Question 1

Consider the following statements about a group of people:

Statement I: All engineers are problem-solvers.
Statement II: Raj is a problem-solver.

Which of the following can be concluded with certainty?

A) Raj is an engineer
B) Raj may or may not be an engineer
C) Raj is definitely not an engineer
D) All problem-solvers are engineers

Accepted Answer

This question tests the ability to distinguish between sufficient and necessary conditions in logical reasoning. Statement I tells us that being an engineer is a SUFFICIENT condition for being a problem-solver (Engineer → Problem-solver). However, Statement II only tells us Raj is a problem-solver, which does NOT allow us to conclude he must be an engineer, because problem-solvers can exist outside the engineer category. The correct answer is B, as Raj could be an engineer OR could be a problem-solver through some other profession (doctor, scientist, etc.).

Question 2

Statements:
I. All roses are flowers.
II. All flowers are plants.

Question: Are all roses plants?

Which of the following is true?
A) The question cannot be answered from the given statements.
B) The question can be answered from statements I and II alone.
C) Only statement I is sufficient.
D) Only statement II is sufficient.

Accepted Answer

From statement I: Roses ⊆ Flowers. From statement II: Flowers ⊆ Plants. By transitive property: Roses ⊆ Plants. Therefore, all roses are plants. The question can be definitively answered using both statements.

Question 3

Statements:
I. No snake is a mammal.
II. All mammals are animals.

Question: Is a snake an animal?

Which of the following is true?
A) The question can be answered from statements I and II alone.
B) The question cannot be answered from statements I and II alone.
C) Only statement I is sufficient.
D) Only statement II is sufficient.

Accepted Answer

From statement I: Snakes ∩ Mammals = ∅ (snakes are not mammals). From statement II: Mammals ⊆ Animals. Statement II tells us mammals are animals, but says nothing about non-mammals. Since snakes are not mammals, we cannot use statement II to determine if snakes are animals. Statement I only tells us what snakes are NOT. Neither statement alone, nor both together, can definitively answer whether snakes are animals.

Question 4

Statements:
I. Some athletes are swimmers.
II. All swimmers are fit.

Question: Are all athletes fit?

Which of the following is true?
A) The question can be answered from statements I and II alone.
B) The question cannot be answered from statements I and II alone.
C) Only statement I is sufficient.
D) Only statement II is sufficient.

Accepted Answer

From statement I: Some Athletes ∩ Swimmers ≠ ∅ (some athletes are swimmers, but not necessarily all). From statement II: Swimmers ⊆ Fit. We can conclude that some athletes are fit (those who are swimmers), but we cannot conclude that ALL athletes are fit because statement I only guarantees that some athletes are swimmers, not all. Therefore, the question cannot be answered with certainty.

Question 5

Statements:
I. All birds have wings.
II. Penguins are birds.

Question: Do penguins have wings?

Which of the following is true?
A) The question cannot be answered from the given statements.
B) The question can be answered from statements I and II alone.
C) Only statement I is sufficient.
D) Only statement II is sufficient.

Accepted Answer

From statement I: Birds ⊆ Have Wings. From statement II: Penguins ⊆ Birds. By transitive property: Penguins ⊆ Have Wings. Therefore, penguins have wings. The question can be definitively answered using both statements through a valid syllogism.

Question 6

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

Question: Are all doctors educated?

Which of the following is true?
A) The question can be answered from statements I and II alone.
B) The question cannot be answered from statements I and II alone.
C) Only statement I is sufficient.
D) Only statement II is sufficient.

Accepted Answer

From statement I: Teachers ⊆ Educated. From statement II: Some Educated ∩ Doctors ≠ ∅. This means some doctors are educated, but we cannot conclude ALL doctors are educated. Statement II only guarantees that some educated people are doctors, not that all doctors come from the educated group. Therefore, the question cannot be answered with certainty.

Question 7

Question: Is person X older than person Y?
Statement I: X's age is twice the age of Z, and Z is 5 years younger than Y.
Statement II: The sum of ages of X and Y is 50, and Y is 10 years old.
Choose the correct option:
(a) Statement I alone is sufficient
(b) Statement II alone is sufficient
(c) Both statements together are sufficient
(d) Neither statement alone nor together is sufficient

Accepted Answer

Statement I: X = 2Z and Z = Y - 5, so X = 2(Y-5) = 2Y - 10. We need to know if X > Y, i.e., 2Y-10 > Y → Y > 10. Since we don't know Y's actual value, Statement I alone is NOT sufficient.
Statement II: X + Y = 50 and Y = 10, so X = 40. Clearly X (40) > Y (10). Statement II alone IS sufficient.
Answer: Statement II alone is sufficient.

Question 8

In a group of 5 people, each person shakes hands with every other person exactly once. Statement I: The total number of handshakes is 10. Statement II: Each person shakes hands with 4 others. Which statement(s) is/are sufficient to determine the total number of handshakes?

Accepted Answer

This is a data sufficiency question where we need to determine if the given statements are sufficient to find the total number of handshakes. Statement I directly gives us the answer (10). Statement II tells us each person shakes hands with 4 others, which means there are 5 people. From this, we can calculate: (5 × 4) / 2 = 10 handshakes (dividing by 2 because each handshake involves 2 people). Both statements independently lead to the same answer.

Question 9

A book costs Rs. X. Statement I: The book costs Rs. 50 more than a pen. Statement II: A pen costs Rs. 150. What is the cost of the book? Which statement(s) is/are necessary to answer the question?

Accepted Answer

To find the cost of the book (X), we need to know both the relationship between the book and pen prices AND the actual price of the pen. Statement I alone tells us the relationship but not the absolute value. Statement II alone tells us the pen's price but not the relationship. Together, they give us: Pen = Rs. 150, Book = Pen + 50 = Rs. 200. Both statements are necessary.

Question 10

A container has red and blue balls. Statement I: The ratio of red balls to blue balls is 3:2. Statement II: There are 15 red balls. How many blue balls are in the container? Which statement(s) is/are sufficient?

Accepted Answer

Statement I gives us the ratio 3:2, meaning for every 3 red balls there are 2 blue balls. However, this ratio alone doesn't tell us the actual count—there could be 3 red and 2 blue, or 6 red and 4 blue, etc. Statement II tells us there are 15 red balls. From Statement I, if red:blue = 3:2, then blue = (2/3) × red = (2/3) × 15 = 10. Statement II alone doesn't tell us the ratio. Both statements together are sufficient: we know the ratio and one actual value, so we can find the other.

Question 11

A person travels from City P to City Q. Statement I: The person travels 60 km by car and then 40 km by train. Statement II: The total distance from P to Q is 100 km. Are the two statements consistent, and is the total distance determinable? Which statement(s) is/are sufficient to determine the total distance?

Accepted Answer

Statement I tells us the person travels 60 km by car and 40 km by train, totaling 60 + 40 = 100 km. Statement II directly states the total distance is 100 km. Both statements are consistent and independently sufficient to determine the total distance. Statement I allows us to calculate the total by adding the segments. Statement II directly provides the total. Either statement alone is sufficient.

Question 12

Five people—A, B, C, D, E—sit in a row facing North. Statement I: B sits immediately to the right of A. Statement II: D sits at one end and C sits immediately to the left of D. Statement III: E is not adjacent to A. Is it possible to determine the exact seating arrangement?

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

Accepted Answer

This question tests whether students can identify when constraints are insufficient to uniquely determine an arrangement, despite appearing to provide specific positional information.

Question 13

A person travels from Point X. Statement I: The person travels 8 km North, then turns right and travels 6 km. Statement II: From the final position in Statement I, the person turns left and travels 4 km, then turns right and travels 3 km. What is the person's final distance from Point X?

(A) 13 km
(B) 15 km
(C) √(100) km
(D) √(205) km

Accepted Answer

This question tests coordinate tracking through multiple directional turns and the ability to apply the distance formula—a common source of calculation errors.

Question 14

Statement I: All members of Club X play either Tennis or Badminton (or both). Statement II: 60% of Club X members play Tennis. Statement III: 40% of Club X members play Badminton. How many members play both Tennis and Badminton?

(A) 0%
(B) 20%
(C) 40%
(D) Cannot be determined from the given statements

Accepted Answer

This question tests set theory and the principle of inclusion-exclusion, with a trap involving the assumption that percentages must sum to 100%.

Question 15

Five boxes—P, Q, R, S, T—are stacked vertically. Statement I: R is above Q. Statement II: S is immediately below P. Statement III: T is at the bottom. Statement IV: Q is not immediately below R. What is the position of Q from the top?

(A) 2nd position
(B) 3rd position
(C) 4th position
(D) Cannot be determined from the given statements

Accepted Answer

This question tests logical constraint satisfaction in a linear ordering problem, with a specific trap involving the negation of an adjacency constraint.

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Data Sufficiency — Reasoning — Practice Questions

60-Second Revision — Data Sufficiency — Reasoning