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 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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

A person invests money in two schemes. Statement I: In Scheme A, ₹5000 is invested at 8% per annum simple interest for 2 years. In Scheme B, ₹3000 is invested at 10% per annum simple interest for 2 years. Statement II: The total interest earned from both schemes is ₹1400. Is the total interest from Scheme A greater than the total interest from Scheme B?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Both statements together are not sufficient

Accepted Answer

To compare interest from both schemes, we need principal, rate, and time for each. Statement I provides all: Scheme A interest = (5000 × 8 × 2)/100 = ₹800. Scheme B interest = (3000 × 10 × 2)/100 = ₹600. So Scheme A interest (₹800) > Scheme B interest (₹600). ✓ Statement I alone is sufficient. Statement II only gives total interest without breakdown.

Question 11

Two trains start from stations A and B respectively and travel towards each other. Statement I: Train X travels at 60 km/h from station A, and Train Y travels at 40 km/h from station B. They meet after 3 hours. Statement II: The distance between stations A and B is 300 km. Do the trains meet at a point 180 km from station A?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Both statements together are not sufficient

Accepted Answer

To verify if trains meet 180 km from A, we need: (1) the distance between A and B, and (2) the speeds and time (or relative speed). Statement I gives speeds and time, so distance = (60+40)×3 = 300 km. Distance from A = 60×3 = 180 km. ✓ Statement I alone is sufficient. Statement II alone only gives total distance without speeds/time, so we cannot determine meeting point.

Question 12

A rectangular tank is being filled with water. Statement I: The tank has length 8 m, width 6 m, and height 5 m. Water is filled at a rate of 12 cubic meters per hour. Statement II: The tank will be completely filled in 20 hours. Is the volume of the tank 240 cubic meters?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Both statements together are not sufficient

Accepted Answer

To find tank volume, we need dimensions (length × width × height). Statement I provides all three dimensions: Volume = 8 × 6 × 5 = 240 m³. ✓ Statement I alone is sufficient. Statement II alone (20 hours to fill) combined with filling rate would give volume, but Statement II doesn't provide the filling rate. Therefore, Statement I alone is sufficient.

Question 13

A shopkeeper sells items at a profit. Statement I: The cost price of item A is ₹100 and it is sold at 40% profit. Statement II: The selling price of item A is ₹140. Is the profit earned on item A equal to ₹40?

A) Statement I alone is sufficient
B) Statement II alone is sufficient
C) Both statements together are sufficient
D) Both statements together are not sufficient

Accepted Answer

To determine if profit = ₹40, we need both cost price AND selling price (or profit percentage with cost price). Statement I gives CP = ₹100 and profit% = 40%, so profit = 40% of ₹100 = ₹40. This is sufficient. Statement II alone only gives SP = ₹140 without CP, so we cannot determine profit. Therefore, Statement I alone is sufficient.

SSC CPO Data Sufficiency — Maths

SSC CPO Data Sufficiency — Maths — Past Exam Questions

Data Sufficiency — Maths— Rules & Concept

Key Points to Remember

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60-Second Revision — Data Sufficiency — Maths