Question 1

Statements:
I. All teachers are educated.
II. Some educated people are doctors.

Question: Can we conclude that some teachers are doctors?

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

Accepted Answer

From Statement I: All teachers are educated. From Statement II: Some educated people are doctors. However, we cannot conclude that some teachers are doctors because the 'some educated people' who are doctors may not include any teachers. The overlap between teachers and doctors is not established.

Question 2

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

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

A) Yes, definitely
B) No, does not follow
C) Probably yes
D) Cannot be determined

Accepted Answer

From Statement I: No politician is honest (Politicians and honest people are disjoint). From Statement II: Some honest people are rich. Since some honest people are rich, and no honest person is a politician, those rich honest people cannot be politicians. Therefore, some rich people are not politicians.

Question 3

Statements:
I. All fruits are sweet.
II. All sweet things are healthy.
III. Some apples are fruits.

Question: Can we conclude that some apples are healthy?

A) Yes, definitely
B) No, does not follow
C) Cannot be determined
D) Probably yes

Accepted Answer

From Statement III: Some apples are fruits. From Statement I: All fruits are sweet. Therefore, some apples are sweet. From Statement II: All sweet things are healthy. Therefore, some apples are healthy. The conclusion follows with certainty.

Question 4

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

Question: Can we conclude that no engineer is lazy?

A) Yes, definitely
B) No, does not follow
C) Cannot be determined
D) Probably yes

Accepted Answer

From Statement I: All engineers are problem-solvers (Engineers ⊆ Problem-solvers). From Statement II: No problem-solver is lazy (Problem-solvers ∩ Lazy = ∅). Since all engineers are problem-solvers, and no problem-solver is lazy, it follows that no engineer is lazy.

Question 5

Statements:
I. All doctors are professionals.
II. Some professionals are wealthy.
III. All wealthy people are educated.

Question: Can we conclude that some doctors are educated?

A) Yes, definitely
B) No, does not follow
C) Cannot be determined
D) Probably yes

Accepted Answer

From Statement I: All doctors are professionals. From Statement II: Some professionals are wealthy. This means some doctors may or may not be wealthy—we cannot conclude that any doctor is wealthy. From Statement III: All wealthy people are educated. Since we cannot establish that any doctor is wealthy, we cannot conclude that any doctor is educated. The conclusion does not follow.

Question 6

Statements:
I. Some students are athletes.
II. All athletes are disciplined.
III. Some disciplined people are not teachers.

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

A) Yes, definitely
B) No, does not follow
C) Cannot be determined
D) Probably yes

Accepted Answer

From Statement I: Some students are athletes. From Statement II: All athletes are disciplined. Therefore, some students are disciplined. However, Statement III says some disciplined people are not teachers—but this does not tell us whether the disciplined students are among those who are not teachers. The disciplined students could be teachers or non-teachers. The conclusion does not follow.

Question 7

Statements:
I. All managers are leaders.
II. Some leaders are innovators.
III. No innovators are followers.

Question: Can we conclude that 'Some managers are not followers'?

A) Yes, the conclusion definitely follows
B) No, the conclusion does not follow
C) The data is insufficient to draw any conclusion
D) Yes, but only if we assume all innovators are leaders

Accepted Answer

This question tests syllogistic reasoning and the ability to identify valid vs. invalid logical deductions from given premises.

Question 8

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

Question: Can we conclude that 'Some doctors are not educated'?

A) Yes, definitely
B) No, it does not follow
C) Only if all professionals are educated
D) Only if some doctors are teachers

Accepted Answer

This tests the ability to trace logical connections and recognize when a conclusion cannot be derived despite seemingly related premises.

Question 9

Statements:
I. Some politicians are honest.
II. All honest people are trustworthy.
III. No trustworthy person is corrupt.

Question: Can we conclude that 'Some politicians are not corrupt'?

A) Yes, the conclusion definitely follows
B) No, the conclusion does not follow
C) Yes, but only if all politicians are honest
D) Cannot be determined from the given information

Accepted Answer

This tests the ability to chain logical statements with 'some' and 'all' to reach valid conclusions about exclusion.

Question 10

Statements:
I. All successful entrepreneurs are risk-takers.
II. No risk-taker is fearful.
III. Some ambitious people are fearful.

Question: Can we conclude that 'Some ambitious people are not successful entrepreneurs'?

A) Yes, the conclusion definitely follows
B) No, the conclusion does not follow
C) Yes, but only if all ambitious people are risk-takers
D) Yes, but only if some risk-takers are ambitious

Accepted Answer

This tests the ability to use contrapositive reasoning and chain logical statements to reach conclusions about exclusion.

Question 11

A person travels from City X to City Y. Statement I: The person travels 40 km north, then 30 km east. Statement II: The person's final displacement from City X is 50 km. Which statement(s) is/are necessary to determine the straight-line distance between City X and City Y?

Accepted Answer

Statement I provides the path taken (40 km north, 30 km east). Using the Pythagorean theorem: distance = √(40² + 30²) = √(1600 + 900) = √2500 = 50 km. Statement II only tells us the final displacement is 50 km but does not tell us the actual path or intermediate directions. Statement I alone is sufficient to calculate the exact distance; Statement II alone is insufficient because it does not specify the direction of travel.

Question 12

A person's age is being determined. Statement I: The person's age is 5 years more than twice the age of their younger sibling. Statement II: The sum of their age and their sibling's age is 35 years. Can we determine the person's exact age?

Accepted Answer

Let the person's age be P and the sibling's age be S. Statement I: P = 2S + 5. Statement II: P + S = 35. Substituting Statement I into Statement II: (2S + 5) + S = 35 → 3S + 5 = 35 → 3S = 30 → S = 10. Therefore, P = 2(10) + 5 = 25. Both statements together are necessary and sufficient to determine the person's age uniquely.

Question 13

In a group of students, some study Mathematics, some study Physics, and some study both. Statement I: 60% of students study Mathematics. Statement II: 40% of students study Physics. Can we determine what percentage of students study both subjects?

Accepted Answer

Statement I tells us 60% study Math. Statement II tells us 40% study Physics. However, without knowing the overlap (intersection), we cannot determine the percentage studying both. For example: if 30% study both, then 30% study only Math and 10% study only Physics (total 70%). Alternatively, if 20% study both, then 40% study only Math and 20% study only Physics (total 80%). Both scenarios satisfy Statements I and II but yield different answers for the overlap.

Question 14

A shopkeeper sells three types of items: X, Y, and Z. Statement I: The ratio of items sold is X:Y:Z = 2:3:5. Statement II: The total number of items sold is 100. Can we determine the exact number of item X sold?

Accepted Answer

Statement I provides the ratio X:Y:Z = 2:3:5, which means for every 2 units of X, there are 3 units of Y and 5 units of Z (total 10 parts). Statement II tells us the total is 100 items. Together: each part = 100/10 = 10. Therefore, X = 2 × 10 = 20 items. Statement I alone is insufficient (we don't know the total). Statement II alone is insufficient (we don't know the ratio). But both together are sufficient.

Question 15

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

Accepted Answer

Statement I tells us Sales = Marketing × 1.20, but does not specify the absolute number of Marketing employees. Without knowing the base number (Marketing), we cannot calculate Sales. For example, if Marketing has 100 employees, Sales has 120. If Marketing has 50 employees, Sales has 60. Statement II provides additional information about Operations but does not help determine the absolute number in Marketing either. Neither statement alone nor both together provide an absolute baseline number.

Question 16

Five people—A, B, C, D, E—sit in a row. Statement I: A sits immediately to the left of C. Statement II: B sits at one end, and D sits immediately to the right of B. Is Statement I alone sufficient to determine the exact seating arrangement?

Accepted Answer

This is a data sufficiency question where we must evaluate whether given statements are sufficient to uniquely determine the arrangement. Statement I alone tells us A is left of C but does not fix their absolute positions or the positions of B, D, E. Statement II alone tells us B is at an end with D next to B, but leaves A, C, E unplaced. Together, both statements still allow multiple valid arrangements (e.g., B-D-A-C-E or B-D-E-A-C). Therefore, neither statement alone nor both together are sufficient.

SSC MTS Data Sufficiency — Reasoning

Data Sufficiency — Reasoning— Rules & Concept

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Data Sufficiency — Reasoning — Practice Questions

60-Second Revision — Data Sufficiency — Reasoning