Question 1

Statements:
I. All honest people are trustworthy.
II. Some trustworthy people are not rich.

Question: Can we conclude that some honest people are not rich?

A) Yes, definitely
B) No, it is not possible to conclude this
C) Yes, but only if all rich people are dishonest
D) No, because all honest people must be rich

Accepted Answer

From Statement I: Honest ⊆ Trustworthy. From Statement II: Some trustworthy people are not rich. However, Statement II does not specify which trustworthy people are not rich. The non-rich trustworthy people could be entirely from the non-honest subset of trustworthy people. We cannot definitively conclude that any honest person is not rich. The answer is: We cannot determine this.

Question 2

Statements:
I. All teachers are educated.
II. Some educated people are not doctors.

Question: Is it possible that all teachers are doctors?

A) Yes, it is definitely possible
B) No, it is definitely not possible
C) Cannot be determined from the given statements
D) Yes, but only if all educated people are teachers

Accepted Answer

From Statement I: All teachers are educated. From Statement II: Some educated people are not doctors. This means the educated group contains both doctors and non-doctors. Since all teachers belong to the educated group, teachers could be entirely within the doctor subset or entirely within the non-doctor subset of educated people. Therefore, it IS possible that all teachers are doctors (they would just be the educated people who are doctors). The statements do not forbid this.

Question 3

Statements:
I. All fruits are sweet.
II. Some sweet things are not healthy.

Question: Which of the following must be true?
(A) All fruits are healthy.
(B) Some fruits are not healthy.
(C) No fruit is healthy.
(D) We cannot determine if any fruit is healthy.

Accepted Answer

From Statement I: All fruits are sweet. From Statement II: Some sweet things are not healthy (meaning at least one sweet thing is not healthy, but this does NOT tell us whether fruits specifically are healthy or not). Since fruits are a subset of sweet things, and we only know that SOME sweet things are not healthy (not all), we cannot conclude anything definitive about whether fruits are healthy. The answer is (D) because the statements do not provide sufficient information to determine the health status of fruits.

Question 4

In a group of 5 people, each person shakes hands with every other person exactly once. How many total handshakes occur?

Statement I: There are 5 people in the group.
Statement II: Each handshake involves exactly 2 people.

Which statement(s) is/are sufficient to answer the question?

(A) Statement I alone is sufficient
(B) Statement II alone is sufficient
(C) Both statements together are necessary
(D) Either statement alone is sufficient

Accepted Answer

To find total handshakes, we need to know: (1) the number of people, and (2) that each pair shakes hands exactly once. Statement I gives us the number of people (5). Statement II confirms the nature of a handshake (2 people per handshake). However, Statement I alone is sufficient because the question already specifies 'each person shakes hands with every other person exactly once'—this establishes the rule. From Statement I alone, we can calculate: C(5,2) = 5×4/2 = 10 handshakes. Statement II merely restates what a handshake is and doesn't add new information needed for the calculation. Therefore, Statement I alone is sufficient.

Question 5

Statements:
I. All teachers are educated.
II. Some educated people are not teachers.

Question: Is it possible for an educated person to not be a teacher?

Which statement(s) is/are sufficient to answer the question?

Accepted Answer

Statement II directly states that some educated people are not teachers, which answers the question affirmatively. Statement I only tells us teachers are educated but does not address whether educated people must be teachers. Therefore, only Statement II is sufficient.

Question 6

Statements:
I. All engineers are problem-solvers.
II. All problem-solvers are intelligent.

Question: Which of the following must be true?
(A) All intelligent people are engineers.
(B) Some engineers are not intelligent.
(C) All engineers are intelligent.
(D) No engineer is intelligent.

Accepted Answer

From Statement I: All engineers are problem-solvers (Engineers ⊆ Problem-solvers). From Statement II: All problem-solvers are intelligent (Problem-solvers ⊆ Intelligent). By transitive property: Engineers ⊆ Problem-solvers ⊆ Intelligent, therefore Engineers ⊆ Intelligent. This means all engineers must be intelligent. The answer is (C).

Question 7

Statements:
I. All flowers are plants.
II. Some plants are green.
III. All roses are flowers.

Question: Which conclusion logically follows?

A) All roses are green
B) Some roses are green
C) All roses are plants
D) No rose is green

Accepted Answer

From Statement III: All roses are flowers. From Statement I: All flowers are plants. By transitivity: All roses are plants. This is a definite logical conclusion. Statement II (some plants are green) does not tell us whether roses specifically are green—only that some plants in general are. Therefore, we cannot conclude roses are green, but we CAN conclude roses are plants.

Question 8

Is Rahul taller than Priya?

Statement I: Rahul is taller than Amit, and Amit is taller than Priya.
Statement II: Priya is shorter than Rahul by 5 cm.

Accepted Answer

To determine if Rahul is taller than Priya, we need to establish a clear height relationship between them.

Statement I alone: 'Rahul > Amit > Priya' directly establishes that Rahul is taller than Priya. This statement is SUFFICIENT on its own.

Statement II alone: 'Priya is shorter than Rahul by 5 cm' directly tells us Rahul is taller than Priya. This statement is also SUFFICIENT on its own.

Since both statements independently provide sufficient information to answer the question, the answer is that the data is sufficient from either statement alone. The question can be definitively answered as 'Yes, Rahul is taller than Priya' using either Statement I or Statement II.

Therefore, the correct answer is (b) - Either Statement I alone or Statement II alone is sufficient.

Question 9

Statements:
I. All fruits are sweet.
II. All mangoes are fruits.
III. Some sweet things are expensive.

Question: Which of the following must be true?

(A) All mangoes are expensive.
(B) Some mangoes are expensive.
(C) All mangoes are sweet.
(D) Some fruits are not sweet.

Accepted Answer

From Statement II: All mangoes are fruits. From Statement I: All fruits are sweet. By transitive logic: All mangoes are sweet. Statement III tells us some sweet things are expensive, but this does NOT mean some mangoes are expensive—mangoes could be among the sweet things that are NOT expensive. Therefore, the only statement that MUST be true is that all mangoes are sweet.

Question 10

Statements:
I. Raj scored more marks than Priya.
II. Priya scored more marks than Karan.

Question: Did Raj score more marks than Karan?

Which statement(s) is/are sufficient to answer the question?

Accepted Answer

Using transitive property: If Raj > Priya (Statement I) and Priya > Karan (Statement II), then Raj > Karan. Both statements together establish a clear ordering, making the answer 'Yes.' Neither statement alone is sufficient because each only compares two people.

Question 11

Statements:
I. No politician is honest.
II. Some honest people are rich.

Question: Can we conclude that no politician is rich?

Which of the following is correct?
(A) Yes, we can definitely conclude this.
(B) No, we cannot conclude this.
(C) Yes, but only if all rich people are honest.
(D) No, because all politicians must be rich.

Accepted Answer

From Statement I: No politician is honest (Politicians and honest people are mutually exclusive). From Statement II: Some honest people are rich. However, this does NOT tell us about the relationship between politicians and rich people. A politician could still be rich without being honest. The statements do not provide sufficient information to conclude whether politicians can or cannot be rich.

Question 12

Statements:
I. No cats are dogs.
II. All pets are either cats or dogs.

Question: Can a pet be a cat?

Which statement(s) is/are sufficient to answer the question?

Accepted Answer

Statement II tells us all pets are either cats or dogs. This directly implies that pets can be cats (since cats are one of the two options). Statement I only clarifies that cats and dogs are mutually exclusive, but doesn't answer whether pets can be cats. Statement II alone is sufficient to answer 'Yes, a pet can be a cat.'

Question 13

Statements:
I. No reptile is a mammal.
II. All snakes are reptiles.

Question: Which of the following must be true?

A) All snakes are mammals
B) No snake is a mammal
C) Some snakes are mammals
D) Some snakes are not reptiles

Accepted Answer

From Statement I: Reptiles and mammals are mutually exclusive (no overlap). From Statement II: All snakes belong to the reptile category. By logical deduction: If snakes are reptiles, and no reptile is a mammal, then no snake can be a mammal. This MUST be true.

Question 14

Statements:
I. No politician is honest.
II. Some honest people are rich.

Question: Can we conclude that no politician is rich?

Which of the following is correct?
(A) Yes, we can definitely conclude this.
(B) No, we cannot conclude this.
(C) The conclusion is definitely false.
(D) We need more information.

Accepted Answer

From Statement I: No politician is honest (Politicians and Honest people are disjoint sets). From Statement II: Some honest people are rich (Honest people overlap with Rich people). The question asks if we can conclude that no politician is rich. Since politicians are excluded from the honest group, and the only link between politicians and rich people would be through the honest group, politicians could still be rich through a non-honest path. The statements do not provide enough information to conclude whether politicians are rich or not. The answer is (B).

Question 15

Statements:
I. All teachers are educated.
II. Some educated people are not doctors.

Question: Is it possible that all teachers are doctors?

Which of the following is correct?
(A) Yes, it is definitely possible.
(B) No, it is definitely not possible.
(C) Cannot be determined from the given statements.
(D) Yes, it is definitely true.

Accepted Answer

From Statement I: All teachers are educated. From Statement II: Some educated people are not doctors (meaning at least one educated person is not a doctor, but this does NOT exclude teachers from being doctors). Since all teachers are educated, and Statement II only tells us that SOME educated people are not doctors (not ALL), it remains possible that all teachers could be doctors. However, it is NOT definitely true—it is merely possible. The correct answer is (A) because the statements do not contradict the possibility that all teachers are doctors.

Question 16

Statements:
I. All students in Class A passed the exam.
II. Some students in Class B failed the exam.
III. All students in Class A are from City X.

Question: Can we conclude that some students from City X failed the exam?

Which of the following is correct?

(A) Yes, we can definitely conclude this.
(B) No, we cannot conclude this.
(C) Yes, because some students in Class B are from City X.
(D) Yes, because all students in Class A are from City X.

Accepted Answer

From Statement I: All students in Class A passed. From Statement III: All students in Class A are from City X. Therefore, all students from City X who are in Class A passed. Statement II tells us some students in Class B failed, but we have no information about whether any students in Class B are from City X. We cannot conclude that some students from City X failed the exam, as the students from City X that we know about (those in Class A) all passed.

Question 17

Statements:
I. All teachers are educated.
II. Some educated people are not doctors.

Question: Is it possible that all teachers are doctors?

Which of the following is correct?
(A) Yes, it is definitely possible.
(B) No, it is definitely not possible.
(C) Cannot be determined from the given statements.
(D) Yes, but only if all educated people are teachers.

Accepted Answer

From Statement I: All teachers are educated. From Statement II: Some educated people are not doctors (meaning at least one educated person is not a doctor). However, this does NOT prevent all teachers from being doctors. Teachers form a subset of educated people, and it's logically possible for all members of this subset to be doctors while some other educated people are not. The statements do not contradict the possibility that all teachers are doctors.

Question 18

Statements:
I. Some athletes are vegetarians.
II. All vegetarians are health-conscious.

Question: Which of the following must be true?
(A) All athletes are health-conscious.
(B) Some athletes are health-conscious.
(C) No athlete is health-conscious.
(D) All health-conscious people are athletes.

Accepted Answer

From Statement I: Some athletes are vegetarians (Athletes ∩ Vegetarians ≠ ∅). From Statement II: All vegetarians are health-conscious (Vegetarians ⊆ Health-conscious). Since some athletes are vegetarians, and all vegetarians are health-conscious, those athletes who are vegetarians must be health-conscious. Therefore, at least some athletes are health-conscious. The answer is (B).

Question 19

Statements:
I. All engineers are problem-solvers.
II. No problem-solver is lazy.
III. Some engineers are not creative.

Question: Which of the following must be true?

(A) All engineers are lazy.
(B) No engineer is lazy.
(C) Some engineers are lazy.
(D) Some problem-solvers are creative.

Accepted Answer

From Statement I: All engineers are problem-solvers. From Statement II: No problem-solver is lazy. By transitive logic: No engineer is lazy (since all engineers are problem-solvers, and no problem-solver is lazy). Statement III about creativity is independent and does not affect this conclusion. Therefore, 'No engineer is lazy' must be true.

Question 20

Statements:
I. All roses are flowers.
II. Some flowers are red.

Question: Are all roses red?

Which statement(s) is/are sufficient to answer the question?

Accepted Answer

Statement I tells us roses are flowers, but Statement II only says some flowers are red—not all flowers, and certainly not all roses. Together, these statements cannot confirm that all roses are red. In fact, we can definitively answer 'No' because Statement II explicitly limits redness to only some flowers. Both statements together are sufficient to answer 'No.'

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