Question 1

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

Question: Are all athletes health-conscious?

Which of the following is correct?
(A) Yes, all athletes are health-conscious.
(B) No, not all athletes are health-conscious.
(C) Cannot be determined from the given statements.
(D) The statements are contradictory.

Accepted Answer

From Statement I: Some athletes are vegetarians (∃ Athletes who are Vegetarians). From Statement II: All vegetarians are health-conscious (Vegetarians ⊆ Health-conscious). This means the athletes who are vegetarians are health-conscious. However, we know nothing about the athletes who are NOT vegetarians. They may or may not be health-conscious. Therefore, we cannot conclude that ALL athletes are health-conscious.

Question 2

Statements:
I. No politician is honest.
II. All honest people are trustworthy.

Question: Can a politician be trustworthy?

(A) Yes, definitely
(B) No, definitely not
(C) Yes, but not necessarily through honesty
(D) Cannot be determined

Accepted Answer

From Statement I: No politician is honest (Politicians ∩ Honest = ∅). From Statement II: All honest people are trustworthy (Honest ⊆ Trustworthy). However, Statement II does NOT say that ONLY honest people are trustworthy. A politician could be trustworthy through other means (reliability, consistency, etc.) without being honest. Therefore, a politician CAN be trustworthy, but not necessarily through honesty.

Question 3

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 possible.
(B) No, it is not possible.
(C) Cannot be determined from the given statements.
(D) The statements are contradictory.

Accepted Answer

From Statement I: All teachers are educated. From Statement II: Some educated people are not doctors. This means at least one educated person is not a doctor. However, this does NOT mean all educated people (including teachers) are not doctors. Teachers could still be doctors because Statement II only says SOME educated people are not doctors, leaving room for teachers to be in the 'educated and doctor' category. Therefore, it IS possible that all teachers are doctors.

Question 4

Statements:
I. All roses are flowers.
II. Some flowers are red.
III. All red things are beautiful.

Question: Are all roses beautiful?

Which of the following is correct?
(A) Yes, all roses are beautiful.
(B) No, not all roses are beautiful.
(C) Cannot be determined from the given statements.
(D) Only some roses are beautiful.

Accepted Answer

From Statement I: All roses are flowers. From Statement II: Some flowers are red (not all). From Statement III: All red things are beautiful. The chain breaks at Statement II because we only know SOME flowers are red, not all. Since not all roses are necessarily red, we cannot conclude that all roses are beautiful. Some roses might not be red, and if they're not red, Statement III doesn't apply to them. Therefore, we cannot determine if all roses are beautiful.

Question 5

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

Question: Are all athletes health-conscious?

(A) Yes, all athletes are health-conscious
(B) No, not all athletes are health-conscious
(C) Cannot be determined from the given statements
(D) Yes, and this must be true

Accepted Answer

From Statement I: Some athletes are vegetarians (a subset of athletes). From Statement II: All vegetarians are health-conscious. This means the athletes who are vegetarians are health-conscious, but we have no information about the other athletes (those who are not vegetarians). They may or may not be health-conscious. Therefore, we cannot conclude that ALL athletes are health-conscious.

Question 6

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 possible
(B) No, it is not possible
(C) Cannot be determined from the given statements
(D) Yes, and it must be 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). 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 even though some other educated people are not. Therefore, it IS possible that all teachers are doctors.

Question 7

Statements:
I. All engineers are problem-solvers.
II. No problem-solver is lazy.

Question: Can an engineer be lazy?

Which of the following is correct?
(A) Yes, an engineer can be lazy.
(B) No, an engineer cannot be lazy.
(C) Cannot be determined from the given statements.
(D) The statements are contradictory.

Accepted Answer

From Statement I: All engineers are problem-solvers (Engineers ⊆ Problem-solvers). From Statement II: No problem-solver is lazy (Problem-solvers ∩ Lazy = ∅). By logical chain: If all engineers are problem-solvers, and no problem-solver is lazy, then no engineer can be lazy. This is a valid categorical syllogism. Therefore, an engineer CANNOT be lazy.

Question 8

Statements:
I. No politician is honest.
II. All honest people are trustworthy.

Question: Can a politician be trustworthy?

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

Accepted Answer

From Statement I: No politician is honest (Politicians ∩ Honest = ∅). From Statement II: All honest people are trustworthy (Honest ⊆ Trustworthy). Since politicians are not honest, Statement II does not apply to them. However, Statement II does NOT say that ONLY honest people are trustworthy. Non-honest people (including politicians) could still be trustworthy. Therefore, it cannot be determined whether a politician is trustworthy or not.

Question 9

Statements:
I. All doctors are professionals.
II. Some professionals are not engineers.

Question: Can a doctor be an engineer?

(A) No, a doctor cannot be an engineer
(B) Yes, a doctor can be an engineer
(C) All doctors must be engineers
(D) Cannot be determined

Accepted Answer

From Statement I: All doctors are professionals (Doctors ⊆ Professionals). From Statement II: Some professionals are not engineers (meaning at least one professional is not an engineer). However, this does NOT mean that ALL professionals are non-engineers. Doctors form a subset of professionals, and it is entirely possible for all doctors to be engineers even though some other professionals are not. Therefore, a doctor CAN be an engineer.

Question 10

Statements:
I. All flowers are plants.
II. Some plants are not green.

Question: Must all flowers be green?

(A) Yes, all flowers must be green
(B) No, not all flowers must be green
(C) All flowers are definitely not green
(D) Cannot be determined from the given statements

Accepted Answer

From Statement I: All flowers are plants (Flowers ⊆ Plants). From Statement II: Some plants are not green (meaning at least one plant lacks the green property). However, this does NOT tell us whether flowers specifically are green or not. The non-green plants could be from other categories of plants (like fungi or non-flowering plants). Flowers, as a subset, could all be green, or some could be non-green. The statements do not provide enough information to determine if all flowers must be green.

Question 11

Five boxes are arranged in a row. Statement I: Box P is to the left of Box Q. Statement II: Box R is immediately to the right of Box P. Which box is in the middle position?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Even both statements together are not sufficient

Accepted Answer

From Statement I: P is left of Q (order: P...Q). From Statement II: R is immediately right of P (order: P-R). Combined: P-R-?-?-Q or variations. However, we don't know the positions of boxes S and T, or the exact positions of P, R, Q relative to the 5 positions. We cannot determine which box is in the middle (position 3) without knowing all box positions or having additional constraints.

Question 12

A company has employees in three departments: Sales, Marketing, and Operations. Statement I: The number of Sales employees is 20% more than Marketing employees. Statement II: The number of Operations employees is 15% less than Marketing employees. What is the ratio of Sales to Operations employees?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Even both statements together are not sufficient

Accepted Answer

Let Marketing = M. Statement I: Sales = M + 0.20M = 1.2M. Statement II: Operations = M - 0.15M = 0.85M. Ratio of Sales to Operations = 1.2M : 0.85M = 1.2 : 0.85 = 120 : 85 = 24 : 17. Both statements together are sufficient to determine the ratio, as the actual value of M cancels out when forming the ratio.

Question 13

Five friends—A, B, C, D, E—sit in a row. Is C sitting in the middle position?

Statement I: A and E are at the two ends.
Statement II: B is immediately to the left of C, and D is immediately to the right of C.

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

Accepted Answer

To determine if C is in the middle (3rd position) of 5 people, we need to know C's exact position. Statement I tells us A and E occupy the ends but doesn't specify which end or C's position. Statement II tells us B-C-D are consecutive with C in the middle of this trio, but doesn't tell us where this trio sits in the overall row. However, combining both: If A and E are at ends (positions 1 and 5), and B-C-D are consecutive with C between them, then B-C-D must occupy positions 2-3-4, making C the 3rd position (middle). Both statements together are sufficient.

Question 14

In a family of 6 people, there are three married couples. Statement I: A is the father of B and C. Statement II: D is the mother of E and F. Is A married to D?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Even both statements together are not sufficient

Accepted Answer

To determine if A is married to D, we need to establish that A and D are a couple. Statement I tells us A is the father of B and C (A is male). Statement II tells us D is the mother of E and F (D is female). However, knowing A is a father and D is a mother does not prove they are married to each other—B, C, E, and F could belong to different families or different marriages. We cannot establish the marital relationship between A and D from either or both statements.

Question 15

A shopkeeper sells three types of items: X, Y, and Z. Is the profit on item Y greater than the profit on item X?

Statement I: The profit margin on Y is 25% and on X is 20%.
Statement II: The cost price of X is ₹100 and the cost price of Y is ₹80.

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

Accepted Answer

Profit (in rupees) = Cost Price × Profit Margin. Statement I gives profit margins (25% vs 20%) but not cost prices. Without cost prices, we cannot compare absolute profits. Statement II gives cost prices but not profit margins. Without margins, we cannot calculate profits. However, combining both: Profit on X = 100 × 20% = ₹20. Profit on Y = 80 × 25% = ₹20. Both profits are equal, so the answer to 'Is Y's profit greater than X's profit?' is NO. Both statements together are sufficient.

Question 16

A person starts at point X and travels. Statement I: The person travels 8 km North, then turns right and travels 6 km. Statement II: After reaching the point described in Statement I, the person turns left and travels 4 km. Where is the person now relative to point X?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Even both statements together are not sufficient

Accepted Answer

Statement I: Start at X, go 8 km North → position (0, 8). Turn right (now facing East), go 6 km → position (6, 8). Statement II: Turn left (now facing North), go 4 km → position (6, 12). Both statements together give us the final position: 6 km East and 12 km North of X. This is sufficient to determine the exact location.

Question 17

In a group of students, some study Math, some study Science. Statement I: 40% of students study Math. Statement II: 30% of students study both Math and Science. What percentage of students study only Science?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Even both statements together are not sufficient

Accepted Answer

Statement I tells us 40% study Math. Statement II tells us 30% study both Math and Science. From these, we can deduce that 40% - 30% = 10% study only Math. However, to find the percentage studying only Science, we need to know the total percentage studying Science. We know 30% study both, but not the total Science percentage. Therefore, both statements together are insufficient.

Question 18

In a family, there are 4 children. Is Priya older than Arjun?

Statement I: Priya is older than Rohan, and Rohan is older than Arjun.
Statement II: Arjun is the youngest among the four children.

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

Accepted Answer

To answer 'Is Priya older than Arjun?', we need to establish a direct or transitive age relationship between them. Statement I provides a transitive chain: Priya > Rohan > Arjun, which directly answers YES. Statement II only tells us Arjun is the youngest but doesn't tell us Priya's position relative to Arjun. Statement I alone is sufficient to answer the question definitively.

Question 19

A train travels from Station A to Station B. Statement I: The train travels at 60 km/h for the first half of the distance. Statement II: The train travels at 90 km/h for the second half of the distance. Can we determine the average speed of the train for the entire journey?

(A) Statement I alone is sufficient.
(B) Statement II alone is sufficient.
(C) Statements I and II together are sufficient.
(D) Even both statements together are not sufficient.

Accepted Answer

This question tests understanding of average speed (harmonic mean for equal distances) vs. average velocity.

Question 20

In a group of students, Statement I: 60% are proficient in English. Statement II: 75% are proficient in Mathematics. Statement III: 50% are proficient in both English and Mathematics. What percentage of students are proficient in at least one of the two subjects?

(A) Statement I alone is sufficient.
(B) Statements I and II together are sufficient.
(C) Statements I, II, and III together are sufficient.
(D) Even all three statements together are not sufficient.

Accepted Answer

This question tests application of set theory (union formula) and sufficiency of constraints.

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60-Second Revision — Data Sufficiency — Reasoning