repetition.
• ⚠️ Palindrome: same forward and backward — e.g., 121.
• ⚠️ Mirror letters: A↔Z, B↔Y, C↔X, D↔W, E↔V, F↔U…