Question 1

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

Question: Which of the following must be true?
A) All doctors are happy.
B) Some doctors are happy.
C) Some doctors are wealthy.
D) Cannot be determined from the given statements.

Accepted Answer

From Statement I: All doctors are professionals. From Statement II: Some professionals are wealthy (not all). From Statement III: All wealthy people are happy. We know doctors are professionals, but we do not know if any specific doctor is wealthy. The wealthy subset of professionals may or may not include any doctors. Therefore, we cannot conclude that any doctor is happy or wealthy. The answer is D.

Question 2

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 true?
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. This means the educated group contains both doctors and non-doctors. Since all teachers are educated, teachers could be in either subset (doctors or non-doctors). Therefore, it is POSSIBLE that all teachers are doctors, but NOT CERTAIN. The correct answer is A.

Question 3

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

Question: Which of the following must be true?
A) All flowers are beautiful.
B) Some flowers are beautiful.
C) No flowers are beautiful.
D) Some flowers are not beautiful.

Accepted Answer

From Statement I: Some flowers are red. From Statement II: All red things are beautiful. Therefore, those flowers that are red must be beautiful. This means at least some flowers are beautiful. The answer is B. Note: We cannot conclude all flowers are beautiful (A is too strong), nor can we conclude none or some are not beautiful (C and D contradict the deduction).

Question 4

In a Data Sufficiency question, we need to determine: 'Is Rajesh taller than Priya?'

Statement I: Rajesh is taller than Amit, and Amit is taller than Priya.
Statement II: Priya is shorter than Rajesh.

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

Accepted Answer

To determine if Rajesh is taller than Priya, we need a direct or logical chain comparing their heights.

Statement I: Rajesh > Amit AND Amit > Priya. By transitivity, Rajesh > Priya. This is SUFFICIENT.

Statement II: Priya is shorter than Rajesh directly means Rajesh > Priya. This is SUFFICIENT.

Both statements independently answer the question. The answer is: Either Statement I alone or Statement II alone is sufficient.

Question 5

Statements:
I. All politicians are ambitious.
II. Some ambitious people are corrupt.

Question: Can we conclude that some politicians are corrupt?
A) Yes, definitely.
B) No, definitely not.
C) Cannot be determined from the given statements.
D) Yes, all politicians are corrupt.

Accepted Answer

From Statement I: All politicians are ambitious. From Statement II: Some ambitious people are corrupt. However, we do not know if the ambitious politicians are among the corrupt ambitious people or not. The corrupt subset of ambitious people may or may not include any politicians. Therefore, we cannot determine whether any politician is corrupt. The answer is C.

Question 6

Statements:
I. No student is lazy.
II. All hardworking people are successful.

Question: Which statement must be true?
A) All students are successful.
B) Some students are successful.
C) No student is successful.
D) Cannot be determined from the given statements.

Accepted Answer

From Statement I: No student is lazy (Students and Lazy are disjoint). From Statement II: All hardworking people are successful. However, we are not told whether students are hardworking or not. Being not lazy does not necessarily mean being hardworking. Therefore, we cannot conclude anything about whether students are successful. The answer is D.

Question 7

In a company, employees are assigned to either Project A or Project B (or both). A total of 120 employees work on at least one project.
Statement I: 45 employees work on Project A only.
Statement II: The number of employees on Project B is 20 more than the number on Project A.

Accepted Answer

Statement I alone: 45 on A only, but we don't know how many are on both or on B only. Not sufficient. Statement II alone: B = A + 20, but we don't know the actual numbers or the overlap. Not sufficient. Together: Let A = total on Project A, B = total on Project B, x = on both. Then A + B - x = 120 (inclusion-exclusion). From I: A - x = 45, so A = 45 + x. From II: B = A + 20 = 45 + x + 20 = 65 + x. Substituting into inclusion-exclusion: (45 + x) + (65 + x) - x = 120, so 110 + x = 120, thus x = 10. Now A = 55, B = 75. We can determine all values. Sufficient together.

Question 8

In a row of 12 students, Rajesh is 5th from the left. How many students are to the right of Rajesh?
Statement I: There are 3 students between Rajesh and the rightmost student.
Statement II: Rajesh is 8th from the right.

Accepted Answer

Statement I: If Rajesh is 5th from left and there are 3 students between him and the rightmost, then rightmost is at position 5+3+1=9. So 12-5=7 students to the right. Statement II: If Rajesh is 8th from right in a row of 12, he is at position 12-8+1=5 from left (consistent). From position 5, there are 12-5=7 students to the right. Both statements independently give the answer.

Question 9

Priya, Qasim, and Ravi are three friends. Each has a different age.
Statement I: Priya is older than Qasim, and Qasim is older than Ravi.
Statement II: The sum of their ages is 60 years, and Priya's age is twice Ravi's age.

Accepted Answer

Statement I alone: Establishes order P > Q > R, but does not give exact ages. Not sufficient. Statement II alone: P + Q + R = 60 and P = 2R. This gives P = 2R and Q = 60 - P - R = 60 - 2R - R = 60 - 3R. We have two equations and three unknowns, so multiple solutions exist (e.g., R=10, P=20, Q=30 or R=15, P=30, Q=15). Not sufficient alone. Together: From II, P = 2R and Q = 60 - 3R. From I, P > Q means 2R > 60 - 3R, so 5R > 60, thus R > 12. Also Q > R means 60 - 3R > R, so 60 > 4R, thus R < 15. So 12 < R < 15. Still a range, not exact. Not sufficient even together.

Question 10

A train travels from City X to City Y. The distance between the cities is unknown.
Statement I: The train travels at 60 km/h for the first half of the distance and 80 km/h for the second half of the distance.
Statement II: The train takes a total of 7 hours to complete the journey.

Accepted Answer

Statement I alone: Gives speeds for each half-distance but not the total distance or time. Not sufficient. Statement II alone: Gives total time (7 hours) but without speed information, cannot determine distance. Not sufficient. Together: Let total distance = D. First half: D/2 at 60 km/h takes (D/2)/60 = D/120 hours. Second half: D/2 at 80 km/h takes (D/2)/80 = D/160 hours. Total time: D/120 + D/160 = 7. Finding common denominator: (4D + 3D)/480 = 7, so 7D/480 = 7, thus D = 480 km. Sufficient together.

Question 11

A person travels from Town X to Town Y. Statement I: The person travels 40 km north, then 30 km east. Statement II: The person's final displacement from X is 50 km. Statement III: The person took exactly 2 hours for the entire journey. What is the person's average speed?

Accepted Answer

Tests whether students conflate displacement with distance and whether they identify which statements are actually needed.

Question 12

Six boxes are arranged in a circle, numbered 1 through 6. Statement I: Box 3 is directly opposite Box 6. Statement II: Box 1 is two positions clockwise from Box 4. Statement III: Box 2 is immediately counterclockwise from Box 5. Can we determine the exact circular arrangement?

Accepted Answer

Tests spatial reasoning in circular arrangements and whether constraints are consistent and sufficient.

Question 13

A company has employees in three departments: Sales, IT, and HR. Statement I: 60% of employees are in Sales or IT. Statement II: The number of IT employees is 25% more than HR employees. Statement III: Sales employees are 50% of the total workforce. Can we determine the percentage of IT employees?

Accepted Answer

Tests logical deduction with percentage relationships and identification of redundant or contradictory constraints.

Question 14

A person's age and their child's age are related. Statement I: The person is currently 3 times the child's age. Statement II: In 5 years, the person will be 2.5 times the child's age. Statement III: The child is currently less than 10 years old. Are Statements I and II sufficient to determine both current ages?

Accepted Answer

Tests algebraic reasoning and whether two equations with two unknowns yield a unique solution, plus verification against a third constraint.

Question 15

Five colleagues—Arun, Bhavna, Chitra, Deepak, and Esha—sit in a row facing North. Each earns a different salary from ₹30,000 to ₹70,000 (in ₹10,000 increments). Statement I: Arun sits to the left of Bhavna. Chitra earns ₹10,000 more than the person sitting immediately to her right. Statement II: Deepak sits at one end. Esha earns ₹20,000 less than Deepak. The person earning ₹50,000 sits between two people earning ₹40,000 and ₹60,000 respectively. Is Statement I alone sufficient to determine Esha's exact salary?

Accepted Answer

This is a complex data sufficiency question requiring logical deduction across multiple constraints. Statement I provides positional and salary relationship information but lacks critical constraints about end positions and specific salary values. Statement II introduces absolute positional anchors (end position) and a direct salary relationship, which when combined with Statement I's constraints, allows determination of Esha's salary through elimination and logical deduction.

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 exactly two seats to the right of D. Statement III: E is not at either end. Is Statement I alone sufficient to determine the exact seating arrangement?

Accepted Answer

This tests whether a single constraint can uniquely determine a complex arrangement when multiple variables exist.

IBPS RRB PO Data Sufficiency — Reasoning

Data Sufficiency — Reasoning— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Data Sufficiency — Reasoning — Practice Questions

60-Second Revision — Data Sufficiency — Reasoning