Question 1

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
D) Yes, probably most athletes are health-conscious

Accepted Answer

From Statement I: Some athletes are vegetarians (Athletes ∩ Vegetarians ≠ ∅, but not all athletes). From Statement II: All vegetarians are health-conscious. We can only conclude that 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: Are all politicians untrustworthy?

A) Yes, definitely
B) No, definitely not
C) Cannot be concluded from the given statements
D) Yes, probably

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, we cannot use Statement II to determine if they are trustworthy or not. Statement II only tells us about honest people, not about non-honest people. Therefore, we cannot conclude whether politicians are trustworthy or untrustworthy.

Question 3

In a Data Sufficiency question, we need to determine: 'How many students in Class X scored above 75 marks?'

Statement I: 40% of the 50 students in Class X scored above 75 marks.
Statement II: The total marks scored by all students is 3750, and the average is 75 marks.

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

Accepted Answer

Statement I directly provides the percentage of students above 75 marks: 40% of 50 = 20 students. This is sufficient. Statement II only tells us the average is 75 marks, which does not tell us how many scored ABOVE 75 (some could be at 75, some below). Therefore, only Statement I is sufficient.

Question 4

Statements:
I. Some flowers are red.
II. All red things are beautiful.
III. Some beautiful things are not flowers.

Question: Which of the following must be true?

A) All flowers are beautiful
B) Some flowers are beautiful
C) No flowers are beautiful
D) All beautiful things are flowers

Accepted Answer

From Statement I: Some flowers are red (Flowers ∩ Red ≠ ∅). From Statement II: All red things are beautiful (Red ⊆ Beautiful). Therefore, the flowers that are red must be beautiful. This means at least some flowers are beautiful. Statement III confirms that not all beautiful things are flowers, but this doesn't contradict our conclusion. The statement that MUST be true is: Some flowers are beautiful.

Question 5

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

Question: Can we conclude that some teachers are not doctors?

A) Yes, the conclusion definitely follows
B) No, the conclusion does not follow
C) Yes, the conclusion probably follows
D) Cannot be determined from the given statements

Accepted Answer

From Statement I: All teachers are educated (Teachers ⊆ Educated). From Statement II: Some educated people are not doctors. However, this tells us nothing about which educated people are not doctors—they could be teachers or non-teachers. We cannot definitively conclude that some teachers are not doctors because the non-doctors among educated people might be a completely different group. The conclusion does not logically follow.

Question 6

Statements:
I. All engineers are problem-solvers.
II. All problem-solvers are logical thinkers.

Question: Can we conclude that all engineers are logical thinkers?

A) No, we cannot conclude this
B) Yes, we can definitely conclude this
C) Yes, but only some engineers
D) Cannot be determined from the statements

Accepted Answer

From Statement I: All engineers are problem-solvers (Engineers ⊆ Problem-solvers). From Statement II: All problem-solvers are logical thinkers (Problem-solvers ⊆ Logical thinkers). By the transitive property: Engineers ⊆ Problem-solvers ⊆ Logical thinkers, therefore Engineers ⊆ Logical thinkers. The conclusion that all engineers are logical thinkers definitely follows.

Question 7

A company has employees in three departments: Sales, Marketing, and IT. Statement I: 40% of employees are in Sales, and 30% are in Marketing. Statement II: The number of IT employees is 60. Which statement(s) is/are sufficient to determine the total number of employees?
(A) Only Statement I is sufficient
(B) Only Statement II is sufficient
(C) Both statements together are sufficient
(D) Neither statement alone nor together is sufficient

Accepted Answer

Statement I: 40% in Sales, 30% in Marketing. This means 30% are in IT (100% - 40% - 30% = 30%). However, knowing only percentages does not give the total number of employees. Statement II: 60 IT employees. Alone, this doesn't tell us the total. Combined: If 30% of total = 60, then total = 60 / 0.30 = 200 employees. Both statements together are sufficient. Statement I alone is insufficient (percentages without absolute numbers). Statement II alone is insufficient (one absolute number without knowing what percentage it represents).

Question 8

In a group of 5 people, each person has a different profession among: Doctor, Engineer, Teacher, Lawyer, and Accountant. Consider the following statements:

Statement I: The Doctor earns more than the Engineer.
Statement II: The Lawyer earns more than the Teacher.
Statement III: The Accountant earns less than the Engineer.

Question: Can we determine whether the Doctor earns more than the Lawyer?

A) Yes, the data in Statement I alone is sufficient.
B) Yes, the data in Statements I and II together are sufficient.
C) Yes, the data in all three statements together are sufficient.
D) No, even with all three statements, we cannot determine this.

Accepted Answer

This is a data sufficiency question testing logical chain-building and constraint analysis. We need to determine if we can establish a definitive earning relationship between Doctor and Lawyer.

Analysis:
- Statement I: Doctor > Engineer
- Statement II: Lawyer > Teacher
- Statement III: Accountant < Engineer

From these three statements, we can establish:
Doctor > Engineer > Accountant (from I and III)
Lawyer > Teacher (from II)

However, there is NO direct or transitive link between the Doctor-Engineer chain and the Lawyer-Teacher chain. The Engineer and Lawyer have no stated relationship. Therefore, we cannot determine whether Doctor > Lawyer or Lawyer > Doctor.

Example: Doctor = 100, Engineer = 80, Accountant = 50, Lawyer = 90, Teacher = 70 (Doctor > Lawyer)
Alternative: Doctor = 100, Engineer = 80, Accountant = 50, Lawyer = 110, Teacher = 70 (Lawyer > Doctor)

Both scenarios satisfy all three statements, proving the relationship between Doctor and Lawyer is indeterminate.

Question 9

A store sells three types of items: Books, Pens, and Notebooks. Statement I: Books cost twice as much as Pens, and Notebooks cost 50% more than Pens. Statement II: The total cost of 2 Books, 3 Pens, and 1 Notebook is Rs. 500. Which statement(s) is/are sufficient to determine the individual price of each item?
(A) Only Statement I is sufficient
(B) Only Statement II is sufficient
(C) Both statements together are sufficient
(D) Neither statement alone nor together is sufficient

Accepted Answer

Statement I: Let Pen price = P. Then Book price = 2P, Notebook price = 1.5P. This establishes ratios but not absolute prices. Statement II: 2(2P) + 3(P) + 1(1.5P) = 500 → 4P + 3P + 1.5P = 500 → 8.5P = 500 → P = 500/8.5 ≈ 58.82. From this, we can find Book = 117.65, Notebook = 88.24. Statement I alone is insufficient (only ratios). Statement II alone is insufficient (no relationship between items). Together, they are sufficient: Statement I provides the relationships, Statement II provides the absolute constraint to solve for actual prices.

Question 10

Five people—P, Q, R, S, T—are standing in a line. Statement I: Q is to the right of P, and S is to the right of Q. Statement II: T is at one end, and R is immediately to the left of S. What is the order of people from left to right?
(A) Only Statement I is sufficient
(B) Only Statement II is sufficient
(C) Both statements together are sufficient
(D) Neither statement alone nor together is sufficient

Accepted Answer

Statement I: Q is right of P, S is right of Q. This gives partial order: P...Q...S (but doesn't place R and T). Statement II: T is at one end, R is immediately left of S. This tells us R-S are adjacent, and T is at an end. Combined: From Statement I, we have P < Q < S (in position). From Statement II, R is immediately left of S, so R-S are adjacent. T is at one end. If T is at the left end: T-P-Q-R-S or T-R-S-P-Q, etc. If T is at the right end: P-Q-R-S-T. Testing: P-Q-R-S-T satisfies both (P < Q < S, R immediately left of S, T at right end). But we need to verify uniqueness. Statement I alone cannot determine the full order. Statement II alone cannot determine the full order. Together: P-Q-R-S-T is the unique solution.

Question 11

In a logic puzzle, Statement A: 'All members of Club X are vegetarians.' Statement B: 'Some vegetarians are members of Club X.' Statement C: 'No non-vegetarian can be a member of Club X.' Which statement(s) logically follow from the others?

Accepted Answer

This question tests understanding of logical equivalence and implication. Statement A ('All members of Club X are vegetarians') is logically equivalent to Statement C ('No non-vegetarian can be a member of Club X'). These are contrapositive forms of the same claim. Statement B ('Some vegetarians are members of Club X') is a weaker claim that is IMPLIED by A and C, but does not imply them (there could be vegetarians outside Club X). Therefore, A and C are equivalent and both imply B, but B does not imply A or C.

Question 12

A company has employees in three departments: Sales, Marketing, and Operations. Statement I: 'The number of Sales employees is twice the number of Marketing employees.' Statement II: 'The total number of employees is 180, and Operations has 20 more employees than Marketing.' Can we determine the exact number of Sales employees?

Accepted Answer

This question tests whether given constraints are sufficient to solve for a unique value. Let M = Marketing employees, S = Sales employees, O = Operations employees. From Statement I: S = 2M. From Statement II: S + M + O = 180 and O = M + 20. Substituting: 2M + M + (M + 20) = 180 → 4M + 20 = 180 → 4M = 160 → M = 40. Therefore S = 2(40) = 80. Both statements together ARE sufficient to determine that Sales has exactly 80 employees.

Question 13

In a family of 6 people, there are three married couples. Each couple has exactly one child together. Statement I: The total number of parent-child relationships is 6. Statement II: If we know that person A is the father of person B, and person B is the father of person C, then A is the grandfather of C. Which statement(s) is/are sufficient to determine the exact family structure?

Accepted Answer

This question tests logical sufficiency in determining family relationships. Statement I alone tells us there are 6 parent-child pairs, but doesn't uniquely determine the structure (could be 3 couples with 3 children, or other configurations). Statement II is a logical tautology (definition of grandfather) and provides no new information about THIS family. Together, they still don't specify which person is related to whom. The answer is that NEITHER statement alone, nor both together, is sufficient.

Question 14

A person travels from City P to City Q. Statement I: The person travels 60 km north, then 80 km east, then 60 km south. Statement II: The straight-line distance from P to Q is 80 km. Are both statements consistent?

Accepted Answer

This question tests spatial reasoning and the ability to recognize when statements are logically consistent. From Statement I: Starting at P (origin), go 60 km north (position: 0, 60), then 80 km east (position: 80, 60), then 60 km south (position: 80, 0). Final position Q is 80 km east of P. The straight-line distance from P to Q is exactly 80 km. Statement II claims this distance is 80 km. Both statements ARE consistent.

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Data Sufficiency — Reasoning — Practice Questions

60-Second Revision — Data Sufficiency — Reasoning