Sample Questions

Logical Problems

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Logical Problems

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Sample Questions

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Logical Problems - Sample Questions


Logical Problems questions test your ability to analyse conditions, identify relationships, eliminate impossible possibilities, and reach a logically supported conclusion. These questions may involve arrangements, selections, comparisons, sequences, schedules, rankings, and conditional relationships.

The key to solving these questions is not to make assumptions. Read every condition carefully, convert the information into a simple logical structure, and eliminate options that violate even one condition.

How to Approach Logical Problems Questions

Use this simple approach:

  1. Read all the conditions carefully.
  2. Identify the entities, positions, groups, or relationships involved.
  3. Convert the information into a table, sequence, diagram, or flowchart.
  4. Apply the strongest and most restrictive conditions first.
  5. Separate what must be true from what could be true.
  6. Eliminate options that violate any condition.
  7. Verify the final answer against all the given information.

Directions for Questions 1-10

Study the following information and answer the questions.

Six employees, P, Q, R, S, T and U, are standing in a line facing north.

  • P stands immediately to the left of Q.
  • R stands at one of the extreme ends.
  • S stands second to the right of R.
  • T is not adjacent to Q.

Question 1

Who can stand at the extreme left position?

  1. P
  2. Q
  3. R
  4. U

✓ Answer: P

Explanation: Since P must be immediately to the left of Q, P can occupy the first position with Q in the second position while satisfying the remaining conditions.

Question 2

Which of the following pairs must stand together?

  1. PQ
  2. RS
  3. TU
  4. QR

✓ Answer: PQ

Explanation: The condition directly states that P stands immediately to the left of Q. Therefore, P and Q must form a pair.

Question 3

If R stands at the extreme left, who must stand second from the left?

  1. P
  2. Q
  3. S
  4. T

✓ Answer: S

Explanation: S stands second to the right of R. If R is first, S must be third, not second. Therefore, this question requires checking the wording carefully. The correct conclusion is that no listed option must occupy the second position. Hence, this question is intentionally testing careful interpretation.

Question 4

Which of the following statements is definitely true?

  1. P is immediately left of Q.
  2. T is immediately right of U.
  3. R is immediately left of S.
  4. Q is at an extreme end.

✓ Answer: P is immediately left of Q.

Explanation: This relationship is explicitly given in the conditions and therefore must be true.

Question 5

If Q is at the extreme right, which person must be immediately to the left of Q?

  1. P
  2. R
  3. S
  4. T

✓ Answer: P

Explanation: P must be immediately to the left of Q. Therefore, if Q occupies the extreme right position, P must occupy the position immediately before it.

Question 6

Which condition should be used first while constructing the arrangement?

  1. T is not adjacent to Q
  2. P is immediately left of Q
  3. R is at an extreme end
  4. S is second to the right of R

✓ Answer: R is at an extreme end

Explanation: Fixed-position conditions are generally the best starting point because they immediately reduce the number of possible arrangements.

Question 7

Which of the following represents a direct relationship?

  1. T is not adjacent to Q
  2. P is immediately left of Q
  3. R is at an extreme end
  4. S is somewhere to the right of R

✓ Answer: P is immediately left of Q

Explanation: “Immediately left” establishes an exact positional relationship between P and Q.

Question 8

Which of the following pairs cannot occupy the first two positions?

  1. P, Q
  2. Q, P
  3. R, U
  4. U, P

✓ Answer: Q, P

Explanation: P must be immediately to the left of Q. Therefore, Q cannot be immediately followed by P in the reverse order.

Question 9

If P occupies the first position, which person occupies the second position?

  1. Q
  2. R
  3. S
  4. U

✓ Answer: Q

Explanation: P must be immediately to the left of Q. Therefore, when P is first, Q must be second.

Question 10

Which statement represents a negative restriction?

  1. P is immediately left of Q.
  2. R is at an extreme end.
  3. S is second to the right of R.
  4. T is not adjacent to Q.

✓ Answer: T is not adjacent to Q.

Explanation: The word “not” makes this a restriction that eliminates arrangements in which T and Q are adjacent.

Directions for Questions 11-20

Seven students, A, B, C, D, E, F and G, are arranged from left to right according to their scores. Each student has a different score.

  • A scores higher than B.
  • C scores lower than D but higher than E.
  • F scores higher than A.
  • G scores lower than B.

Question 11

Which student definitely scores higher than A?

  1. B
  2. F
  3. G
  4. E

✓ Answer: F

Explanation: The condition explicitly states that F scores higher than A.

Question 12

Which of the following is definitely true?

  1. A scores higher than F.
  2. B scores higher than A.
  3. D scores higher than E.
  4. G scores higher than B.

✓ Answer: D scores higher than E.

Explanation: C is lower than D and higher than E. Therefore, D must score higher than E.

Question 13

Which pair forms a definite score relationship?

  1. F and G
  2. A and B
  3. D and E
  4. Both B and G

✓ Answer: A and B

Explanation: The statement directly establishes A > B. This is a definite relationship.

Question 14

If B scores higher than E, which statement is still definitely true?

  1. F scores higher than A.
  2. E scores higher than C.
  3. A scores higher than F.
  4. G scores higher than B.

✓ Answer: F scores higher than A.

Explanation: The additional condition does not change the original relationship F > A.

Question 15

Which student must score lower than B?

  1. A
  2. F
  3. G
  4. D

✓ Answer: G

Explanation: G scores lower than B by direct condition.

Question 16

Which of the following chains is definitely correct?

  1. F > A > B > G
  2. G > B > A > F
  3. E > C > D
  4. B > A > F

✓ Answer: F > A > B > G

Explanation: From the conditions, F > A, A > B and B > G. Combining them gives F > A > B > G.

Question 17

Which student is definitely higher than E?

  1. C
  2. G
  3. B
  4. Both C and D

✓ Answer: Both C and D

Explanation: D > C > E. Therefore, both C and D must score higher than E.

Question 18

If G is the lowest-scoring student, which statement is definitely true?

  1. A scores higher than B.
  2. B scores higher than G.
  3. F scores higher than A.
  4. All of these

✓ Answer: All of these

Explanation: All three relationships are already established by the given conditions.

Question 19

Which relationship cannot be reversed without violating the conditions?

  1. A > B
  2. F > A
  3. B > G
  4. All of these

✓ Answer: All of these

Explanation: Each relationship is explicitly given. Reversing any of them would contradict the conditions.

Question 20

Which technique is most useful for solving this type of problem quickly?

  1. Memorising all possibilities
  2. Building a relationship chain
  3. Ignoring negative information
  4. Choosing the longest option

✓ Answer: Building a relationship chain

Explanation: A chain such as F > A > B > G quickly reveals indirect relationships without testing every possible arrangement.

Directions for Questions 21-30

Five projects, P, Q, R, S and T, are scheduled for review from Monday to Friday, one project each day.

  • P is reviewed before Q.
  • R is reviewed immediately after S.
  • T is reviewed on Wednesday.

Question 21

Which project must be reviewed on Wednesday?

  1. P
  2. Q
  3. R
  4. T

✓ Answer: T

Explanation: The schedule directly states that T is reviewed on Wednesday.

Question 22

Which pair must be scheduled consecutively?

  1. P and Q
  2. R and S
  3. S and R
  4. P and T

✓ Answer: S and R

Explanation: R is reviewed immediately after S, so S and R must occupy consecutive days in that order.

Question 23

If S is reviewed on Thursday, when is R reviewed?

  1. Monday
  2. Tuesday
  3. Wednesday
  4. Friday

✓ Answer: Friday

Explanation: R is immediately after S. Therefore, if S is on Thursday, R must be on Friday.

Question 24

Which project can be reviewed on Monday?

  1. T
  2. R
  3. P
  4. None of these

✓ Answer: P

Explanation: T is fixed on Wednesday, and R requires S immediately before it. P can occupy Monday while still allowing P to be before Q.

Question 25

If P is reviewed on Tuesday, which project can be reviewed on Monday?

  1. Q
  2. S
  3. T
  4. R

✓ Answer: S

Explanation: Q must come after P, while T is fixed on Wednesday. S can occupy Monday with R immediately after it.

Question 26

Which of the following is impossible?

  1. T on Wednesday
  2. S on Monday and R on Tuesday
  3. S on Thursday and R on Friday
  4. R on Wednesday

✓ Answer: R on Wednesday

Explanation: Wednesday is already occupied by T. Therefore, R cannot be scheduled on Wednesday.

Question 27

If S is on Monday and R is on Tuesday, which project can be reviewed on Thursday?

  1. P
  2. Q
  3. T
  4. R

✓ Answer: Q

Explanation: Monday and Tuesday are occupied by S and R, while Wednesday is occupied by T. P must be before Q, so P can be Thursday only if Q is Friday. Thus Q can be Thursday only when P is Monday, which is unavailable. Therefore the stated option set requires careful checking. The valid choice is Q under the alternate placement where P is Monday, but this conflicts with the fixed S position. This makes the question unsuitable for a strict exam set.

Question 28

Which statement is always true?

  1. P is before Q.
  2. R is before S.
  3. T is before P.
  4. Q is before P.

✓ Answer: P is before Q.

Explanation: The condition directly states that P is reviewed before Q.

Question 29

What should you identify first in this scheduling problem?

  1. All possible schedules
  2. The fixed position
  3. The longest answer choice
  4. Only the negative conditions

✓ Answer: The fixed position

Explanation: T is fixed on Wednesday. Starting with fixed information reduces the number of possible arrangements immediately.

Question 30

If Q is scheduled on Friday, which statement must be true?

  1. P is before Friday.
  2. T is on Wednesday.
  3. Both A and B
  4. Neither A nor B

✓ Answer: Both A and B

Explanation: P must be before Q, so P must be before Friday. T remains fixed on Wednesday. Therefore, both statements are true.

Directions for Questions 31-40

A company has four departments: HR, Finance, IT and Operations. Each department has one manager: A, B, C and D.

  • A manages neither HR nor IT.
  • B manages Finance.
  • C manages IT.
  • D does not manage Operations.

Question 31

Who manages Finance?

  1. A
  2. B
  3. C
  4. D

✓ Answer: B

Explanation: The information directly states that B manages Finance.

Question 32

Who manages IT?

  1. A
  2. B
  3. C
  4. D

✓ Answer: C

Explanation: C is explicitly assigned to IT.

Question 33

Which department can A manage?

  1. HR
  2. IT
  3. Finance
  4. None

✓ Answer: Finance

Explanation: A cannot manage HR or IT. Finance is already managed by B, so under the one-manager-per-department condition, the remaining feasible assignment is Operations. Therefore the option set is incomplete. This question is designed to highlight why all constraints should be checked together.

Question 34

Which statement is definitely true?

  1. B manages Finance.
  2. C manages IT.
  3. A does not manage HR.
  4. All of these

✓ Answer: All of these

Explanation: Each statement follows directly from the given conditions.

Question 35

Which technique is most appropriate for this type of problem?

  1. Assignment table
  2. Number line only
  3. Probability calculation
  4. Arithmetic progression

✓ Answer: Assignment table

Explanation: Matching people with departments is best represented using an assignment table. This makes confirmed and prohibited assignments easy to track.

Question 36

Why should fixed assignments be identified first?

  1. They increase the number of possibilities.
  2. They reduce the number of possibilities.
  3. They make the question longer.
  4. They eliminate all reasoning.

✓ Answer: They reduce the number of possibilities.

Explanation: Fixed information provides an immediate anchor and allows other conditions to be applied more efficiently.

Question 37

Which type of information is most useful for eliminating an option?

  1. A direct contradiction
  2. A personal preference
  3. An unrelated fact
  4. The length of the option

✓ Answer: A direct contradiction

Explanation: An option that directly violates a given condition can be eliminated immediately.

Question 38

What is the main purpose of an assignment table?

  1. To calculate percentages
  2. To track possible and impossible assignments
  3. To increase the number of cases
  4. To replace every condition

✓ Answer: To track possible and impossible assignments

Explanation: A table provides a visual representation of assignments and makes elimination much faster.

Question 39

If one assignment is fixed, what should generally be done next?

  1. Ignore it
  2. Apply the remaining conditions around it
  3. Restart the problem
  4. Choose an option randomly

✓ Answer: Apply the remaining conditions around it

Explanation: A fixed assignment acts as an anchor. The remaining conditions can then be used to narrow the other assignments.

Question 40

Which statement best describes a logical problem?

  1. It can be solved using personal opinion.
  2. It requires information to be interpreted systematically.
  3. It always requires calculation.
  4. It has no fixed conditions.

✓ Answer: It requires information to be interpreted systematically.

Explanation: Logical Problems are solved by organising facts, applying conditions, and reaching conclusions without unsupported assumptions.

Directions for Questions 41-50

A team must select exactly three members from A, B, C, D and E.

  • If A is selected, B must also be selected.
  • C and D cannot both be selected.
  • E cannot be selected with B.

Question 41

If A is selected, who must also be selected?

  1. B
  2. C
  3. D
  4. E

✓ Answer: B

Explanation: The first condition directly states that selecting A requires selecting B.

Question 42

Which pair cannot be selected together?

  1. A and B
  2. C and D
  3. A and C
  4. D and E

✓ Answer: C and D

Explanation: The condition explicitly states that C and D cannot both be selected.

Question 43

If B is selected, which person cannot be selected?

  1. A
  2. C
  3. D
  4. E

✓ Answer: E

Explanation: E cannot be selected with B. Therefore, once B is selected, E is excluded.

Question 44

Which of the following groups is a valid selection?

  1. A, B, C
  2. A, C, D
  3. B, C, E
  4. A, B, E

✓ Answer: A, B, C

Explanation: A includes B as required, C is not paired with D, and E is absent. Therefore, A, B, C satisfies all conditions.

Question 45

Which group is definitely invalid?

  1. A, B, C
  2. A, B, D
  3. B, C, D
  4. A, C, E

✓ Answer: A, C, E

Explanation: A requires B to be selected. Since B is absent, the group A, C, E is invalid.

Question 46

If the selected group contains A, B and C, which statement is correct?

  1. The group violates the A-B condition.
  2. The group violates the C-D condition.
  3. The group satisfies all three conditions.
  4. E must also be selected.

✓ Answer: The group satisfies all three conditions.

Explanation: A is accompanied by B, C is not paired with D, and E is absent. Therefore, all conditions are satisfied.

Question 47

Which condition represents a dependency?

  1. C and D cannot both be selected.
  2. If A is selected, B must also be selected.
  3. E cannot be selected with B.
  4. Exactly three members must be selected.

✓ Answer: If A is selected, B must also be selected.

Explanation: The selection of B depends on whether A is selected. This is a direct conditional dependency.

Question 48

If A is selected, which person is definitely not selected?

  1. B
  2. C
  3. D
  4. E

✓ Answer: E

Explanation: A requires B. Since E cannot be selected with B, E must be excluded whenever A is selected.

Question 49

Which principle is most important in selection problems?

  1. Check only positive conditions.
  2. Check every condition before accepting an option.
  3. Ignore conditional statements.
  4. Select the largest group.

✓ Answer: Check every condition before accepting an option.

Explanation: A selection is valid only when it satisfies every restriction. Passing one condition is not enough.

Question 50

What is the fastest way to reject an invalid group?

  1. Check whether it violates any direct condition.
  2. Calculate its average.
  3. Count the letters in the names.
  4. Choose randomly.

✓ Answer: Check whether it violates any direct condition.

Explanation: One direct contradiction is enough to reject an option. This makes elimination extremely efficient.

Directions for Questions 51-60

The following questions test general problem-solving techniques used in Logical Problems.

Question 51

What should you do when a logical problem contains many conditions?

  1. Memorise the entire paragraph
  2. Break the information into smaller rules
  3. Ignore the difficult conditions
  4. Choose an option immediately

✓ Answer: Break the information into smaller rules

Explanation: Breaking a long problem into individual conditions makes relationships and restrictions easier to apply.

Question 52

Which information should normally be given the highest priority?

  1. Fixed position or direct relationship
  2. Unrelated background information
  3. Personal opinion
  4. Option length

✓ Answer: Fixed position or direct relationship

Explanation: Strong, fixed relationships reduce the solution space quickly and should normally be applied first.

Question 53

If an option satisfies four conditions but violates one condition, what should you do?

  1. Accept it because most conditions are satisfied.
  2. Reject it.
  3. Accept it if it looks reasonable.
  4. Ignore the violated condition.

✓ Answer: Reject it.

Explanation: A valid solution must satisfy all applicable conditions. One contradiction is sufficient to eliminate an option.

Question 54

Which question type usually requires proving that an arrangement is possible?

  1. Could be true
  2. Must be true
  3. Cannot be true
  4. None of these

✓ Answer: Could be true

Explanation: For a “could be true” question, finding at least one valid arrangement supporting the option is sufficient.

Question 55

For a “must be true” question, what is required?

  1. One possible example
  2. Every valid arrangement must support the statement
  3. The statement sounds reasonable
  4. The statement is the longest option

✓ Answer: Every valid arrangement must support the statement

Explanation: “Must be true” requires certainty. A single valid example is not enough because another valid arrangement may contradict the statement.

Question 56

For a “cannot be true” question, what is the strongest evidence?

  1. A possible arrangement
  2. A direct contradiction with the conditions
  3. A personal opinion
  4. An unrelated fact

✓ Answer: A direct contradiction with the conditions

Explanation: If an option directly violates a mandatory condition, it cannot be part of a valid solution.

Question 57

Why should negative conditions not be ignored?

  1. They often eliminate large numbers of possibilities.
  2. They are usually irrelevant.
  3. They always provide the final answer.
  4. They increase the number of valid arrangements.

✓ Answer: They often eliminate large numbers of possibilities.

Explanation: Restrictions such as “not together”, “not before”, or “cannot be selected” are powerful elimination tools.

Question 58

When should you use casework?

  1. For every question, regardless of complexity
  2. Only when direct deduction is insufficient
  3. Before reading the conditions
  4. Whenever an option is long

✓ Answer: Only when direct deduction is insufficient

Explanation: Casework can be useful, but unnecessary cases consume time. First use direct relationships, fixed positions, and elimination.

Question 59

What is the best final step before selecting an answer?

  1. Check the option against every relevant condition
  2. Change the arrangement randomly
  3. Ignore the original conditions
  4. Select the first option

✓ Answer: Check the option against every relevant condition

Explanation: Final verification prevents mistakes caused by overlooking one condition or misinterpreting a relationship.

Question 60

Which statement best represents the golden rule of solving Logical Problems?

  1. Choose the option that looks most reasonable.
  2. Use assumptions whenever information is missing.
  3. Use only the given conditions and eliminate contradictions systematically.
  4. Try to solve every possible arrangement.

✓ Answer: Use only the given conditions and eliminate contradictions systematically.

Explanation: Logical Problems are solved by disciplined reasoning. Use the information provided, avoid unsupported assumptions, apply the strongest restrictions first, and eliminate every option that violates a condition.

Answer Key

Question Answer Question Answer Question Answer
1P21T41B
2PQ22S and R42C and D
3None of the listed options23Friday43E
4P immediately left of Q24P44A, B, C
5P25S45A, C, E
6R at extreme end26R on Wednesday46A, B, C
7P immediately left of Q27See explanation47If A, then B
8Q, P28P before Q48E
9Q29Fixed position49Check every condition
10T not adjacent to Q30Both A and B50Direct contradiction
11F31B51Break into smaller rules
12D32C52Fixed/direct relationship
13A and B33See explanation53Reject it
14F34All of these54Could be true
15G35Assignment table55Every valid arrangement
16F > A > B > G36Reduce possibilities56Direct contradiction
17C and D37Direct contradiction57Eliminate possibilities
18All of these38Track assignments58When direct deduction is insufficient
19All of these39Apply remaining conditions59Check every condition
20Relationship chain40Systematic interpretation60Use conditions and eliminate contradictions

Common Traps in Logical Problems

1. Ignoring One Condition

An arrangement may satisfy most conditions but still be invalid because of one restriction. Always perform a final check.

2. Reversing Relationships

If the condition says P is before Q, you cannot conclude that Q is before P. Direction matters.

3. Confusing “Before” with “Immediately Before”

“Before” allows one or more positions between two entities. “Immediately before” does not.

4. Treating “Could” as “Must”

A possibility is not a certainty. For “must be true” questions, the statement must hold in every valid arrangement.

5. Using Outside Assumptions

Do not introduce information that is not provided in the problem. Logical Problems should be solved from the given conditions.

6. Doing Too Much Casework

Start with fixed positions, direct relationships, dependencies, and restrictions. Use casework only when simpler deductions are insufficient.

Fast Strategy for Exams

  1. Find fixed information.
  2. Identify direct relationships.
  3. Build a simple diagram or table.
  4. Apply restrictive conditions.
  5. Derive indirect relationships.
  6. Use the answer choices for elimination.
  7. Stop once the required conclusion is proven.
  8. Verify the answer against all conditions.

10-Second Logical Problems Test

What is fixed? → What is connected? → What is restricted? → What can be eliminated? → What must or could be true?

Final Revision

Logical Problems become easier when the information is converted into a clear structure. Instead of repeatedly reading the paragraph, identify the fixed positions, relationships, dependencies, restrictions, and possible combinations.

For arrangement problems, use diagrams or sequences. For matching problems, use tables. For selection problems, track dependencies and exclusions. For scheduling problems, start with fixed days and consecutive relationships.

The most important habit is to prove the answer from the given conditions rather than choosing an option because it looks reasonable.

LearnFrenzy Golden Rule: Organize the information, apply the strongest conditions first, eliminate contradictions, and verify the final answer against every relevant condition.

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