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Logical Problems — Questions and Answers

Logical Problems give you a set of facts and ask what must be true. The distinction that decides every question is between what MUST follow and what merely COULD be true. Draw the relationships out — an ordering line, a simple grid — and test each option against every arrangement the facts allow.

10 solved questionsLogical ReasoningFree · no signup

Logical Problems— Concepts, Formulas & Shortcuts

  • Distinguish "must be true" from "could be true" — only the former counts as following.
  • For ranking problems, draw a line and place the certain relations first.
  • A conclusion fails if you can construct even ONE arrangement consistent with the facts where it is false.
  • Comparative statements (taller, older, faster) are transitive: if A > B and B > C then A > C.
  • Do not import real-world knowledge; use only the stated facts.
  • When the facts leave several orders possible, the answer is usually the one relation common to all of them.

Logical Problems Practice Questions with Answers

Attempt each question first, then open the explanation. All 10 questions below are free to read and require no signup.

  1. Q1.A is taller than B. C is shorter than B. Which must be true?

    Easy
    • AA is taller than C
    • BC is taller than A
    • CA and C are equal
    • DCannot be determined
    +Show Answer & Explanation

    Answer: A. A is taller than C

    Explanation: A > B and B > C, so by transitivity A > C.

    Logical Problems question 1 of 10

  2. Q2.All roses in the garden are red. Some flowers in the garden are roses. Which must be true?

    Moderate
    • AAll flowers are red
    • BSome flowers in the garden are red
    • CNo flower is red
    • DAll red things are roses
    +Show Answer & Explanation

    Answer: B. Some flowers in the garden are red

    Explanation: The flowers that are roses must be red, so at least some flowers are red.

    Logical Problems question 2 of 10

  3. Q3.P is heavier than Q. R is heavier than P. Who is the heaviest?

    Easy
    • AP
    • BQ
    • CR
    • DCannot be determined
    +Show Answer & Explanation

    Answer: C. R

    Explanation: R > P and P > Q, so R is heaviest.

    Logical Problems question 3 of 10

  4. Q4.If it rains, the match is cancelled. The match was not cancelled. Which must be true?

    Moderate
    • AIt rained
    • BIt did not rain
    • CThe match was postponed
    • DNothing can be concluded
    +Show Answer & Explanation

    Answer: B. It did not rain

    Explanation: This is valid contraposition: if rain implies cancellation, then no cancellation implies no rain.

    Logical Problems question 4 of 10

  5. Q5.Only members may enter the club. Ravi entered the club. Which must be true?

    Easy
    • ARavi is a member
    • BRavi is a guest
    • CRavi paid a fee
    • DRavi was invited
    +Show Answer & Explanation

    Answer: A. Ravi is a member

    Explanation: If entry is restricted to members and Ravi entered, he must be a member.

    Logical Problems question 5 of 10

  6. Q6.Some doctors are writers. All writers are readers. Which must be true?

    Moderate
    • AAll doctors are readers
    • BSome doctors are readers
    • CNo doctor is a reader
    • DAll readers are doctors
    +Show Answer & Explanation

    Answer: B. Some doctors are readers

    Explanation: The doctors who are writers must be readers, so some doctors are readers.

    Logical Problems question 6 of 10

  7. Q7.In a queue, X is ahead of Y and Y is ahead of Z. Who is last?

    Easy
    • AX
    • BY
    • CZ
    • DCannot be determined
    +Show Answer & Explanation

    Answer: C. Z

    Explanation: The order is X, Y, Z, so Z stands last.

    Logical Problems question 7 of 10

  8. Q8.If a number is divisible by 6, it is divisible by 3. The number 14 is not divisible by 3. Which follows?

    Moderate
    • A14 is divisible by 6
    • B14 is not divisible by 6
    • C14 is prime
    • DNothing follows
    +Show Answer & Explanation

    Answer: B. 14 is not divisible by 6

    Explanation: Contraposition again: not divisible by 3 implies not divisible by 6.

    Logical Problems question 8 of 10

  9. Q9.Every student who passed studied hard. Meena did not study hard. Which must be true?

    Moderate
    • AMeena passed
    • BMeena did not pass
    • CMeena studied a little
    • DCannot be determined
    +Show Answer & Explanation

    Answer: B. Meena did not pass

    Explanation: If passing requires studying hard, then not studying hard means not passing.

    Logical Problems question 9 of 10

  10. Q10.A is older than B, C is older than A, and D is younger than B. Who is the youngest?

    Moderate
    • AA
    • BB
    • CC
    • DD
    +Show Answer & Explanation

    Answer: D. D

    Explanation: The order is C > A > B > D, so D is the youngest.

    Logical Problems question 10 of 10

Logical Problems — Frequently Asked Questions

How do I test whether a conclusion must be true?+

Try to build an arrangement that satisfies all the given facts but makes the conclusion false. If you can, the conclusion does not follow. If every valid arrangement supports it, it must be true.

What is transitivity and why does it matter?+

If A is taller than B and B taller than C, then A is taller than C. Most ranking questions are solved by chaining such relations rather than by trial and error.

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