Question 1

What is the value of y?
Statement I: 2y + 5 = 15
Statement II: y is a natural number less than 10.

(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: 2y + 5 = 15 → 2y = 10 → y = 5. This uniquely determines y. Statement I alone is sufficient. Statement II: y is a natural number less than 10 means y ∈ {1, 2, 3, 4, 5, 6, 7, 8, 9}. This does not uniquely determine y. Therefore, Statement I alone is sufficient to find the value of y.

Question 2

Is x a positive number?
Statement I: x² = 25
Statement II: x > 0

(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: x² = 25 means x = 5 or x = −5. This does NOT tell us if x is positive (could be negative). Statement I alone is insufficient. Statement II: x > 0 directly states that x is positive. This is sufficient by itself. Therefore, Statement II alone is sufficient to answer the question.

Question 3

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 4

What is the cost price of an item?
Statement I: The selling price is ₹500 and profit is 25%.
Statement II: The profit amount is ₹100.

(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: If profit = 25%, then SP = CP × 1.25. So 500 = CP × 1.25 → CP = 400. Statement I is sufficient. Statement II: Profit = ₹100, but without knowing SP or profit percentage, CP cannot be determined. Statement II alone is insufficient. Answer: (A).

Question 5

What is the area of a rectangle?
Statement I: The length of the rectangle is 12 cm.
Statement II: The breadth of the rectangle is 8 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 breadth (Area = length × breadth). Statement I gives only length (12 cm). Statement II gives only breadth (8 cm). Neither statement alone provides sufficient information. However, when both statements are combined, we have length = 12 cm and breadth = 8 cm, so Area = 12 × 8 = 96 cm². Therefore, both statements together are sufficient.

Question 6

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

To find the average of three numbers, we need their sum (Average = Sum ÷ 3). Statement I: Sum = 45, so Average = 45 ÷ 3 = 15. This is sufficient. Statement II tells us the numbers are consecutive integers (e.g., 5, 6, 7 or 10, 11, 12), but without knowing their sum, we cannot find the average. Therefore, Statement I alone is sufficient.

Question 7

What is the price of one apple?
Statement I: 5 apples and 3 oranges cost ₹110 together.
Statement II: 1 orange costs ₹15.

Accepted Answer

To find the price of one apple, we need to determine its individual cost.

Statement I alone: 5A + 3O = 110 (where A = price of apple, O = price of orange). This equation has two unknowns, so we cannot find A uniquely.

Statement II alone: O = 15. This tells us only the orange price, nothing about apples.

Both statements together: From Statement II, O = 15. Substituting in Statement I: 5A + 3(15) = 110 → 5A + 45 = 110 → 5A = 65 → A = 13. We can uniquely determine that one apple costs ₹13.

Therefore, both statements together are sufficient, but neither alone is sufficient.

Question 8

What is the perimeter of a triangle?
Statement I: All three sides of the triangle are equal (equilateral triangle).
Statement II: Each side of the triangle is 6 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

Perimeter of a triangle = sum of all three sides. Statement I: All three sides are equal, but we don't know the length of each side. This is insufficient. Statement II: Each side is 6 cm, so Perimeter = 6 + 6 + 6 = 18 cm. This is sufficient. Therefore, Statement II alone is sufficient to find the perimeter.

Question 9

A train travels between two cities. The distance between the cities and the train's speed determine the travel time.

Statement I: The distance between the two cities is 480 kilometers, and the train travels at an average speed of 60 kilometers per hour.
Statement II: The train takes 8 hours to travel between the two cities.

Can we determine the average speed of the train?

Accepted Answer

Statement I directly provides the average speed (60 km/h). Statement II only gives time without distance information. Statement I alone is sufficient to answer the question about average speed.

Question 10

A person invests money in two different schemes: Scheme A offers simple interest and Scheme B offers compound interest. The person invested a total of Rs. 50,000.

Statement I: Rs. 30,000 was invested in Scheme A at 8% per annum for 3 years, and Rs. 20,000 was invested in Scheme B at 10% per annum for 2 years (compounded annually).
Statement II: The total interest earned from both schemes combined is Rs. 9,200.

Can we determine the total amount (principal + interest) after the investment period?

Accepted Answer

Statement I provides all necessary details to calculate interest from both schemes independently. Statement II only gives the combined interest total without scheme-wise breakdown. Statement I alone is sufficient.

Question 11

A shopkeeper has apples and oranges in a basket. The total number of fruits and their individual prices determine the total value.

Statement I: There are 40 apples at Rs. 5 each and 60 oranges at Rs. 3 each in the basket.
Statement II: The total value of fruits in the basket is Rs. 380, and there are 100 fruits in total.

Can we determine the number of apples in the basket?

Accepted Answer

Statement I directly states there are 40 apples. Statement II provides only total value and total count without individual prices or quantities. Statement I alone is sufficient to answer the question.

Question 12

A rectangular tank has length, width, and height. Water is being filled into the tank at a constant rate.

Statement I: The tank's length is 10 meters, width is 8 meters, and height is 6 meters. Water is filled at 5 cubic meters per hour.
Statement II: The tank will be completely filled in 9.6 hours.

Can we determine the rate at which water is being filled?

Accepted Answer

Statement I directly provides the filling rate (5 cubic meters per hour). Statement II only tells us the time to fill a tank of unknown dimensions. Statement I alone is sufficient to answer the question.

Question 13

A mixture contains milk and water. Statement I: The ratio of milk to water is 5:3. Statement II: If 8 liters of water is added, the ratio becomes 5:4. What is the original quantity of milk in the mixture?

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

Let original milk = 5x liters, original water = 3x liters (from the ratio 5:3).

From Statement I: We know the ratio but not the actual quantities. We cannot determine the original milk quantity without knowing the total or one component's absolute value.

From Statement II: After adding 8 liters of water, the ratio becomes 5:4. This means milk/(water+8) = 5/4. But without knowing the original amounts, we cannot set up the equation.

Using both: Original milk = 5x, original water = 3x (from I). After adding 8 liters of water: 5x/(3x+8) = 5/4.
Cross-multiply: 4(5x) = 5(3x+8) → 20x = 15x + 40 → 5x = 40 → x = 8.
Original milk = 5(8) = 40 liters.

Both statements together are sufficient.

Question 14

A shopkeeper sells three types of items: A, B, and C. The cost price of A is Rs. 100. Statement I: The profit on A is 20% and the profit on B is 25%. Statement II: The selling price of B is Rs. 150. Is the cost price of B less than the cost price of A?

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 determine if cost price of B < cost price of A (which is Rs. 100), we need to find the cost price of B.

From Statement I: We know profit percentages (20% on A, 25% on B) but NOT the cost price of B. We cannot determine CP(B).

From Statement II: SP(B) = Rs. 150, but without knowing the profit percentage on B, we cannot find CP(B).

Using both: From Statement I, profit on B is 25%. From Statement II, SP(B) = Rs. 150.
Using SP = CP + Profit: 150 = CP(B) + 0.25×CP(B) → 150 = 1.25×CP(B) → CP(B) = Rs. 120.
Since 120 > 100, the answer is NO, but we CAN determine this.

Both statements together are sufficient to answer the question.

Question 15

A train travels from Station X to Station Y. 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 X and Y 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 sufficient
D) Neither statement alone nor together is sufficient

Accepted Answer

To find average speed when speeds differ over segments, we need to know the distance covered at each speed.

From Statement I: We know the speeds (60 km/h and 80 km/h) for each half of the distance, but we don't know the total distance. Without distance, we cannot calculate time, and thus cannot find average speed.

From Statement II: Total distance is 280 km, but we don't know the speeds. Without speeds, we cannot calculate time.

Using both: Total distance = 280 km. First half distance = 140 km at 60 km/h → time = 140/60 = 7/3 hours. Second half distance = 140 km at 80 km/h → time = 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 together are sufficient.

Question 16

A rectangular garden has a perimeter of P meters. Statement I: The length is 5 meters more than the 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 sufficient
D) Neither statement alone nor together is sufficient

Accepted Answer

Let length = L, width = W. Perimeter P = 2(L + W).

From Statement I: L = W + 5. This gives us a relationship but not the actual values. We cannot find P without knowing at least one dimension.

From Statement II: L × W = 84. This alone doesn't determine L and W uniquely (e.g., 12×7=84 or other factor pairs).

Using both: L = W + 5 and L × W = 84.
Substitute: (W + 5) × W = 84 → W² + 5W - 84 = 0 → (W + 12)(W - 7) = 0.
Since W > 0, W = 7 meters. Thus L = 12 meters.
Perimeter = 2(12 + 7) = 38 meters.

Both statements together are sufficient.

Question 17

A person invests money in two schemes: Scheme A and Scheme B. Statement I: The ratio of amounts invested in A to B is 3:2, and the total investment is Rs. 50,000. Statement II: Scheme A gives 8% annual interest and Scheme B gives 10% annual interest. What is the total annual interest earned?

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 total annual interest, we need: (Amount in A × Rate A) + (Amount in B × Rate B).

From Statement I: Ratio A:B = 3:2, total = 50,000. This gives us the amounts: A = 30,000, B = 20,000. But we don't know the interest rates.

From Statement II: Rate A = 8%, Rate B = 10%. But we don't know the amounts invested.

Using both: From I, A = 30,000 and B = 20,000. From II, rates are 8% and 10%.
Total interest = (30,000 × 0.08) + (20,000 × 0.10) = 2,400 + 2,000 = Rs. 4,400.

Both statements together are sufficient.

Question 18

A shopkeeper sells three types of items: pens, notebooks, and erasers. The cost price of a pen is Rs. 5, a notebook is Rs. 20, and an eraser is Rs. 2. In a particular transaction, the shopkeeper sold some items and made a profit of Rs. 100.

Statement I: The shopkeeper sold 10 pens, 5 notebooks, and 20 erasers at a markup of 40% on all items.
Statement II: The shopkeeper sold items with a total cost price of Rs. 500.

Is the given information sufficient to determine the profit made?

Accepted Answer

Statement I alone provides markup percentage and quantities, allowing calculation of selling price and profit. Statement II alone only gives total cost price without markup information. Together, both statements are redundant since Statement I is already sufficient.

Question 19

A man invests money in two schemes A and B. Scheme A offers compound interest at rate r% per annum, and Scheme B offers simple interest at rate s% per annum. After 2 years, the difference between the amounts is Rs. 480. What is the principal amount invested in Scheme A?

Statement I: The rate of interest in Scheme A is 20% per annum.
Statement II: The principal invested in Scheme A is twice the principal invested in Scheme B, and s = 10%.

Accepted Answer

To find the principal in Scheme A, we need to establish a relationship between the two investments and their interest rates. Statement I alone gives only the rate for A (20%), but without knowing the principal ratio or rate s, we cannot determine the principal. Statement II provides the principal ratio (A = 2B) and rate s (10%), but without knowing r, we cannot calculate the difference. Together, both statements provide: r = 20%, s = 10%, and P_A = 2P_B. Using the formula: Amount_A = P_A(1.20)² = 1.44P_A and Amount_B = P_B + 0.10(P_B)(2) = 1.20P_B. Difference = 1.44(2P_B) - 1.20P_B = 2.88P_B - 1.20P_B = 1.68P_B = 480, so P_B = 285.71 and P_A = 571.43. However, this yields a non-round answer, suggesting we need to verify the calculation or that the statements together are sufficient but require careful computation.

Question 20

A shopkeeper sells three types of items: X, Y, and Z. The cost price of X is Rs. 100. The shopkeeper makes a profit on X, a loss on Y, and breaks even on Z. What is the overall profit or loss percentage?

Statement I: The cost price of Y is Rs. 150, the cost price of Z is Rs. 200, and the profit on X is 20%.
Statement II: The selling price of X is Rs. 120, the selling price of Y is Rs. 120, and the selling price of Z is Rs. 200. The shopkeeper sells 2 units of X, 3 units of Y, and 1 unit of Z.

Accepted Answer

To find the overall profit/loss percentage, we need total cost price and total selling price. Statement I gives: CP(X) = 100, CP(Y) = 150, CP(Z) = 200, and profit on X is 20%, so SP(X) = 120. However, Statement I does not specify the quantities sold, so we cannot calculate total profit/loss. Statement II gives: SP(X) = 120, SP(Y) = 120, SP(Z) = 200, and quantities: 2 units of X, 3 units of Y, 1 unit of Z. We know CP(X) = 100 from the question stem. From SP(X) = 120 and CP(X) = 100, profit on X is 20%, which matches Statement I. For Y: SP(Y) = 120, CP(Y) = 150 (from Statement I), so loss per unit = 30. For Z: SP(Z) = 200, CP(Z) = 200 (from Statement I), so break-even. Total CP = 2(100) + 3(150) + 1(200) = 200 + 450 + 200 = 850. Total SP = 2(120) + 3(120) + 1(200) = 240 + 360 + 200 = 800. Overall loss = 850 - 800 = 50. Loss% = (50/850) × 100 = 5.88%. Both statements together are necessary.

SSC CHSL Data Sufficiency — Maths

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Data Sufficiency — Maths — Practice Questions

60-Second Revision — Data Sufficiency — Maths