Question 1

In a group of 5 people, each person shakes hands with every other person exactly once. How many handshakes occur in total?

Statement I: There are 5 people in the group.
Statement II: Each handshake involves exactly 2 people.

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

Accepted Answer

This is a data sufficiency question testing whether given statements provide enough information to solve a combinatorics problem. Statement I alone tells us the number of people (5). Statement II alone tells us the definition of a handshake (2 people). Together, they allow us to calculate: C(5,2) = 5×4/2 = 10 handshakes. However, Statement I alone is sufficient because once we know there are 5 people and understand the standard meaning of 'each person shakes hands with every other person exactly once,' we can calculate the answer without needing Statement II to redefine what a handshake is.

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 correct?
(A) Yes, it is possible.
(B) No, it is not possible.
(C) Cannot be determined from the given statements.
(D) The statements are contradictory.

Accepted Answer

From Statement I: All teachers are educated. From Statement II: Some educated people are not doctors (meaning at least one educated person is not a doctor). However, this does NOT prevent all teachers from being doctors. Teachers form a subset of educated people, and it's logically possible for all members of this subset to be doctors even though some other educated people are not. Therefore, the answer is YES, it is possible.

Question 3

Statements:
I. All flowers are plants.
II. All plants need water.
III. Some flowers are roses.

Question: Do all roses need water?

Which of the following is correct?
(A) Yes, definitely.
(B) No, definitely not.
(C) Cannot be determined from the given statements.
(D) Only some roses need water.

Accepted Answer

From Statement I: All flowers are plants. From Statement III: Some flowers are roses (meaning roses are a subset of flowers). By transitivity: If all flowers are plants, and roses are flowers, then all roses are plants. From Statement II: All plants need water. Therefore, all roses (being plants) need water. The answer is YES, definitely.

Question 4

Statements:
I. All doctors are professionals.
II. Some professionals are teachers.
III. No teacher is a doctor.

Question: Are the given statements logically consistent?

Which of the following is correct?
(A) Yes, the statements are consistent.
(B) No, the statements are contradictory.
(C) The statements are partially consistent.
(D) Cannot be determined from the given statements.

Accepted Answer

From Statement I: All doctors are professionals (Doctors ⊆ Professionals). From Statement III: No teacher is a doctor (Teachers ∩ Doctors = ∅). From Statement II: Some professionals are teachers (Teachers ∩ Professionals ≠ ∅). These statements are logically consistent. Doctors are professionals, some professionals are teachers, but no teacher is a doctor. This means the teachers who are professionals are from the non-doctor subset of professionals. There is no logical contradiction. The answer is YES, the statements are consistent.

Question 5

A person walks from point A to point B. Statement I: The person walks 8 km North, then 6 km East. Statement II: The straight-line distance from A to B is 10 km. Is Statement II sufficient to determine the path taken by the person?

Accepted Answer

This question tests understanding of the difference between distance traveled (path) and displacement (straight-line distance). Statement II provides only the final displacement, not the actual route taken.

Question 6

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: If we add one more person, the total number of handshakes becomes 15. Which statement(s) is/are sufficient to determine the total number of handshakes in the original group?

Accepted Answer

This is a data sufficiency question testing combinatorial reasoning. Statement I directly gives us the answer (10 handshakes). Statement II provides information about a modified scenario but requires us to work backward to verify the original group. Both statements independently confirm the same answer through different logical paths.

Question 7

A person's age is being determined. Statement I: The person's age is a two-digit number. Statement II: When the digits are reversed, the resulting number is 27 less than the original age. If the person's current age is between 30 and 60, what is their age?

Accepted Answer

This question tests algebraic reasoning combined with constraint satisfaction—students must set up equations from digit manipulation and verify against boundary conditions.

Question 8

In a group of 5 people, each person knows at least one language among English, Hindi, and Tamil. Statement I: The number of people who know English is equal to the number of people who know Hindi. Statement II: Exactly 2 people know Tamil, and no one knows all three languages. Is the data sufficient to determine the exact number of people who know only English?

Accepted Answer

This is a Data Sufficiency question requiring logical deduction about set overlaps and constraints. Statement I alone cannot determine the distribution because it only equates two sets without specifying overlaps. Statement II provides specific information about Tamil speakers and a constraint (no one knows all three), but doesn't directly tell us about English-only speakers. Together, both statements still leave ambiguity about how English and Hindi speakers overlap, making it impossible to uniquely determine English-only speakers.

Question 9

In a family, there are three children. Statement I: The sum of their ages is 15 years. Statement II: The product of their ages is 24 years. What is the age of the youngest child?

Accepted Answer

This question tests whether students can use multiple constraints to uniquely determine a solution in a system with limited possibilities.

Question 10

Statement I: All members of Club A are also members of Club B. Statement II: Some members of Club B are not members of Club A. Can we determine whether Club A and Club B have the same membership?

Accepted Answer

This question tests logical deduction from set relationships and syllogistic reasoning about subset relationships.

Question 11

A company manufactures products A and B. Statement I: The production cost of A is ₹40 per unit. Statement II: The production cost of B is 25% more than A. Statement III: The selling price of A is ₹60 per unit. Statement IV: The profit margin on B is 20%. Statement V: The company produced 100 units of A and some units of B, with a combined total profit of ₹2,400. Can we determine the number of units of B produced?

Accepted Answer

Tests whether multiple constraints can be combined to solve for an unknown in a multi-variable profit problem.

Question 12

A shopkeeper sells three types of items: X, Y, Z. Statement I: The profit on X is 20% more than on Y. Statement II: The profit on Z is 15% less than on Y. Statement III: The total profit from selling 10 units of X, 15 units of Y, and 20 units of Z is ₹2,500. Can we determine the individual profit per unit on Y?

Accepted Answer

Tests whether algebraic constraints with multiple unknowns can be solved with the given data.

SSC CPO Data Sufficiency — Reasoning

SSC CPO Data Sufficiency — Reasoning — Past Exam Questions

Data Sufficiency — Reasoning— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Data Sufficiency — Reasoning