1. How is A related to B?
I. A is the daughter of C, who is the wife of B.
II. B is the husband of C.
Options:
(A) I alone sufficient, II not sufficient
(B) II alone sufficient, I not sufficient
(C) Both together sufficient, neither alone sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: From I, A is daughter of C and C is wife of B → A is daughter of B. So I alone is sufficient.
2. What is the code for ‘BOOK’?
I. ‘BOOK IS GOOD’ → XO PQ NO
II. ‘THIS BOOK IS NICE’ → RO XO PQ MO
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Comparing I & II → common code PQ = IS, so XO = BOOK.
3. Which direction is Ravi facing?
I. Ravi faces opposite of Sunil who faces East.
II. Ravi faces the same direction as Mohan who faces West.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II alone tells Ravi faces West.
4. How many students are in the class?
I. Boys are twice the number of girls.
II. There are 45 students in total.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II directly gives total students.
5. Is Rahul younger than Priya?
I. The average of their ages is 22.
II. Priya is 2 years older than Rahul.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II directly says Priya > Rahul.
6. Who is taller – Neha or Riya?
I. Neha is taller than Meena.
II. Riya is taller than Meena but shorter than Neha.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II alone shows Neha > Riya.
7. Is 24 a multiple of 3?
I. 24 ÷ 3 gives remainder 0.
II. 3 × 8 = 24.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Each alone confirms 24 is multiple of 3.
8. Which city is farther from Delhi – Mumbai or Kolkata?
I. Mumbai is 1400 km from Delhi.
II. Kolkata is 1500 km from Delhi.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Need both distances to compare.
9. What is the color of Ram’s car?
I. Ram’s car is same as Shyam’s.
II. Shyam’s car is red.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → Ram’s car is red.
10. Is X > Y?
I. X + Y = 10.
II. X – Y = 2.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II alone gives X > Y.
11. Is the number even?
I. The number is divisible by 2.
II. The number ends with 0.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either fact proves the number is even.
12. Who is oldest among A, B, C?
I. A is older than B.
II. B is older than C.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → A > B > C → A oldest.
13. Can the project be completed on time?
I. It requires 10 workers for 6 days.
II. There are 15 workers available.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Work rate unknown, both insufficient.
14. What is the actual time?
I. Clock shows 2 hours earlier than actual.
II. Clock shows 10:00.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → actual time = 12:00.
15. How many brothers does Anil have?
I. Anil’s father has 3 sons.
II. Anil is one of the sons.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → Anil has 2 brothers.
16. Is the number prime?
I. It is an odd number.
II. It has no divisors other thn 1 and itself.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II alone defines primality.
17. Who is sitting in the middle?
I. A is between B and C.
II. B is to the left of A.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: From I → A is in middle.
18. Is it raining outside?
I. People are carrying umbrellas.
II. The ground is wet.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Both can happen without rain; not conclusive.
19. Is Sita married?
I. Sita’s husband works in Delhi.
II. Sita wears a mangalsutra.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: I alone proves she has a husband → married.
20. Is P a teacher?
I. P teaches students in a school.
II. P has a degree in education.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: I alone confirms the profession.
21. Is Mohan a doctor?
I. Mohan works in a hospital.
II. All doctors work in hospitals.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: From I, Mohan works in hospital, but could be nurse or clerk. II is a general fact. Both not sufficient.
22. Is the train on time?
I. The train arrived at 7:00 p.m.
II. The scheduled time was 7:00 p.m.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Need both actual and scheduled time → Together sufficient.
23. Is 15% of x greater than 10% of y?
I. x = y
II. x > y
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: If x > y → 15% of x > 10% of y.
24. What is Ramesh’s rank from the top?
I. Ramesh’s rank from the bottom is 10th.
II. There are 30 students in the class.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: From both, rank from top = 30 – 10 + 1 = 21st.
25. Is the number divisible by 4?
I. The number ends with 48.
II. The number ends with 28.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: 48 divisible by 4 → number divisible. II not divisible.
26. How is P related to Q?
I. P is the brother of R, who is the father of Q.
II. Q is the daughter of R.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: From I, P is brother of R → P is uncle of Q.
27. Is Seema an engineer?
I. All engineers are graduates.
II. Seema is a graduate.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Being a graduate doesn’t ensure she’s an engineer.
28. Which day was 15th August 2025?
I. 1st August 2025 was a Friday.
II. 31st August 2025 was a Sunday.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: From 1st August = Friday → 15th = Friday + 14 days → Friday again.
29. Is A older than D?
I. A is older than B and C.
II. C is older than D.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: From I and II, A > C > D → A older than D.
30. Is number 49 a perfect square?
I. 7 × 7 = 49.
II. √49 = 7.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either alone confirms perfect square.
31. How many girls are in the group?
I. There are 20 students total.
II. There are 12 boys.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: 20 – 12 = 8 girls.
32. Is the pen blue?
I. The pen is of the same color as the sky.
II. The sky is blue.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → pen is blue.
33. Is 9 a factor of 81?
I. 81 ÷ 9 = 9.
II. 9 × 9 = 81.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Each alone confirms divisibility.
34. Is A married to B?
I. B refers to A as husband.
II. A refers to B as wife.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either statement sufficient.
35. Is the product positive?
I. One number is positive, other is negative.
II. The magnitude of each is 5.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: Positive × Negative = Negative → product not positive.
36. Can the meeting start before 10 a.m.?
I. The chairman will arrive at 9:45 a.m.
II. The meeting starts only after chairman arrives.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together show meeting can start after 9:45 → Yes, before 10.
37. Who scored highest marks?
I. A scored more than B but less than C.
II. D scored less than C.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → C highest.
38. Is the sum of two numbers even?
I. Both numbers are even.
II. One number is even and one is odd.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: Even + Even = Even → I alone sufficient.
39. Does the bus go to Mysuru?
I. The bus goes to Mandya.
II. Mandya is on the route to Mysuru.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → bus goes via Mandya → goes to Mysuru.
40. Is Neeraj left-handed?
I. Neeraj writes with his left hand.
II. Neeraj bats left-handed.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: I alone proves left-handedness.
41. Is the box made of wood?
I. The box floats on water.
II. All wooden boxes float on water.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Some other materials also float; both not conclusive.
42. Is the person an Indian citizen?
I. He was born in India.
II. He holds an Indian passport.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: Passport is legal proof → II alone sufficient.
43. Is x an even number?
I. x is divisible by 4.
II. x is divisible by 2.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Divisible by 2 or 4 → both individually prove evenness.
44. Who is the mother of D?
I. B is the wife of A.
II. D is the daughter of A and B.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: From both → B is mother of D.
45. Is the bulb fused?
I. There is no light in the room.
II. The switch is ON.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: If switch ON but no light → bulb fused.
46. Is A taller than B?
I. A is taller than C.
II. C is taller than B.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: From I & II → A > C > B → A taller than B.
47. Is the pen costly?
I. The pen costs ₹500.
II. All pens costing more than ₹100 are costly.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → ₹500 > ₹100 → costly.
48. Is 36 divisible by 9?
I. 9 × 4 = 36.
II. 36 ÷ 9 = 4.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Each alone proves divisibility.
49. Is John older than Peter?
I. Peter was born in 1995.
II. John was born in 1990.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Need both birth years → 1990 < 1995 → John older.
50. Is the candidate qualified?
I. The candidate passed the written exam.
II. The candidate passed the interview.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Both steps required → together sufficient.
51. Who among P, Q, R is the youngest?
I. Q is older than R.
II. P is older than Q.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: P > Q > R → R youngest.
52. Is the word “CAT” coded as “DBU”?
I. In the code, each letter is replaced by next letter.
II. The code for “BAT” is “CBU”.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either I or II gives rule → CAT → DBU.
53. Is Ramesh married?
I. Ramesh’s wife works in a bank.
II. Ramesh is wearing a wedding ring.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: I alone proves marriage.
54. Is the train late?
I. The train scheduled time is 6:00 p.m.
II. The train arrived at 6:30 p.m.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Compare both → train is 30 min late.
55. Is number 27 divisible by 6?
I. 27 is divisible by 3.
II. 27 is odd.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Need divisibility by both 2 & 3; not enough.
56. Is Neha’s birthday in March?
I. Her birthday is after February.
II. Her birthday is before April.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → March only fits between Feb & April.
57. Is the bottle glass or plastic?
I. The bottle breaks when dropped.
II. Plastic bottles don’t break when dropped.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → breaks → must be glass.
58. Who lives in the red house?
I. Ramesh lives next to the red house.
II. The green house is on the other side of Ramesh’s house.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Neither statement identifies who lives in the red house.
59. Is the student eligible for admission?
I. Minimum age required is 18 years.
II. The student’s age is 19 years.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Need both rule and data → 19 ≥ 18 → eligible.
60. Is the sum of digits of 234 divisible by 3?
I. Sum of digits = 9.
II. A number is divisible by 3 if sum of digits divisible by 3.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: From both → 9 divisible by 3 → Yes.
61. Is the person a student?
I. The person attends classes regularly.
II. The person studies in a college.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: Studying in a college implies being a student → II alone sufficient.
62. Is 64 greater than 8 × 7?
I. 8 × 7 = 56.
II. 64 > 56.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Need both to compare values → 64 > 56.
63. Is Ravi younger than Suresh?
I. Suresh was born in 1998.
II. Ravi was born in 2000.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Both birth years required → 2000 > 1998 → Ravi younger.
64. Is the number divisible by 5?
I. The number ends with 0.
II. The number ends with 5.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either ending with 0 or 5 → divisible by 5.
65. Is A the sister of B?
I. A and B are children of the same parents.
II. A is female.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Same parents + A is female → A is sister of B.
66. Is today Sunday?
I. Yesterday was Saturday.
II. Tomorrow is Monday.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either statement alone implies today = Sunday.
67. Is x = y?
I. 2x = 2y.
II. x – y = 0.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either condition implies x = y.
68. Is Seema working in a bank?
I. All bank employees wear ID cards.
II. Seema wears an ID card of a bank.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together show she’s a bank employee.
69. Is x a negative number?
I. x² = 9.
II. x < 0.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: From I → x = ±3; II → negative → x = –3.
70. Is the triangle equilateral?
I. All sides are equal.
II. All angles are equal.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either property defines an equilateral triangle.
71. Is the sum of two numbers odd?
I. One number is even.
II. The other number is odd.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Even + Odd = Odd → both together sufficient.
72. Does the person have a driving license?
I. The person is 18 years old.
II. The person drives a car.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Age or driving doesn’t prove possession of license.
73. Is x > 5?
I. x + 2 = 8.
II. x – 3 = 4.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Each gives x = 6 → x > 5.
74. Is the shop open on Sunday?
I. The shop opens every day except Monday.
II. Today is Sunday.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → open on Sunday.
75. Is the number 121 a perfect square?
I. 11 × 11 = 121.
II. √121 = 11.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either statement proves 121 is a perfect square.
76. Is Kavya married?
I. Kavya’s husband works abroad.
II. Kavya has a wedding ring.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: I alone confirms she has a husband → married.
77. Is the bottle full?
I. The bottle cannot hold any more water.
II. The water level is at the top.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Each statement independently confirms fullness.
78. Is the teacher present today?
I. The teacher’s car is parked outside.
II. The teacher is taking class.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (B)
Explanation: II alone directly confirms presence.
79. Is the number divisible by 9?
I. Sum of digits of the number is 18.
II. A number is divisible by 9 if sum of digits is divisible by 9.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Together → 18 divisible by 9 → Yes.
80. Is Ramesh’s father a teacher?
I. Ramesh’s father works in a school.
II. All teachers work in schools.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: Working in school ≠ teacher; both not sufficient.
81. Is the lamp switched ON?
I. The bulb is glowing.
II. The switch of the lamp is in ‘ON’ position.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: If bulb is glowing, lamp must be ON — I alone sufficient.
82. Is the book available in the library?
I. The librarian says the book is issued.
II. The book is not on the shelf.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: If librarian says it’s issued and it’s not on shelf, together confirm it’s currently unavailable (issued). Need both for certainty.
83. Is x > 0?
I. x² = 25.
II. x is an integer.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: From I, x = ±5; II alone gives no sign info. Even together we only know x = ±5 (integer) — not enough to decide positive.
84. Is the road closed?
I. There is a signboard saying ‘Road Closed’.
II. Traffic policemen are diverting vehicles.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Signboard or diversion individually suggest closure, but together definitively indicate road is closed.
85. Is A the father of B?
I. B calls A ‘father’.
II. A is male and lives with B.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: B calling A ‘father’ directly indicates relationship — I alone sufficient.
86. Is 50 a multiple of 10?
I. 5 × 10 = 50.
II. 50 ends with 0.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Each statement independently shows 50 is a multiple of 10.
87. Is the candidate eligible for the post which requires MBA?
I. The candidate has an MBA degree.
II. The candidate has 2 years’ experience.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: Requirement is MBA — I alone sufficient; experience irrelevant to the given criterion.
88. Can the file be opened?
I. The file is not corrupted.
II. The correct software to open the file is installed.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: File uncorrupted and appropriate software are both required → together sufficient.
89. Is the sum of digits of 358 equal to 16?
I. 3 + 5 + 8 = 16.
II. Sum of digits of any three-digit number equals its digits added.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: I explicitly gives the sum =16 → I alone sufficient.
90. Is the student eligible for scholarship requiring GPA ≥ 3.5?
I. The student’s GPA is 3.7.
II. The scholarship requires GPA ≥ 3.5 and income < ₹3 lakh.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: I confirms GPA criterion; II gives rule and income criterion but not student’s income. Together we have GPA meets requirement but we still lack income info — wait: careful — need both to conclude eligibility requires both GPA and income; since II says scholarship needs both conditions, and I only gives GPA, we still don’t know income. Correction: Answer should be (E) if income unknown. But we must choose between options — re-evaluate.
Corrected Answer: (E)
Corrected Explanation: I shows GPA meets the GPA criterion, II only states the scholarship’s rules (requires GPA and income). Since student’s income is not given, even both statements together are insufficient to confirm eligibility.
(Note: In Data Sufficiency, a statement that states the rule (II) plus a data point about one condition (I) still leaves the other condition unknown — so insufficient.)
91. Is the train from City A to City B cancelled?
I. The railway website shows ‘Cancelled’ for that train.
II. Passengers standing on platform say earlier trains ran on time.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: Official website showing ‘Cancelled’ confirms cancellation — I alone sufficient.
92. Is the product defective?
I. The product fails the quality test.
II. The product was manufactured last week.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: Failing quality test indicates defectiveness — I alone sufficient.
93. Is x divisible by 6?
I. x is divisible by 2.
II. x is divisible by 3.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Divisibility by both 2 and 3 together implies divisibility by 6.
94. Is Rahul the eldest among 4 siblings?
I. Rahul is older than Sita and Amit.
II. Rahul is younger than Ravi.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (E)
Explanation: From I and II we know Rahul older than two but younger than Ravi — cannot determine if Rahul is eldest overall (Ravi might not be eldest or there could be others). Insufficient.
95. Is the function f(x) even?
I. f(x) = f(−x) for all x.
II. f(x) + f(−x) = 0 for all x.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: Definition: if f(x) = f(−x) for all x, f is even — I alone sufficient. II implies odd function (f(−x) = −f(x)), not even.
96. Is the medicine safe to use?
I. Clinical trials show no adverse effects.
II. The medicine has approval from the regulatory authority.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (C)
Explanation: Approval + clean clinical trials together strongly indicate safety — in Data Sufficiency terms, both together provide the needed confirmation.
97. Is x a rational number?
I. x = 1/3.
II. x = 0.333… (repeating).
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Both forms represent a rational number; either statement alone suffices.
98. Is the meeting scheduled for 3 p.m.?
I. The notice says ‘Meeting at 15:00 hrs’.
II. The invitation mentions ‘Meeting in the afternoon’.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: 15:00 hrs is 3 p.m. — I alone sufficient; II is too vague.
99. Is the rectangle a square?
I. All sides of the rectangle are equal.
II. Adjacent sides are equal in length.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (D)
Explanation: Either ‘all sides equal’ or ‘adjacent sides equal’ (for rectangle that implies all sides equal) individually confirm a square.
100. Is the patient allergic to penicillin?
I. The patient had an allergic reaction after receiving a penicillin injection.
II. The patient has taken penicillin earlier with no reaction.
Options:
(A) I alone sufficient
(B) II alone sufficient
(C) Both together sufficient
(D) Each alone sufficient
(E) Both not sufficient
Answer: (A)
Explanation: An allergic reaction after penicillin indicates allergy — I alone sufficient. Prior tolerance (II) contradicts but does not alone disprove an allergy (sensitization can change).