Logical Reasoning 22 Solved Past Papers 2022 – 2025 Archives

Letter Series & Coding-Decoding Past Papers

Solved past paper MCQs for Letter Series & Coding-Decoding from official UHS, NUMS, SZABMU, DUHS, and KMU examinations. Includes verified distractor autopsies and step-by-step cognitive explanations.

Boards Included: BUMHS MDCAT NUMS SZABMU UHS
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#1 of 22 Balochistan MDCAT 2025
[Balochistan MDCAT 2025]

CAT is to DOG, as MOUSE is to:
A
RAT
B
CAT
C
DOG
D
CHEESE
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Verbal Analogies – Category Categorization.

Formula: N/A

Solution: Cat and Dog form a pair of common household domestic animals. Similarly, Mouse and Rat form a pair of closely related common rodents.

Why other options are incorrect:

Option D: 'Cheese' is a food associated with mice, not a taxonomic/category equivalent.
#2 of 22 Federal MDCAT 2025
[Federal MDCAT 2025]

ZX, WU, TR, QO.. What comes next?
A
NL
B
LN
C
NM
D
KH
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Letter Pair Series Progression.

Formula: Shift both letters back by 3 positions (\(-3\)).

Solution:

  • 1st letters: Z \(\xrightarrow{-3}\) W \(\xrightarrow{-3}\) T \(\xrightarrow{-3}\) Q \(\xrightarrow{-3}\) N


  • 2nd letters: X \(\xrightarrow{-3}\) U \(\xrightarrow{-3}\) R \(\xrightarrow{-3}\) O \(\xrightarrow{-3}\) L


Result pair = NL.

Why other options are incorrect:

Option B: Reverses the letter order (LN instead of NL).
#3 of 22 NUMS 2025
What comes next? ZX, WU, TR, QO, ____
A
NL
B
LN
C
NM
D
KH
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Alphabetical Decrement Pattern.

Formula: Step back 3 letters per variable.

Solution:

  • \(Q - 3 = N\)


  • \(O - 3 = L\)


Term = NL.

Why other options are incorrect:

Option B: Incorrect letter ordering.
#4 of 22 Sindh MDCAT 2025
[Sindh MDCAT 2025]

A spying agent coded POWER as QPXFS.

Using this pattern, what will be the code for GUNBD?
A
HVPFE
B
HVOCE
C
HVNDE
D
HVODE
View Answer & Propolis Autopsy
Correct Key: Option B Diagnostic Explanation
Concept: Substitution Coding – Forward Alphabet Shift.

Formula: \(\text{Code Letter} = \text{Original Letter} + 1\)

Solution:

  • G \(\xrightarrow{+1}\) H


  • U \(\xrightarrow{+1}\) V


  • N \(\xrightarrow{+1}\) O


  • B \(\xrightarrow{+1}\) C


  • D \(\xrightarrow{+1}\) E


Resulting code = HVOCE.

Why other options are incorrect:

Option A: Shifts 'N' incorrectly to 'P'.

Option C: Leaves 'N' unchanged.
#5 of 22 Sindh MDCAT 2025
[Sindh MDCAT 2025]

Identify the next letter in the pattern:

M, N, P, Q, S, ??
A
T
B
U
C
V
D
W
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Alphabetical Position Series.

Formula: Sequential pattern of \(+1, +2, +1, +2, +1\).

Solution:

  • M (13) \(\xrightarrow{+1}\) N (14)


  • N (14) \(\xrightarrow{+2}\) P (16)


  • P (16) \(\xrightarrow{+1}\) Q (17)


  • Q (17) \(\xrightarrow{+2}\) S (19)


  • S (19) \(\xrightarrow{+1}\) T (20)


Why other options are incorrect:

Options B, C, and D: Represent incorrect step sizes.
#6 of 22 BUMHS 2025
[BUMHS 2025]

CAT is to DOG, as MOUSE is to:
A
RAT
B
CAT
C
DOG
D
CHEESE
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Semantic Category Pairings.

Formula: N/A

Solution: Cat and Dog pair as household pets; Mouse and Rat pair as common rodents.

Why other options are incorrect:

Option D: 'Cheese' is a food, not a taxonomic pair.
#7 of 22 DUHS 2025
[DUHS 2025]

A spying agent coded POWER as QPXFS. Using this pattern, what will be the code for GUNBD?
A
HVPFE
B
HVOCE
C
HVNDE
D
HVODE
View Answer & Propolis Autopsy
Correct Key: Option B Diagnostic Explanation
Concept: Shift Coding.

Formula: \(+1\) shift.

Solution: G\(\to\)H, U\(\to\)V, N\(\to\)O, B\(\to\)C, D\(\to\)E \(\implies\) HVOCE.

Why other options are incorrect:

Option A: Shifts N incorrectly to P.
#8 of 22 DUHS 2025
[DUHS 2025]

M, N, P, Q, S, ??
A
T
B
U
C
V
D
W
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Letter Progression.

Formula: Alternating \(+1, +2\) step.

Solution: \(S (19) + 1 = T (20)\).

Why other options are incorrect:

Option B: Adds 2 instead of 1.
#9 of 22 SZABMU 2025
[SZABMU 2025]

What comes next? ZX, WU, TR, QO, ____
A
NL
B
LN
C
NM
D
KH
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Letter Pair Decrement.

Formula: \(-3\) per letter.

Solution: Q(-3)\(\to\)N, O(-3)\(\to\)L \(\implies\) NL.

Why other options are incorrect:

Option B: Reversed letter pair.
#10 of 22 FMDC 2024 / SZABMU 2024
[FMDC 2024 / SZABMU 2024]

What are the missing alphabets in the sequence:

EZFA, GBHY, IXJC, _?
A
KDLW
B
KLDW
C
KWLD
D
LDKW
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Four-Variable Letter Progression.

Formula: Apply individual positional increments.

Solution:

  • 1st letter: E \(\xrightarrow{+2}\) G \(\xrightarrow{+2}\) I \(\xrightarrow{+2}\) K


  • 2nd letter: Z \(\xrightarrow{+2}\) B \(\xrightarrow{+2}\) D... (Wait, Z \(\to\) B \(\to\) X \(\to\) D pattern): D


  • 3rd letter: F \(\xrightarrow{+2}\) H \(\xrightarrow{+2}\) J \(\xrightarrow{+2}\) L


  • 4th letter: A \(\xrightarrow{-2}\) Y \(\xrightarrow{+4}\) C \(\xrightarrow{-6}\) W


Term = KDLW.

Why other options are incorrect:

Options B, C, and D: Transpose character positions.
#11 of 22 Sindh MDCAT 2024 / DUHS 2024
[Sindh MDCAT 2024 / DUHS 2024]

Identify the pattern and choose the correct option that should follow next:

VSA, WRD, XQG, YPJ, _
A
VTC
B
TLK
C
MOZ
D
ZOM
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Triple Letter Series.

Formula: Apply distinct positional shifts per letter position.

Solution:

  • 1st letter: V \(\xrightarrow{+1}\) W \(\xrightarrow{+1}\) X \(\xrightarrow{+1}\) Y \(\xrightarrow{+1}\) Z


  • 2nd letter: S \(\xrightarrow{-1}\) R \(\xrightarrow{-1}\) Q \(\xrightarrow{-1}\) P \(\xrightarrow{-1}\) O


  • 3rd letter: A \(\xrightarrow{+3}\) D \(\xrightarrow{+3}\) G \(\xrightarrow{+3}\) J \(\xrightarrow{+3}\) M


Term = ZOM.

Why other options are incorrect:

Options A and B: Apply backward shifts to the first variable.
#12 of 22 UHS MDCAT 2024
[UHS MDCAT 2024]

Observe the pattern and select the next term in the sequence:

JEQ, HEO, FEM, _?
A
GFN
B
DEK
C
GEL
D
DFK
View Answer & Propolis Autopsy
Correct Key: Option B Diagnostic Explanation
Concept: Pattern Dissection.

Formula: Shift positions 1 and 3 by \(-2\); keep center constant.

Solution:

  • 1st letter: J \(\xrightarrow{-2}\) H \(\xrightarrow{-2}\) F \(\xrightarrow{-2}\) D


  • 2nd letter: E \(\to\) E \(\to\) E \(\to\) E


  • 3rd letter: Q \(\xrightarrow{-2}\) O \(\xrightarrow{-2}\) M \(\xrightarrow{-2}\) K


Term = DEK.

Why other options are incorrect:

Option A: Shifts first letter forward.
#13 of 22 Balochistan MDCAT 2023
[Balochistan MDCAT 2023]

Observe the pattern and select the next term in the series:

TEAM, TAME, TMEA, ____
A
MUET
B
TEAM
C
TAUM
D
MEAT
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Positional Letter Permutation.

Formula: Cyclic swap steps.

Solution: Swapping the first character ('T') to the end progressively yields MEAT.

Why other options are incorrect:

Option A: Introduces 'U' which is not in the original word.
#14 of 22 KMU MDCAT 2023 Retake
[KMU MDCAT 2023 Retake]

Mice are to cats as goats are to:
A
Snakes
B
Hippos
C
Horses
D
Lions
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Trophic Predator-Prey Analogies.

Formula: N/A

Solution: Cats prey on mice; lions prey on goats.

Why other options are incorrect:

Options A, B, and C: Non-predatory relationships to goats.
#15 of 22 KMU MDCAT 2023 Retake
[KMU MDCAT 2023 Retake]

Observe the pattern and select the next term in the sequence:

P5QR, P4QS, P3QT, _, P1QV
A
P2QU
B
PQ3U2
C
P2QUY
D
PQ3U
View Answer & Propolis Autopsy
Correct Key: Option A Diagnostic Explanation
Concept: Alphanumeric Sequence Progression.

Formula: Number decrements by 1; last letter advances by 1.

Solution:

  • Number: 5 \(\to\) 4 \(\to\) 3 \(\to\) 2 \(\to\) 1


  • Suffix: R \(\to\) S \(\to\) T \(\to\) U \(\to\) V


Term = P2QU.

Why other options are incorrect:

Option B: Scrambles variable position.
#16 of 22 KMU MDCAT 2023
[KMU MDCAT 2023]

Complete the following series:

KCD, LEF, MGH, _ , OKL.
A
NQM
B
PJI
C
NIJ
D
NJI
View Answer & Propolis Autopsy
Correct Key: Option C Diagnostic Explanation
Concept: Triple-Letter Incremental Pattern.

Formula: \(+1\) shift for first letter, \(+2\) shift for second and third letters.

Solution:

  • 1st letter: K \(\xrightarrow{+1}\) L \(\xrightarrow{+1}\) M \(\xrightarrow{+1}\) N


  • 2nd letter: C \(\xrightarrow{+2}\) E \(\xrightarrow{+2}\) G \(\xrightarrow{+2}\) I


  • 3rd letter: D \(\xrightarrow{+2}\) F \(\xrightarrow{+2}\) H \(\xrightarrow{+2}\) J


Term = NIJ.

Why other options are incorrect:

Option D: Reverses the last two letters.
#17 of 22 Sindh MDCAT 2023
[Sindh MDCAT 2023]

If 'blue' is called 'green', 'green' is called 'white', 'white' is called 'red', and 'red' is called 'yellow', what is the color of milk?
A
White
B
Green
C
Yellow
D
Red
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Artificial Language Substitution.

Formula: N/A

Solution: Natural color of milk is white. In this code, 'white' is designated as 'red'.

Why other options are incorrect:

Option A: Uses the uncoded literal color.
#18 of 22 UHS MDCAT 2023
[UHS MDCAT 2023]

Observe the pattern and select the next term in the sequence:

SSSSSS, SSRSS, SRQRS, RQPQR, ?
A
RQDQR
B
QRORQ
C
RQPOPQR
D
QPOPQ
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Symmetrical Central Letter Shift.

Formula: Inner letters shift backward in alphabet.

Solution: Following the inward expansion of reverse alphabetical characters yields QPOPQ.

Why other options are incorrect:

Options A and B: Violate the inner character sequence.
#19 of 22 KPK MDCAT / KMU 2022
[KPK MDCAT / KMU 2022]

In a certain language, REMOTE is coded as ROTEME. Which word would be coded as PNIICC?
A
PINCIC
B
PNICIC
C
PICNIC
D
PICCIN
View Answer & Propolis Autopsy
Correct Key: Option C Diagnostic Explanation
Concept: Structural Transposition Coding.

Formula: Swap letters 2\(\leftrightarrow\)4 and 3\(\leftrightarrow\)5.

Solution: Applying the swap rule to PICNIC yields PNIICC.

Why other options are incorrect:

Option A: Produces incorrect letter ordering.
#20 of 22 KPK MDCAT / KMU 2022
[KPK MDCAT / KMU 2022]

Find the term which does NOT fit into the sequence:

1 CV, 5 FU, 9 IT, 15 LS, 17 OR
A
17 OR
B
5 FU
C
9 IT
D
15 LS
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Sequence Anomaly Detection.

Formula: Number pattern = \(+4\); 1st letter = \(+3\); 2nd letter = \(-1\).

Solution:

  • Numbers: 1 \(\xrightarrow{+4}\) 5 \(\xrightarrow{+4}\) 9 \(\xrightarrow{+4}\) 13 (not 15) \(\xrightarrow{+4}\) 17.


  • Letters: C \(\xrightarrow{+3}\) F \(\xrightarrow{+3}\) I \(\xrightarrow{+3}\) L \(\xrightarrow{+3}\) O.


  • Letters: V \(\xrightarrow{-1}\) U \(\xrightarrow{-1}\) T \(\xrightarrow{-1}\) S \(\xrightarrow{-1}\) R.


The term 15 LS breaks the arithmetic number progression (should be 13 LS).

Why other options are incorrect:

Options A, B, and C: Conform strictly to the arithmetic and alphabetical rules.
#21 of 22 Sindh MDCAT / DUHS 2022
[Sindh MDCAT / DUHS 2022]

What should come next in the series?

7C, 10F, 14J, 19O, ___
A
23Q
B
26N
C
27X
D
25U
View Answer & Propolis Autopsy
Correct Key: Option D Diagnostic Explanation
Concept: Dual Incremental Progression.

Formula: Add consecutive natural integers (\(+3, +4, +5, +6\)).

Solution:

  • Number sequence: 7 \(\xrightarrow{+3}\) 10 \(\xrightarrow{+4}\) 14 \(\xrightarrow{+5}\) 19 \(\xrightarrow{+6}\) 25


  • Letter sequence: C (3) \(\xrightarrow{+3}\) F (6) \(\xrightarrow{+4}\) J (10) \(\xrightarrow{+5}\) O (15) \(\xrightarrow{+6}\) U (21)


Combined term = 25U.

Why other options are incorrect:

Option A: Uses a constant \(+4\) step on numbers.
#22 of 22 Punjab MDCAT / UHS 2022
[Punjab MDCAT / UHS 2022]

Observe the pattern and select the next term in the sequence:

CAB, FAE, IAH, ___
A
JHK
B
LAK
C
JGK
D
IGJ
View Answer & Propolis Autopsy
Correct Key: Option B Diagnostic Explanation
Concept: Constant and Variable Letter Shifts.

Formula: First/Third letters shift by \(+3\); middle letter remains constant ('A').

Solution:

  • 1st letter: C \(\xrightarrow{+3}\) F \(\xrightarrow{+3}\) I \(\xrightarrow{+3}\) L


  • 2nd letter: A \(\to\) A \(\to\) A \(\to\) A


  • 3rd letter: B \(\xrightarrow{+3}\) E \(\xrightarrow{+3}\) H \(\xrightarrow{+3}\) K


Term = LAK.

Why other options are incorrect:

Option A: Shifts first letter by \(+1\) instead of \(+3\).
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