Question 1

Statements:
I. All teachers are educated.
II. Some educated people are not teachers.

Question: Is it possible for a person to be educated but not a teacher?

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

Accepted Answer

Statement I alone tells us all teachers are educated, but says nothing about whether non-teachers can be educated. Statement II directly states that some educated people are not teachers, which directly answers the question affirmatively. Therefore, Statement II alone is sufficient.

Question 2

Statements:
I. Raj is taller than Priya.
II. Priya is taller than Karan.

Question: Is Raj taller than Karan?

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

Accepted Answer

Statement I tells us Raj > Priya in height. Statement II tells us Priya > Karan in height. Using transitivity: Raj > Priya > Karan, therefore Raj > Karan. Both statements together are necessary and sufficient to establish this relationship.

Question 3

Statements:
I. All roses are flowers.
II. Some flowers are red.

Question: Are all roses red?

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

Accepted Answer

Statement I tells us roses are a subset of flowers. Statement II tells us some (not all) flowers are red. This does not tell us whether all roses are red—roses could be red, or only some roses could be red. Neither statement alone nor both together can definitively answer whether ALL roses are red.

Question 4

Statements:
I. Mohan is older than Sohan.
II. Sohan is older than Rohan.
III. Rohan is older than Mohan.

Question: What is the age order of the three?

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

Accepted Answer

Statements I and II together give: Mohan > Sohan > Rohan. However, Statement III contradicts this by saying Rohan > Mohan. The three statements are logically inconsistent and cannot all be true simultaneously. Therefore, no consistent answer can be derived from these statements.

Question 5

Statements:
I. All doctors are professionals.
II. Rajesh is a professional.

Question: Is Rajesh a doctor?

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

Accepted Answer

Statement I tells us doctors ⊆ professionals (all doctors are in the professional set). Statement II tells us Rajesh is in the professional set. However, being a professional does not guarantee being a doctor—Rajesh could be an engineer, lawyer, or other professional. The statements do not provide sufficient information to confirm Rajesh is a doctor.

Question 6

In a row of 8 students, Priya is 3rd from the left. When all students are arranged in reverse order, what is Priya's position from the right?
Statement I: The row contains exactly 8 students.
Statement II: Priya was originally 3rd from the left.
A) Only Statement I is sufficient
B) Only Statement II is sufficient
C) Both statements together are sufficient
D) Neither statement alone is sufficient

Accepted Answer

When a row is reversed, position from left becomes position from right using the formula: New position from right = (Total students + 1) - Old position from left. Here: (8 + 1) - 3 = 6. Both statements are needed: Statement I gives total count (8), Statement II gives original position (3rd from left). Without either, the answer cannot be determined.

Question 7

A shopkeeper sells three types of items: X, Y, and Z. The profit on X is 20%, on Y is 15%, and on Z is 25%.
Statement I: The shopkeeper sold 10 units of X, 8 units of Y, and 12 units of Z.
Statement II: The cost price of X is ₹100, Y is ₹150, and Z is ₹200 per unit.
Can we determine the total profit earned?
A) Only Statement I is sufficient
B) Only Statement II is sufficient
C) Both statements together are sufficient
D) Neither statement alone is sufficient

Accepted Answer

To find total profit, we need: (Quantity × Cost Price × Profit%) for each item, then sum. Statement I provides quantities but no cost prices. Statement II provides cost prices but no quantities. Neither alone suffices. Together: Total profit = (10×100×0.20) + (8×150×0.15) + (12×200×0.25) = 200 + 180 + 600 = ₹980.

Question 8

In a family, there are 5 members. The average age of all members is 30 years.
Statement I: The sum of ages of the two youngest members is 40 years.
Statement II: The oldest member is 50 years old.
Can we determine the sum of ages of the three oldest members?
A) Only Statement I is sufficient
B) Only Statement II is sufficient
C) Both statements together are sufficient
D) Neither statement alone is sufficient

Accepted Answer

Total age of all 5 members = 5 × 30 = 150 years. Statement I tells us the two youngest sum to 40, so the three oldest sum to 150 - 40 = 110 years. This directly answers the question. Statement II alone (oldest is 50) doesn't determine the sum of the three oldest without knowing the other two. Only Statement I is sufficient.

Question 9

A person travels from Town P to Town Q. Statement I: The person travels 40 km North, then 30 km East, then 20 km South. Statement II: The person's final displacement from P is 50 km. What is the person's final displacement from P?

(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

This tests whether students can calculate displacement from directional movements versus recognizing when a direct statement is given.

Question 10

Six boxes are arranged in a line. Box P contains either 10 or 20 items. Statement I: If Box P contains 10 items, then the total items in all boxes is 100. Statement II: If Box P contains 20 items, then the total items in all boxes is 110. How many items does Box P contain?

(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

This tests whether students can recognize that conditional statements do not determine a fact unless the condition itself is established.

Question 11

A committee has members from three departments: Sales, Marketing, and Operations. Statement I: The number of Sales members is twice the number of Marketing members. Statement II: The total committee size is 15, and Operations has 3 members. What is the number of Sales members?

(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

This tests whether students recognize that a ratio without a total is insufficient, but combining a ratio with a total allows calculation.

Question 12

A person's age and their sibling's age satisfy a relationship. Statement I: The person is currently 5 years older than their sibling. Statement II: Five years ago, the person was twice as old as their sibling. What is the person's current age?

(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

This tests whether students can solve a system of linear equations using two independent constraints.

Question 13

A code uses letters and numbers. Statement I: Every vowel is replaced by the digit that is 1 more than its position in the alphabet (A=2, E=6, I=10, O=16, U=22). Statement II: The word 'AUDIO' is coded as '2 22 5 10 16'. Is the code consistent?

(A) Statement I alone is sufficient to verify consistency
(B) Statement II alone is sufficient to verify consistency
(C) Both statements together are sufficient to verify consistency
(D) The statements are contradictory

Accepted Answer

This tests whether students can identify logical contradictions between a rule and an example, and recognize when statements are inconsistent.

SSC GD Constable 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