Logical Reasoning 14 Solved Past Papers 2022 – 2025 Archives

Set Theory, Integer Bounds & Arithmetic Past Papers

Solved past paper MCQs for Set Theory, Integer Bounds & Arithmetic 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

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#1 of 14 Balochistan MDCAT 2025

[Balochistan MDCAT 2025]

What would be the result of: \(10 - 3 \times 2\)?

View Answer & Propolis Autopsy

Correct Key: Option A Diagnostic Explanation

Concept: Arithmetic Order of Operations (BODMAS/PEMDAS).

Formula: Perform multiplication before subtraction.

Solution:

First multiply: \(3 \times 2 = 6\)

Then subtract: \(10 - 6 = 4\)

Why other options are incorrect:

• Option C: Incorrectly performs subtraction first: \((10 - 3) \times 2 = 14\).

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#2 of 14 Federal MDCAT 2025

[Federal MDCAT 2025]

Every alphabet in the word "SURGEON" represents a fixed numerical value and the numbers when added, sum up to 99. Based on this, what will be the sum of the word "EORGNSU"?

102

View Answer & Propolis Autopsy

Correct Key: Option C Diagnostic Explanation

Concept: Anagram Numerical Equivalence.

Formula: \(\sum \text{Letter values} = \text{Constant}\)

Solution: "EORGNSU" is an anagram containing the exact same set of letters as "SURGEON". Since each letter's numerical value is fixed, the total sum remains unchanged at 99.

Why other options are incorrect:

• Options A, B, and D: Arbitrary numbers that ignore the principle of algebraic addition of identical variables.

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#3 of 14 NUMS 2025

Every alphabet in the word "SURGEON" represent a fixed numerical value and the numbers when added, sum up to 99. Based on this, what will be the sum of the word "EORGNSU".

102

View Answer & Propolis Autopsy

Correct Key: Option C Diagnostic Explanation

Concept: Commutative Property of Variable Sums.

Formula: \(A+B+C = C+B+A\)

Solution: Reordering letter variables leaves their numerical total invariant.

Why other options are incorrect:

• Options A, B, and D: Disregard the basic algebraic principle that changing variable order does not alter sum.

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#4 of 14 BUMHS 2025

[BUMHS 2025]

What would be the result of: \(10 - 3 \times 2\)?

View Answer & Propolis Autopsy

Correct Key: Option A Diagnostic Explanation

Concept: Order of Operations.

Formula: Multiplication before subtraction.

Solution:

\(10 - (3 \times 2) = 10 - 6 = 4\).

Why other options are incorrect:

• Option C: Evaluates left-to-right: \((10 - 3) \times 2 = 14\).

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#5 of 14 SZABMU 2025

[SZABMU 2025]

Every alphabet in the word "SURGEON" represent a fixed numerical value and the numbers when added, sum up to 99. Based on this, what will be the sum of the word "EORGNSU".

102

View Answer & Propolis Autopsy

Correct Key: Option C Diagnostic Explanation

Concept: Anagram Sum Equivalence.

Formula: N/A

Solution: Identical letters maintain an identical total sum of 99.

Why other options are incorrect:

• Options A, B, and D: Violate fixed variable algebraic sum rules.

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#6 of 14 FMDC 2024 / SZABMU 2024

[FMDC 2024 / SZABMU 2024]

In a group of 100 players, 70 play football, 50 play hockey, and 55 play cricket. 30 play both hockey and cricket, 25 play both football and hockey, and 20 play all three games. How many players play both football and cricket?

View Answer & Propolis Autopsy

Correct Key: Option C Diagnostic Explanation

Concept: Three-Set Inclusion-Exclusion Principle.

Formula: \(|F \cap C| = (F \cap H) + (H \cap C) - (F \cap H \cap C)\)

Solution:

Using set overlaps: \(25 + 30 - 20 = 35\).

Why other options are incorrect:

• Options A, B, and D: Fail to account for the triple-intersection set of 20 players.

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#7 of 14 Sindh MDCAT 2024 / DUHS 2024

[Sindh MDCAT 2024 / DUHS 2024]

Which number is a multiple of its digits?

View Answer & Propolis Autopsy

Correct Key: Option D Diagnostic Explanation

Concept: Divisibility & Digit Product Rules.

Formula: \(N \pmod{d_1 \times d_2} = 0\)

Solution: Digits of 24 are 2 and 4. Product = \(2 \times 4 = 8\). Since \(24 / 8 = 3\), 24 is a multiple of its digits' product.

Why other options are incorrect:

• Option A: Digits product = 2; 21 is odd (not divisible by 2).

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#8 of 14 UHS MDCAT 2024

[UHS MDCAT 2024]

P, Q and R are one-digit, non-negative numbers. P is the smallest even number. Q is the largest odd number. R is 5.

Which of the following is true?

P + Q + R = 16

P + Q + R = 12

(Q + R) × P = 30

(Q + R) × P = 8

View Answer & Propolis Autopsy

Correct Key: Option A Diagnostic Explanation

Concept: Number Property Evaluation.

Formula: \(P = 2, Q = 9, R = 5\)

Solution:

Smallest positive single-digit even number \(P = 2\).

Largest single-digit odd number \(Q = 9\).

\(P + Q + R = 2 + 9 + 5 = 16\).

Why other options are incorrect:

• Option C: Calculates \((9 + 5) \times 2 = 28\) (not 30).

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#9 of 14 UHS MDCAT 2024

[UHS MDCAT 2024]

X, Y and Z are three whole numbers less than 24 but greater than 11. X is the smallest prime number in this range. Y is the largest number divisible by 3. Z is the smallest number divisible by 11.

X is 13, Y is 24, Z is 11

X is 13, Y is 21, Z is 22

X is 11, Y is 21, Z is 11

X is 11, Y is 24, Z is 22

View Answer & Propolis Autopsy

Correct Key: Option B Diagnostic Explanation

Concept: Number Bounds & Factors.

Formula: Bounds = \(12 \le N \le 23\).

Solution:

Smallest prime in range = 13 (\(X\)).

Largest multiple of 3 in range = 21 (\(Y\)).

Smallest multiple of 11 in range = 22 (\(Z\)).

Why other options are incorrect:

• Option A: Includes 24 and 11 which violate strictly 'less than 24 and greater than 11'.

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#10 of 14 Balochistan MDCAT 2023

[Balochistan MDCAT 2023]

X, Y and Z are three whole numbers less than 31 but greater than 23. X is a prime number. Y is the largest odd number smaller than 31. Z is the smallest even number.

X is 31, Y is 29 and Z is 24

X is 29, Y is 29 and Z is 24

X is 23, Y is 29 and Z is 24

X is 27, Y is 31 and Z is 26

View Answer & Propolis Autopsy

Correct Key: Option B Diagnostic Explanation

Concept: Integer Range Boundaries.

Formula: Range = \(24 \le N \le 30\).

Solution:

Prime in range = 29 (\(X\)).

Largest odd < 31 in range = 29 (\(Y\)).

Smallest even > 23 in range = 24 (\(Z\)).

Why other options are incorrect:

• Option A: Includes 31 which violates 'less than 31'.

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#11 of 14 KMU MDCAT 2023 Retake

[KMU MDCAT 2023 Retake]

Some months have 31 days, how many have 28?

One month and that is February

February, every 4 years

All months have 28 days

None

View Answer & Propolis Autopsy

Correct Key: Option C Diagnostic Explanation

Concept: Literal Word Riddles.

Formula: N/A

Solution: Every single month of the calendar year contains at least 28 days.

Why other options are incorrect:

• Options A and B: Fall for the misinterpretation that only February has 28 days.

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#12 of 14 UHS MDCAT 2023

[UHS MDCAT 2023]

X, Y and Z are three whole numbers less than 31 but greater than 23. X is a prime number. Y is the largest odd number smaller than 35. Z is the smallest even number?

X is 31, Y is 29 and Z is 24

X is 29, Y is 29 and Z is 24

X is 23, Y is 29 and Z is 24

X is 27, Y is 31 and Z is 26

View Answer & Propolis Autopsy

Correct Key: Option B Diagnostic Explanation

Concept: Bounded Interval Whole Numbers.

Formula: Interval = \((23, 31)\).

Solution: Prime = 29 (X), Max odd < 35 in range = 29 (Y), Min even = 24 (Z).

Why other options are incorrect:

• Option A: Includes interval boundary 31.

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#13 of 14 Balochistan MDCAT / BUMHS 2022

[Balochistan MDCAT / BUMHS 2022]

X, Y and Z are three whole numbers less than 31 but greater than 23. X is a prime number. Y is the largest odd number smaller than 35. Z is the smallest even number.

X is 31, Y is 29 and Z is 24

X is 29, Y is 29 and Z is 24

X is 23, Y is 29 and Z is 24

X is 27, Y is 31 and Z is 26

View Answer & Propolis Autopsy

Correct Key: Option B Diagnostic Explanation

Concept: Whole Number Sets.

Formula: Interval = \((23, 31)\).

Solution: Prime = 29, Max odd = 29, Min even = 24.

Why other options are incorrect:

• Option A: Includes upper boundary 31.

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#14 of 14 FMDC / SZABMU 2022

[FMDC / SZABMU 2022]

X, Y and Z are three whole numbers less than 24 but greater than 11. X is the smallest prime number. Y is the largest number divisible by 3. Z is the smallest number divisible by 11.

X is 13, Y is 24, Z is 11

X is 13, Y is 21, Z is 22

X is 11, Y is 21, Z is 11

X is 11, Y is 24, Z is 22

View Answer & Propolis Autopsy

Correct Key: Option B Diagnostic Explanation

Concept: Integer Interval Bounds.

Formula: Interval = \((11, 24)\).

Solution: Smallest prime = 13 (X), Largest multiple of 3 = 21 (Y), Smallest multiple of 11 = 22 (Z).

Why other options are incorrect:

• Option A: Includes boundary values 24 and 11.

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Percentages, Ratios & Unit Calculations

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Linear Ranking, Ordering & Inequalities

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