1. Question 1 of 50

   Which of the following is a tautology (always true)?

   A p ∨ ¬p B p ∧ ¬p C p → ¬p D p ↔ ¬p
2. Question 2 of 50

   What is the average of three integers a, b and c? (each from 1 to 20) I. a + b + c = 36. II. a = 10 and b = 12.

   A Either statement alone is sufficient B Both statements together are sufficient, but neither alone is sufficient C Both statements together are not sufficient D Statement I alone is sufficient, but Statement II alone is not
3. Question 3 of 50

   Consider the following 4 statements. Statement 1: 'Exactly 3 of these 4 statements are false.' Statement 2: 'Exactly 2 of these 4 statements are false.' Statement 3: 'Exactly 3 of these 4 statements are false.' Statement 4: 'Exactly 1 of these 4 statements is false.' Which statements are true?

   A Statements 1 and 4 are true B Only statement 4 is true C Only statement 3 is true D None of the statements is true
4. Question 4 of 50

   Each of A, B and C is either always truthful or always a liar. A says: 'B is truthful'. B says: 'A and C are of the same type'. C says: 'B is a liar'. Who is truthful?

   A None of them is truthful B A and B are truthful C A and C are truthful D C only
5. Question 5 of 50

   What is the value of the integer x? (x is between -10 and 10) I. x² = 9. II. x > 0.

   A Both statements together are sufficient, but neither alone is sufficient B Statement I alone is sufficient, but Statement II alone is not C Both statements together are not sufficient D Statement II alone is sufficient, but Statement I alone is not
6. Question 6 of 50

   What is the speed s = d / t of a car? (distance d in km from 1 to 200, time t in hours from 1 to 10) I. d = 120 km. II. t = 2 hours.

   A Both statements together are sufficient, but neither alone is sufficient B Either statement alone is sufficient C Statement II alone is sufficient, but Statement I alone is not D Statement I alone is sufficient, but Statement II alone is not
7. Question 7 of 50

   Each of A, B and C is either always truthful or always a liar. A says: 'B is a liar'. B says: 'at least one of A and C is truthful'. C says: 'A and B are of different types'. Who is truthful?

   A B and C are truthful B A and C are truthful C B only D All three are truthful
8. Question 8 of 50

   Each of A, B and C is either always truthful or always a liar. A says: 'at least one of B and C is truthful'. B says: 'A and C are of different types'. C says: 'B is truthful'. Who is truthful?

   A B and C are truthful B A only C All three are truthful D None of them is truthful
9. Question 9 of 50

   What is the value of the positive integer x (at most 30)? I. x is a prime number. II. x < 10.

   A Either statement alone is sufficient B Statement I alone is sufficient, but Statement II alone is not C Both statements together are not sufficient D Both statements together are sufficient, but neither alone is sufficient
10. Question 10 of 50

    If p is True and q is False, the truth value of the biconditional p ↔ q is

    A False B True C Cannot be determined D True if q is later proved
11. Question 11 of 50

    The conditional p → q is logically equivalent to

    A p ∨ ¬q B ¬p ∨ q C ¬p ∧ q D p ∧ q
12. Question 12 of 50

    By De Morgan's law, ¬(p ∨ q) is equivalent to

    A ¬p ∨ ¬q B p ∧ q C p → ¬q D ¬p ∧ ¬q
13. Question 13 of 50

    Is x greater than y? (x and y are positive integers) I. x = y + 3. II. x² > y².

    A Both statements together are sufficient, but neither alone is sufficient B Statement I alone is sufficient, but Statement II alone is not C Either statement alone is sufficient D Statement II alone is sufficient, but Statement I alone is not
14. Question 14 of 50

    If p → q is true and q is false, then p must be

    A True B True or false C False D Undefined
15. Question 15 of 50

    What is the value of xy? (x and y are positive integers) I. x + y = 5. II. x − y = 1.

    A Statement II alone is sufficient, but Statement I alone is not B Both statements together are not sufficient C Statement I alone is sufficient, but Statement II alone is not D Both statements together are sufficient, but neither alone is sufficient
16. Question 16 of 50

    Consider the following 4 statements. Statement 1: 'Exactly 2 of these 4 statements are false.' Statement 2: 'Exactly 4 of these 4 statements are false.' Statement 3: 'Exactly 2 of these 4 statements are false.' Statement 4: 'Exactly 1 of these 4 statements is false.' Which statements are true?

    A Only statement 2 is true B Only statement 3 is true C None of the statements is true D Statements 1 and 3 are true
17. Question 17 of 50

    The negation of the conditional p → q is

    A ¬p → ¬q B p ∧ ¬q C ¬p ∧ q D q → p
18. Question 18 of 50

    Is Ali taller than Bilal? (heights are distinct integers in cm from 150 to 155) I. Ali is taller than Chand. II. Chand is taller than Bilal.

    A Both statements together are sufficient, but neither alone is sufficient B Either statement alone is sufficient C Both statements together are not sufficient D Statement I alone is sufficient, but Statement II alone is not
19. Question 19 of 50

    Is the positive integer x even? I. x² is even. II. x + 1 is odd.

    A Either statement alone is sufficient B Statement II alone is sufficient, but Statement I alone is not C Both statements together are sufficient, but neither alone is sufficient D Statement I alone is sufficient, but Statement II alone is not
20. Question 20 of 50

    'The team wins only if it plays well' is symbolised as (w = wins, p = plays well)

    A w → p B p → w C w ↔ p D p ∨ w
21. Question 21 of 50

    What is the cost p of one pen? (pen price p and pencil price q are positive integers up to 50) I. 3p + 2q = 24. II. p + q = 9.

    A Both statements together are not sufficient B Statement I alone is sufficient, but Statement II alone is not C Both statements together are sufficient, but neither alone is sufficient D Either statement alone is sufficient
22. Question 22 of 50

    By De Morgan's law, ¬(p ∧ q) is equivalent to

    A ¬p ∧ ¬q B p ∨ q C ¬p → q D ¬p ∨ ¬q
23. Question 23 of 50

    What is the value of x? (x and y are integers from 1 to 20) I. x + y = 10. II. x − y = 2.

    A Statement I alone is sufficient, but Statement II alone is not B Both statements together are sufficient, but neither alone is sufficient C Statement II alone is sufficient, but Statement I alone is not D Either statement alone is sufficient
24. Question 24 of 50

    Consider the following 4 statements. Statement 1: 'Exactly 1 of these 4 statements is false.' Statement 2: 'Exactly 0 of these 4 statements are false.' Statement 3: 'Exactly 4 of these 4 statements are false.' Statement 4: 'Exactly 3 of these 4 statements are false.' Which statements are true?

    A Statements 2 and 4 are true B Only statement 4 is true C Statements 2 and 3 are true D Statements 1 and 2 are true
25. Question 25 of 50

    The contrapositive of 'If it rains, the match is cancelled' is

    A If the match is cancelled, then it rains B If the match is not cancelled, then it does not rain C If it does not rain, the match is not cancelled D If it rains, the match is not cancelled
26. Question 26 of 50

    What is the value of x? (x is a positive integer up to 20) I. x² − 5x + 6 = 0. II. x > 2.

    A Both statements together are sufficient, but neither alone is sufficient B Both statements together are not sufficient C Statement II alone is sufficient, but Statement I alone is not D Statement I alone is sufficient, but Statement II alone is not
27. Question 27 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'B is a liar'. B says: 'A and C are of the same type'. C says: 'B is truthful'. Who is truthful?

    A None of them is truthful B A only C All three are truthful D C only
28. Question 28 of 50

    Consider the following 4 statements. Statement 1: 'Exactly 3 of these 4 statements are false.' Statement 2: 'Exactly 4 of these 4 statements are false.' Statement 3: 'Exactly 4 of these 4 statements are false.' Statement 4: 'Exactly 2 of these 4 statements are false.' Which statements are true?

    A Only statement 1 is true B Statements 2 and 4 are true C None of the statements is true D Only statement 2 is true
29. Question 29 of 50

    Is the integer p (between 2 and 30) a prime number? I. p is odd. II. p is less than 4.

    A Both statements together are not sufficient B Both statements together are sufficient, but neither alone is sufficient C Statement II alone is sufficient, but Statement I alone is not D Statement I alone is sufficient, but Statement II alone is not
30. Question 30 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'B is truthful'. B says: 'both A and C are liars'. C says: 'both A and B are liars'. Who is truthful?

    A C only B A only C None of them is truthful D B only
31. Question 31 of 50

    Is the positive integer x (at most 100) divisible by 4? I. x is divisible by 8. II. x is divisible by 12.

    A Both statements together are not sufficient B Either statement alone is sufficient C Both statements together are sufficient, but neither alone is sufficient D Statement II alone is sufficient, but Statement I alone is not
32. Question 32 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'B is truthful'. B says: 'at least one of A and C is truthful'. C says: 'both A and B are liars'. Who is truthful?

    A B and C are truthful B A and B are truthful C A and C are truthful D B only
33. Question 33 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'B and C are of the same type'. B says: 'at least one of A and C is truthful'. C says: 'B is truthful'. Who is truthful?

    A B only B All three are truthful C A and C are truthful D B and C are truthful
34. Question 34 of 50

    What is A's age (in whole years)? I. A is 5 years older than B. II. B is 20 years old.

    A Either statement alone is sufficient B Statement II alone is sufficient, but Statement I alone is not C Both statements together are sufficient, but neither alone is sufficient D Statement I alone is sufficient, but Statement II alone is not
35. Question 35 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'B and C are of the same type'. B says: 'A is a liar'. C says: 'B is a liar'. Who is truthful?

    A A and C are truthful B B only C A and B are truthful D B and C are truthful
36. Question 36 of 50

    If p is True and q is False, the truth value of the conditional p → q is

    A True B Cannot be determined C False D True or False depending on r
37. Question 37 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'at least one of B and C is truthful'. B says: 'both A and C are liars'. C says: 'A is truthful'. Who is truthful?

    A C only B B and C are truthful C A and C are truthful D A and B are truthful
38. Question 38 of 50

    Is the positive integer x (at most 60) a multiple of 3? I. x is a multiple of 6. II. x is even.

    A Either statement alone is sufficient B Statement II alone is sufficient, but Statement I alone is not C Statement I alone is sufficient, but Statement II alone is not D Both statements together are sufficient, but neither alone is sufficient
39. Question 39 of 50

    How many students are in a class? (the number is a positive integer up to 100) I. The number is greater than 30, less than 40 and a multiple of 8. II. The number is even.

    A Statement II alone is sufficient, but Statement I alone is not B Both statements together are sufficient, but neither alone is sufficient C Statement I alone is sufficient, but Statement II alone is not D Either statement alone is sufficient
40. Question 40 of 50

    The inverse of 'If a number is divisible by 4, then it is even' is

    A If a number is even, then it is divisible by 4 B If a number is not even, then it is not divisible by 4 C If a number is not divisible by 4, then it is not even D If a number is odd, then it is divisible by 4
41. Question 41 of 50

    Consider the following 4 statements. Statement 1: 'Exactly 1 of these 4 statements is false.' Statement 2: 'Exactly 4 of these 4 statements are false.' Statement 3: 'Exactly 3 of these 4 statements are false.' Statement 4: 'Exactly 0 of these 4 statements are false.' Which statements are true?

    A None of the statements is true B Statements 2 and 4 are true C Only statement 2 is true D Only statement 3 is true
42. Question 42 of 50

    Is the product ab positive? (a and b are non-zero integers between -10 and 10) I. a > 0. II. b > 0.

    A Statement I alone is sufficient, but Statement II alone is not B Both statements together are sufficient, but neither alone is sufficient C Either statement alone is sufficient D Both statements together are not sufficient
43. Question 43 of 50

    If p is True and q is True, the truth value of the exclusive or p ⊕ q is

    A True B Cannot be determined C True only if r is true D False
44. Question 44 of 50

    'p unless q' is equivalent to

    A q → p B p → ¬q C ¬q → p D ¬p → ¬q
45. Question 45 of 50

    Is x less than 5? (x is a positive integer up to 10) I. x² < 30. II. x is a prime number less than 7.

    A Both statements together are not sufficient B Either statement alone is sufficient C Statement I alone is sufficient, but Statement II alone is not D Statement II alone is sufficient, but Statement I alone is not
46. Question 46 of 50

    The converse of 'If x is even, then x² is even' is

    A If x is odd, then x² is odd B If x is not even, then x² is not even C If x² is odd, then x is even D If x² is even, then x is even
47. Question 47 of 50

    If p is False and q is False, the truth value of p → q is

    A True B False C Cannot be determined D Undefined
48. Question 48 of 50

    What is the perimeter of a rectangle with integer sides (length l, width w, each from 1 to 30)? I. l = 6 and the area is 24. II. l − w = 2.

    A Either statement alone is sufficient B Both statements together are not sufficient C Both statements together are sufficient, but neither alone is sufficient D Statement I alone is sufficient, but Statement II alone is not
49. Question 49 of 50

    Each of A, B and C is either always truthful or always a liar. A says: 'C is truthful'. B says: 'both A and C are liars'. C says: 'both A and B are liars'. Who is truthful?

    A A and B are truthful B B only C None of them is truthful D A only
50. Question 50 of 50

    Is the sum of two positive integers a and b (each up to 20) even? I. Both a and b are odd. II. The product ab is odd.

    A Statement I alone is sufficient, but Statement II alone is not B Either statement alone is sufficient C Both statements together are not sufficient D Statement II alone is sufficient, but Statement I alone is not

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