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Binary Logic Questions for CAT

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93 easy87 medium150 hard

20 free Binary Logic questions

1EasyPassage, 4 questions

Among three people - A, B and C - exactly one is a Truth-teller (every statement true), one is a Liar (every statement false), and one is an Alternator (may say anything). A says: 'B is the liar.' B says: 'C is the alternator.' C says: 'A is the truth-teller.' Answer the questions that follow.

Question 1

If we assume A is the truth-teller, what happens?

  1. A

    Everything is consistent

  2. B

    It leads to a contradiction

  3. C

    C becomes the liar

  4. D

    Two alternators appear

Question 2

Who is the truth-teller?

  1. A

    A

  2. B

    B

  3. C

    C

  4. D

    Cannot be determined

Question 3

Who is the liar?

  1. A

    A

  2. B

    B

  3. C

    C

  4. D

    Cannot be determined

Question 4

Who is the alternator?

  1. A

    A

  2. B

    B

  3. C

    C

  4. D

    Cannot be determined

Show solution
2EasyPassage, 4 questions

Among three people - G, H and I - exactly one is a Truth-teller, one is a Liar, and one is an Alternator. G says: 'H is the truth-teller.' H says: 'I is the alternator.' I says: 'G is the liar.' Answer the questions that follow.

Question 1

If we assume G is the truth-teller, what happens?

  1. A

    Everything is consistent

  2. B

    It leads to a contradiction (two truth-tellers)

  3. C

    H becomes the liar

  4. D

    I becomes the alternator

Question 2

Who is the truth-teller?

  1. A

    G

  2. B

    H

  3. C

    I

  4. D

    Cannot be determined

Question 3

Who is the liar?

  1. A

    G

  2. B

    H

  3. C

    I

  4. D

    Cannot be determined

Question 4

Who is the alternator?

  1. A

    G

  2. B

    H

  3. C

    I

  4. D

    Cannot be determined

Show solution
3MediumPassage, 4 questions

Among three people - M, N and O - exactly one is a Truth-teller, one is a Liar, and one is an Alternator. Each makes two statements. M: 'N is the truth-teller. O is the liar.' N: 'M is the alternator. O is the truth-teller.' O: 'I am the truth-teller. M is the liar.' Answer the questions that follow.

Question 1

If we assume M is the truth-teller, what happens?

  1. A

    Everything is consistent

  2. B

    It leads to a contradiction (two truth-tellers)

  3. C

    O becomes the alternator

  4. D

    N becomes the liar

Question 2

Who is the truth-teller?

  1. A

    M

  2. B

    N

  3. C

    O

  4. D

    Cannot be determined

Question 3

N's two statements turn out to be one true and one false. What does that tell us?

  1. A

    N must be the alternator

  2. B

    N must be the truth-teller

  3. C

    N must be the liar

  4. D

    N said nothing useful

Question 4

Who is the liar?

  1. A

    M

  2. B

    N

  3. C

    O

  4. D

    Cannot be determined

Show solution
4MediumPassage, 4 questions

Three switches X, Y, Z are each ON (true) or OFF (false). Constraints: (i) X XOR Y is true (exactly one of X, Y is ON). (ii) Y OR Z (at least one is ON). (iii) NOT(X AND Z) - X and Z are not both ON. Build the 8-row truth table, keep the valid rows, and answer the questions that follow.

Question 1

How many of the 8 combinations are valid?

Question 2

What is X in every valid scenario?

  1. A

    Definitely ON

  2. B

    Definitely OFF

  3. C

    Possibly ON

  4. D

    Undefined

Question 3

What is Y in every valid scenario?

  1. A

    Definitely ON

  2. B

    Definitely OFF

  3. C

    Possibly ON

  4. D

    Undefined

Question 4

What is the status of Z?

  1. A

    Definitely ON

  2. B

    Definitely OFF

  3. C

    Possibly ON (could be ON or OFF)

  4. D

    Undefined

Show solution
5HardPassage, 4 questions

Five propositions A, B, C, D, E are each true or false. All constraints below must hold: (i) A and B have the same truth value. (ii) B and C have opposite truth values. (iii) C and D have the same truth value. (iv) A and E have opposite truth values. (v) Exactly 3 of A, B, C, D, E are true. Answer the questions that follow.

Question 1

Expressing everything in terms of A, how do B, C, D, E relate to A?

  1. A

    B = A, and C = D = E = NOT A

  2. B

    All five equal A

  3. C

    B = C = A, D = E = NOT A

  4. D

    All five are the opposite of A

Question 2

If A were true, how many of the five would be true?

  1. A

    2

  2. B

    3

  3. C

    4

  4. D

    5

Question 3

In the valid solution, which propositions are true?

  1. A

    A and B

  2. B

    C, D and E

  3. C

    A, C and E

  4. D

    B, D and E

Question 4

In the valid solution, how many of the five propositions are true?

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