20 Logical Reasoning Practice Questions & Answers

1. 1. An agent follows this rule: If an agent is on the night shift, then the agent carries a radio. A certain agent does NOT carry a radio. What must be true?

   • A.The agent is on the night shift.
   • B.The agent carries a radio.
   • C.It cannot be determined.
   • D.The agent is not on the night shift.✓ Answer

   This is modus tollens: from 'if P then Q' and 'not Q,' it validly follows that 'not P.' Since carrying a radio is required for the night shift, lacking a radio means the agent cannot be on the night shift.

   Source: Modus tollens (denying the consequent) — valid deductive inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

2. 2. Consider these statements: If it rains, then the ground is wet. The ground is wet. Which conclusion necessarily follows?

   • A.The ground is dry.
   • B.It rained.
   • C.It cannot be determined whether it rained.✓ Answer
   • D.It did not rain.

   Concluding 'it rained' from a wet ground commits the fallacy of affirming the consequent. Wet ground can have other causes (a hose, dew), so rain cannot be validly inferred.

   Source: Affirming the consequent fallacy — invalid inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

3. 3. All agents are officers. All officers are trained. Which conclusion must be true?

   • A.Some officers are not agents.
   • B.All trained people are agents.
   • C.No agents are trained.
   • D.All agents are trained.✓ Answer

   By the transitivity of universal statements (a categorical syllogism), if every A is B and every B is C, then every A is C. So every agent, being an officer, is trained.

   Source: Categorical syllogism (Barbara) — valid transitive inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

4. 4. Ana is taller than Ben. Ben is taller than Carl. Who is the shortest of the three?

   • A.Ben
   • B.It cannot be determined.
   • C.Carl✓ Answer
   • D.Ana

   The 'taller than' relation is transitive and orders them Ana > Ben > Carl. Carl, being shorter than Ben who is shorter than Ana, is the shortest.

   Source: Transitivity of ordering relations; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

5. 5. Four tasks were finished in sequence: A finished before B, B before C, and C before D. Which statement must be true?

   • A.A finished before D.✓ Answer
   • B.D finished before A.
   • C.B finished before A.
   • D.C finished before B.

   'Finished before' is transitive, giving the order A, B, C, D. Since A precedes B, C, and D in this chain, A necessarily finished before D.

   Source: Transitivity of ordering relations; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

6. 6. Rule: To enter the facility, an agent must show a badge. Which statement is necessarily true?

   • A.Showing a badge guarantees entry.
   • B.No agent shows a badge.
   • C.Anyone who shows a badge enters the facility.
   • D.An agent who does not show a badge cannot enter the facility.✓ Answer

   'Must show a badge' states a necessary condition for entry, not a sufficient one. So lacking a badge blocks entry, but a badge alone does not guarantee it.

   Source: Necessary vs. sufficient conditions; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

7. 7. Rule: If a vehicle is red, then it is flagged for inspection. A particular vehicle is not red. What can be concluded?

   • A.The vehicle is not flagged for inspection.
   • B.All red vehicles are unflagged.
   • C.The vehicle is flagged for inspection.
   • D.It cannot be determined whether the vehicle is flagged.✓ Answer

   Inferring anything about a non-red vehicle commits the fallacy of denying the antecedent. The rule only tells us what happens when a vehicle IS red, so a non-red vehicle might still be flagged for another reason.

   Source: Denying the antecedent fallacy — invalid inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

8. 8. All dogs are mammals. Some pets are dogs. Which conclusion must be true?

   • A.All mammals are pets.
   • B.Some pets are mammals.✓ Answer
   • C.All pets are mammals.
   • D.No pets are mammals.

   The pets that are dogs must be mammals, since all dogs are mammals. Therefore at least some pets are mammals, though not necessarily all of them.

   Source: Categorical syllogism (Darii) — valid particular inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

9. 9. Every item in Box 1 is blue. A certain pen is blue. What can be concluded about the pen?

   • A.The pen is in Box 1.
   • B.It cannot be determined whether the pen is in Box 1.✓ Answer
   • C.The pen is not in Box 1.
   • D.Box 1 is empty.

   'Every item in Box 1 is blue' does not mean every blue item is in Box 1. Being blue is consistent with the pen being inside or outside the box, so its location cannot be determined.

   Source: Illicit conversion of a universal affirmative — invalid inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

10. 10. If the alarm sounds, the door locks. If the door locks, the lights turn on. The lights did NOT turn on. What must be true?

    • A.The door locked.
    • B.The lights turned on.
    • C.The alarm sounded.
    • D.The alarm did not sound.✓ Answer

    Chaining the conditionals gives 'if the alarm sounds, the lights turn on.' Because the lights did not turn on, modus tollens forces the conclusion that the alarm did not sound.

    Source: Hypothetical syllogism + modus tollens; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

11. 11. Four agents—P, Q, R, and S—stand in a single row. P is at the far left and S is at the far right. Q stands immediately to the left of R. Who is second from the left?

    • A.P
    • B.Q✓ Answer
    • C.R
    • D.S

    With P at position 1 and S at position 4, only positions 2 and 3 remain for Q and R. Since Q is immediately left of R, Q takes position 2 and R position 3, so Q is second from the left.

    Source: Constraint-based ordering deduction; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

12. 12. Either the report is on the desk or it is in the drawer. The report is not on the desk. What must be true?

    • A.It cannot be determined where the report is.
    • B.The report is in the drawer.✓ Answer
    • C.The report is on the desk.
    • D.The report is in neither place.

    This is disjunctive syllogism: given 'P or Q' and 'not P,' it validly follows that Q. With the desk ruled out, the report must be in the drawer.

    Source: Disjunctive syllogism — valid inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

13. 13. All squares are rectangles. Assuming at least one square exists, which conclusion is valid?

    • A.Some rectangles are squares.✓ Answer
    • B.No rectangles are squares.
    • C.No squares are rectangles.
    • D.All rectangles are squares.

    From 'all squares are rectangles,' a square is an example of a rectangle, so 'some rectangles are squares' follows. The universal cannot be reversed to claim all rectangles are squares.

    Source: Conversion per accidens (valid) vs. simple conversion (invalid); CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

14. 14. In a race, five runners finished with no ties: M finished before N, N before O, O before P, and P before Q. Who finished third?

    • A.O✓ Answer
    • B.P
    • C.N
    • D.It cannot be determined.

    The chain of 'finished before' relations fixes the full order M, N, O, P, Q. Counting from first place, the third finisher is O.

    Source: Transitivity of ordering relations; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

15. 15. A signal turns green if and only if the button is pressed. The button was not pressed. What must be true?

    • A.The signal turned green.
    • B.The button was pressed.
    • C.It cannot be determined.
    • D.The signal did not turn green.✓ Answer

    'If and only if' makes green and pressing the button equivalent: green occurs exactly when the button is pressed. Since it was not pressed, the signal did not turn green.

    Source: Biconditional (necessary and sufficient condition); CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

16. 16. No reptiles are mammals. All snakes are reptiles. Which conclusion must be true?

    • A.No snakes are mammals.✓ Answer
    • B.All snakes are mammals.
    • C.Some mammals are snakes.
    • D.Some snakes are mammals.

    Since every snake is a reptile and no reptile is a mammal, no snake can be a mammal. The exclusion carries down from reptiles to the snakes contained within them.

    Source: Categorical syllogism (Celarent) — valid inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

17. 17. Some agents speak Spanish. Everyone who speaks Spanish can interview witnesses. Which conclusion must be true?

    • A.All agents can interview witnesses.
    • B.No agents can interview witnesses.
    • C.Some agents can interview witnesses.✓ Answer
    • D.Only Spanish speakers are agents.

    The agents who speak Spanish can all interview witnesses, so at least some agents can. It does not follow that all agents can, since some agents may not speak Spanish.

    Source: Categorical syllogism (Darii) — valid particular inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

18. 18. Three friends each own exactly one pet: a cat, a dog, or a bird, all different. Sam owns neither the cat nor the bird. Which pet does Sam own?

    • A.The dog✓ Answer
    • B.The bird
    • C.The cat
    • D.It cannot be determined.

    By elimination, if Sam owns neither the cat nor the bird, the only remaining option among the three pets is the dog, so Sam owns the dog.

    Source: Deduction by elimination (process of elimination); CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

19. 19. Rule: If a package is heavy, then it requires two handlers. A certain package requires only one handler. What must be true?

    • A.It cannot be determined.
    • B.The package requires two handlers.
    • C.The package is heavy.
    • D.The package is not heavy.✓ Answer

    Requiring two handlers is a necessary consequence of being heavy. Since the package requires only one handler, modus tollens shows it cannot be heavy.

    Source: Modus tollens — valid deductive inference; CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

20. 20. Three lockers numbered 1, 2, and 3 each hold exactly one of a hat, a scarf, and gloves. The hat is in locker 1, and the gloves are not in locker 3. Which item is in locker 3?

    • A.It cannot be determined.
    • B.The gloves
    • C.The hat
    • D.The scarf✓ Answer

    The hat occupies locker 1, and the gloves cannot be in locker 3, so the gloves must be in locker 2. That leaves only the scarf for locker 3.

    Source: Constraint-based grouping deduction (process of elimination); CBP Border Patrol Entrance Exam, Logical Reasoning domainReport a problem with this question

Practice questions modeled on the general aptitude domains of the CBP Border Patrol Agent entrance exam (logical reasoning, reading comprehension, artificial-language test, situational reasoning). Not legal or immigration advice and not affiliated with or endorsed by U.S. Customs and Border Protection. Check the official announcement for the current exam format. CBP Careers →