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Logical Reasoning · Unit 2

Letter and Symbol Series: MDCAT Notes and MCQs

Number series — what to check (in order)

  1. Differences (constant → arithmetic progression; increasing → check second differences): 2, 6, 12, 20, 30 → diffs 4, 6, 8, 10 → next 42.
  2. Ratios (geometric progression): 3, 9, 27, 81 → ×3.
  3. Squares / cubes: 1, 4, 9, 16 (n²); 1, 8, 27, 64 (n³); n² ± 1.
  4. Mixed operations: ×2 + 1 → 5, 11, 23, 47, 95.
  5. Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29…
  6. Alternate series: two interleaved patterns in odd and even positions.

Letter series

  • Memorize positions: A1 B2 C3 D4 E5 F6 G7 H8 I9 J10 K11 L12 M13 N14 O15 P16 Q17 R18 S19 T20 U21 V22 W23 X24 Y25 Z26. Trick "EJOTY" = 5, 10, 15, 20, 25.
  • Opposite letters sum to 27: A–Z, B–Y, C–X, D–W, M–N.
  • Look for skips (+1, +2, +3…), reverse order, pairs (AZ, BY, CX → DW).

Coding–decoding

Find the shift rule: MEDICAL → NFEJDBM (each letter +1). Letter-value codes: CAT = 3 + 1 + 20 = 24.

PMDC learning outcomes for this unit
  • Series: 5.2.1 Develop arithmetical operations as per numbers.
  • Series: 5.2.2 Develop geometrical progression as per numbers
  • Series: 5.2.3 Develop series / sequential orders as per letters and symbols (according to specific rules).

Letter and Symbol Series MCQs with answers

Practise and track your score →
Q1
Find the next number: 2, 6, 12, 20, 30, ?
A44
B36
C40
D42
Show answer
Answer: D (42). Differences 4, 6, 8, 10, 12 → 30 + 12 = 42 (also n(n+1)).
Q2
Find the next number: 3, 9, 27, 81, ?
A162
B324
C243
D108
Show answer
Answer: C (243). Each term × 3 → 81 × 3 = 243.
Q3
Find the next number: 5, 11, 23, 47, ?
A93
B96
C94
D95
Show answer
Answer: D (95). Rule: × 2 + 1 → 47 × 2 + 1 = 95.
Q4
Find the next letter: A, C, F, J, O, ?
AT
BU
CS
DV
Show answer
Answer: B (U). Gaps +2, +3, +4, +5, +6 → O(15) + 6 = U(21).
Q5
Find the next pair: AZ, BY, CX, ?
AEW
BDW
CDX
DDV
Show answer
Answer: B (DW). First letter moves forward, second backward: D and W.
Q6
Find the next term: Z, X, V, T, ?
AR
BP
CQ
DS
Show answer
Answer: A (R). Skip one letter backwards each time: T → R.
Q7
Find the odd one out: 8, 27, 64, 100, 125
A27
B125
C100
D64
Show answer
Answer: C (100). All others are perfect cubes; 100 is not.
Q8
If MEDICAL is coded as NFEJDBM, how is DOCTOR coded?
AEPCUPS
BEPDUQS
CEPDUPS
DCNBSNQ
Show answer
Answer: C (EPDUPS). Each letter is shifted +1: D→E, O→P, C→D, T→U, O→P, R→S.
Q9
If CAT = 24 (sum of letter positions), then DOG = ?
A26
B24
C25
D27
Show answer
Answer: A (26). D(4) + O(15) + G(7) = 26.
Q10
Find the next number: 2, 3, 5, 7, 11, ?
A12
B13
C17
D15
Show answer
Answer: B (13). Series of prime numbers; next is 13.