Question 1

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

Statement I: There are 40 students in the class, and 60% of them scored above 75 marks.
Statement II: 24 students scored above 75 marks, and 16 students scored 75 marks or below.

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

Accepted Answer

To answer 'How many students scored above 75 marks?', we need a definite numerical value.

Statement I: 60% of 40 = 0.60 × 40 = 24 students scored above 75 marks. This gives a definite answer.

Statement II: Directly states that 24 students scored above 75 marks. This also gives a definite answer.

Both statements independently provide the same definite answer (24 students). Therefore, either statement alone is sufficient.

Question 2

Five friends—Arun, Bhavna, Chitra, Deepak, and Esha—sit in a row facing North. Bhavna sits third from the left. Deepak sits immediately to the right of Bhavna. Arun sits to the left of Bhavna but not at the extreme left. Chitra sits at one of the ends. Is it possible to determine the exact seating arrangement?
Statement I: Esha sits at the extreme left.
Statement II: Arun sits second from the left.

Accepted Answer

This question tests whether given constraints are sufficient to uniquely determine a linear arrangement.

Question 3

In a coding system, each letter is replaced by a digit such that the same letter always gets the same digit, and different letters get different digits. In the code, MATH + MATH = GAMES. What is the value of M?
Statement I: G = 1.
Statement II: A = 9.

Accepted Answer

Cryptarithmetic problem testing whether given digit assignments are sufficient to uniquely determine another digit.

Question 4

Six people—P, Q, R, S, T, U—have different ages. R is older than Q. S is younger than T. U is the oldest. Can we determine whether P is older than Q?
Statement I: P is older than R.
Statement II: T is older than Q.

Accepted Answer

Comparative reasoning problem testing whether given age relationships are sufficient to establish a specific comparison.

Question 5

In a family, there are five members: A, B, C, D, and E. A is the father of B. C is the mother of D. B and D are siblings. Is E male or female?
Statement I: E is the spouse of A.
Statement II: E is the mother of B.

Accepted Answer

Blood relation problem testing logical deduction about family relationships and gender inference.

Question 6

A shopkeeper has a total of 100 items consisting of pens, pencils, and erasers. The number of pens is twice the number of pencils. Is it possible to determine the exact number of erasers?
Statement I: The number of pens is 40.
Statement II: The number of pencils and erasers combined is 60.

Accepted Answer

Quantitative reasoning problem testing whether given constraints are sufficient to uniquely determine an unknown quantity.

Question 7

Five people—A, B, C, D, E—sit in a row. Statement I: B sits immediately to the right of A. Statement II: D sits at one end and C sits immediately to the right of D. 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 only tells us B is right of A, but leaves 3 other people (C, D, E) with multiple possible positions. Statement II adds constraints but doesn't fix A and B's position relative to D and C. Neither statement alone, nor both together, uniquely determines the arrangement because we don't know the relative positions of the A-B pair versus the D-C pair, nor where E fits.

Question 8

A shopkeeper sells three types of items: X, Y, Z. Statement I: The ratio of X sold to Y sold is 3:2. Statement II: The total items sold is 100, and Z accounts for 20% of total sales. What is the number of X items sold? Determine sufficiency.

Accepted Answer

Statement I gives the ratio X:Y = 3:2, but doesn't tell us the absolute quantities or how many Z items exist. Statement II tells us total is 100 and Z = 20 items, so X + Y = 80. Combined: X:Y = 3:2 means X = 3k, Y = 2k for some k. Then 3k + 2k = 80 → 5k = 80 → k = 16 → X = 48. Both statements together are necessary and sufficient.

Question 9

A company has three departments: Sales, HR, and IT. Statement I: The number of employees in Sales is 40% more than in HR. Statement II: The number of employees in IT is 25% less than in Sales. Statement III: The total number of employees is 500. Can we determine the exact number of employees in HR?

Accepted Answer

Let HR = h. Then Sales = 1.4h (40% more). IT = 0.75 × 1.4h = 1.05h (25% less than Sales). Total: h + 1.4h + 1.05h = 500 → 3.45h = 500 → h = 500/3.45 ≈ 144.93. We can solve for HR uniquely using all three statements. Statements I and II alone are insufficient (two equations, three unknowns). Statements I and III alone are insufficient (we don't know IT's relationship to Sales). Statements II and III alone are insufficient (we don't know Sales' relationship to HR). All three statements together are necessary and sufficient.

Question 10

A train travels from City A to City B. Statement I: The train travels at 60 km/h for the first half of the distance and 90 km/h for the second half. Statement II: The total distance is 300 km. What is the total time taken? Determine sufficiency.

Accepted Answer

Statement I describes the speed profile (60 km/h for first 150 km, 90 km/h for second 150 km). Statement II gives the total distance (300 km). Combined: Time = Distance/Speed. First half: 150/60 = 2.5 hours. Second half: 150/90 = 1.67 hours. Total ≈ 4.17 hours. Both statements are necessary and sufficient. Statement I alone is insufficient (we don't know the distance). Statement II alone is insufficient (we don't know the speeds). Neither alone is sufficient; both together are sufficient.

Question 11

Six boxes are arranged in a circle. Statement I: Box P is directly opposite Box Q. Statement II: Box R is two positions clockwise from Box P. Is the position of Box R uniquely determined relative to Box Q?

Accepted Answer

In a circle of 6 boxes, 'directly opposite' means 3 positions away. If P is at position 1, Q is at position 4. 'Two positions clockwise from P' means R is at position 3 (1 + 2 = 3). Relative to Q at position 4, R at position 3 is one position counter-clockwise. However, we don't know the absolute starting position of P—it could be any of the 6 positions. But the relative position of R to Q is always the same: one position counter-clockwise. Both statements together determine R's position relative to Q uniquely.

IBPS Clerk Data Sufficiency — Reasoning

IBPS Clerk Data Sufficiency — Reasoning — Past Exam Questions

Data Sufficiency — Reasoning— Rules & Concept

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60-Second Revision — Data Sufficiency — Reasoning