Question 1

What is the average of three numbers?
Statement I: The sum of the three numbers is 45.
Statement II: The three numbers are consecutive integers.
(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

Average = Sum ÷ Count. Statement I gives the sum (45) and we know there are 3 numbers, so Average = 45 ÷ 3 = 15. This is sufficient. Statement II tells us the numbers are consecutive integers (e.g., 14, 15, 16) but does not give their sum or specific values. Therefore, Statement I alone is sufficient.

Question 2

What is the value of y?
Statement I: y + 5 = 12
Statement II: 2y = 14
(A) Statement I alone is sufficient
(B) Statement II alone is sufficient
(C) Both statements together are sufficient
(D) Either statement alone is sufficient

Accepted Answer

From Statement I: y + 5 = 12 → y = 7. From Statement II: 2y = 14 → y = 7. Both statements independently give the same unique value of y = 7. Therefore, either statement alone is sufficient to determine y.

Question 3

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 4

What is the area of a rectangle?
Statement I: The length of the rectangle is 12 cm.
Statement II: The perimeter of the rectangle is 40 cm.
(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

To find the area of a rectangle, we need both length AND width. Statement I gives only length (12 cm). Statement II gives perimeter (40 cm), from which we can derive: 2(l + w) = 40, so l + w = 20. Since l = 12, we get w = 8. Therefore, Area = 12 × 8 = 96 cm². Both statements together are sufficient.

Question 5

Is the number x divisible by 6?
Statement I: x is divisible by 2.
Statement II: x is divisible by 3.
(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

A number is divisible by 6 if and only if it is divisible by both 2 AND 3 (since 6 = 2 × 3 and 2, 3 are coprime). Statement I alone tells us x is divisible by 2, but not whether it's divisible by 3. Statement II alone tells us x is divisible by 3, but not whether it's divisible by 2. Together, both statements confirm x is divisible by both 2 and 3, therefore divisible by 6.

Question 6

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 7

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 8

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 9

What is the speed of a car?
Statement I: The car travels 120 km in 2 hours.
Statement II: The car travels at a constant speed.
(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

Speed = Distance ÷ Time. Statement I provides both distance (120 km) and time (2 hours), so Speed = 120 ÷ 2 = 60 km/h. This is sufficient. Statement II only tells us the speed is constant but gives no numerical values. Therefore, Statement I alone is sufficient.

Question 10

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 11

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 12

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 13

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 14

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 15

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 16

A shopkeeper sells two types of items. The cost price of item A is Rs. 200 and item B is Rs. 300. He sells item A at a profit of x% and item B at a profit of y%. Statement I: The profit on item A is Rs. 40. Statement II: The profit on item B is Rs. 90. What is the selling price of item B? (a) Statement I alone is sufficient. (b) Statement II alone is sufficient. (c) Both statements together are necessary. (d) Neither statement is sufficient.

Accepted Answer

To find the selling price of item B, we need: Selling Price = Cost Price + Profit. Cost price of B is given as Rs. 300. Statement I gives profit on A (Rs. 40), which doesn't help with B. Statement II gives profit on B as Rs. 90. Using Statement II: Selling Price of B = 300 + 90 = Rs. 390. Therefore, Statement II alone is sufficient.

Question 17

A train travels from Station P to Station Q. Statement I: The train travels at 60 km/h for the first half of the distance and 80 km/h for the second half. Statement II: The total distance between P and Q is 280 km. What is the average speed of the train? (a) Statement I alone is sufficient. (b) Statement II alone is sufficient. (c) Both statements together are necessary. (d) Neither statement is sufficient.

Accepted Answer

Average speed = Total Distance / Total Time. Statement I gives the speeds for each half of the distance but not the total distance, so time cannot be calculated. Statement II gives only the total distance. Neither alone is sufficient. Together: Total distance = 280 km. First half = 140 km at 60 km/h takes 140/60 = 7/3 hours. Second half = 140 km at 80 km/h takes 140/80 = 7/4 hours. Total time = 7/3 + 7/4 = 49/12 hours. Average speed = 280 ÷ (49/12) = 280 × 12/49 ≈ 68.57 km/h. Both statements are necessary.

Question 18

A rectangular garden has a perimeter of P meters. Statement I: The length of the garden is 5 meters more than its width. Statement II: The area of the garden is 84 square meters. What is the perimeter of the garden? (a) Statement I alone is sufficient. (b) Statement II alone is sufficient. (c) Both statements together are necessary. (d) Neither statement is sufficient.

Accepted Answer

Let length = l, width = w. Perimeter P = 2(l + w). Statement I: l = w + 5. This alone doesn't give numerical values for l and w, so P cannot be determined. Statement II: l × w = 84. This alone doesn't establish the relationship between l and w. Using both: l = w + 5 and l × w = 84. Substituting: (w + 5) × w = 84 → w² + 5w - 84 = 0 → (w + 12)(w - 7) = 0 → w = 7 (taking positive value). Therefore l = 12. Perimeter = 2(12 + 7) = 38 meters. Both statements are necessary.

Question 19

A student scored marks in three subjects: Mathematics, English, and Science. Statement I: The average score across all three subjects is 75 marks. Statement II: The score in Mathematics is 10 marks more than in English, and the score in Science is 5 marks less than in English. What is the score in Mathematics? (a) Statement I alone is sufficient. (b) Statement II alone is sufficient. (c) Both statements together are necessary. (d) Neither statement is sufficient.

Accepted Answer

Let M = Mathematics, E = English, S = Science. Statement I: (M + E + S) / 3 = 75 → M + E + S = 225. This alone doesn't determine individual scores. Statement II: M = E + 10 and S = E - 5. This gives relationships but no numerical values. Using both: From II, substitute into I: (E + 10) + E + (E - 5) = 225 → 3E + 5 = 225 → 3E = 220 → E = 73.33. Therefore, M = 73.33 + 10 = 83.33 marks. Both statements are necessary.

Question 20

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 Questions

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