Question 1

What is the average age of three friends?
Statement I: The sum of ages of two friends is 48 years.
Statement II: The third friend is 6 years older than the average age of the first two friends.

Accepted Answer

From Statement I: Age of Friend 1 + Age of Friend 2 = 48. From Statement II: Age of Friend 3 = (48/2) + 6 = 24 + 6 = 30. Total age = 48 + 30 = 78. Average = 78/3 = 26 years. Both statements are necessary and sufficient.

Question 2

What is the cost price of a shirt?
Statement I: The shirt is sold at a profit of 25%, and the selling price is ₹500.
Statement II: The cost price of the shirt is ₹100 less than the selling price.

Accepted Answer

This is a Data Sufficiency question where we need to determine if the given statements are sufficient to find the cost price of the shirt.

Statement I: Selling Price = ₹500, Profit = 25%
Using the formula: SP = CP × (1 + Profit%/100)
500 = CP × (1 + 25/100)
500 = CP × 1.25
CP = 500/1.25 = ₹400
Statement I ALONE is sufficient.

Statement II: CP = SP - 100
We know SP = ₹500 (from Statement I context, but Statement II doesn't give SP directly)
Without knowing the selling price, we cannot find the cost price from Statement II alone.
Statement II ALONE is NOT sufficient.

Since Statement I alone gives us the answer, the correct option is (a).

Question 3

What is the simple interest earned on a principal amount?
Statement I: The principal is Rs. 5,000 and the rate of interest is 8% per annum.
Statement II: The time period is 3 years.

Accepted Answer

To find simple interest, we use the formula: SI = (P × R × T) / 100. Statement I gives us P = 5,000 and R = 8%. Statement II gives us T = 3 years. Both statements together are necessary and sufficient to calculate SI = (5,000 × 8 × 3) / 100 = Rs. 1,200.

Question 4

A rectangular plot has length and width in a specific ratio. The perimeter of the plot is known to be 120 meters.

Statement I: The length is 20 meters more than the width.
Statement II: The ratio of length to width is 5:3.

What is the area of the rectangular plot?

Accepted Answer

For a rectangle: Perimeter = 2(L + W) = 120, so L + W = 60. Statement I: L = W + 20. Substituting: (W + 20) + W = 60 → 2W = 40 → W = 20, L = 40. Area = 800 m². Statement II: L/W = 5/3 → L = 5W/3. Substituting: 5W/3 + W = 60 → 8W/3 = 60 → W = 22.5, L = 37.5. Area = 843.75 m². Both statements individually are sufficient to find the area, though they give different answers (indicating they describe different plots).

Question 5

A person invests money in two schemes: Scheme X (simple interest) and Scheme Y (compound interest). The principal amounts and rates are unknown.

Statement I: The principal in Scheme X is Rs. 5000 at 8% per annum for 3 years, and the principal in Scheme Y is Rs. 5000 at 8% per annum for 3 years (compounded annually).
Statement II: The difference between the compound interest and simple interest earned over 3 years is Rs. 98.56.

What is the total interest earned from both schemes combined?

Accepted Answer

Statement I provides all necessary information: SI from X = (5000 × 8 × 3)/100 = 1200. CI from Y = 5000(1.08)³ - 5000 = 5000(1.259712 - 1) = 1298.56. Total = 2498.56. Statement II only gives the difference (CI - SI = 98.56), which is insufficient to find the total interest without knowing the principal and rate. Statement I alone is sufficient.

Question 6

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 25% and item B at a loss of 10%. What is the total profit or loss percentage on the combined transaction?

Statement I: He sells 40 items of type A and 30 items of type B.
Statement II: The ratio of items sold is A:B = 4:3.

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

Accepted Answer

To find overall profit/loss percentage, we need: (Total SP - Total CP) / Total CP × 100. We know individual CP and profit/loss percentages. Statement I gives exact quantities (40 and 30), allowing calculation of total CP and SP. Statement II gives only the ratio (4:3), which is insufficient because profit/loss percentage depends on absolute quantities, not ratios. For example, 4 items of A and 3 of B gives different percentage than 40 and 30.

Question 7

A shopkeeper sells two types of items: notebooks and pens. The cost price of a notebook is Rs. 20 and the cost price of a pen is Rs. 5. He sells notebooks at a profit of P% and pens at a profit of Q%. In a particular transaction, he sells 15 notebooks and 40 pens for a total selling price of Rs. 525.

Statement I: The profit percentage on notebooks is 25%.
Statement II: The total profit earned on this transaction is Rs. 75.

Which statement(s) is/are sufficient to find the profit percentage on pens?

(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 Q (profit % on pens), we need to determine the selling price of pens or the total profit on pens.

Given:
- Cost price of notebook = Rs. 20; Cost price of pen = Rs. 5
- Quantity: 15 notebooks, 40 pens
- Total selling price = Rs. 525
- Total cost price = (15 × 20) + (40 × 5) = 300 + 200 = Rs. 500

From Statement I alone:
If P = 25%, then selling price of notebooks = 15 × 20 × 1.25 = Rs. 375
Selling price of pens = 525 - 375 = Rs. 150
Profit on pens = 150 - 200 = -Rs. 50 (loss)
Profit % on pens = (-50/200) × 100 = -25%
Statement I alone is sufficient.

From Statement II alone:
Total profit = Rs. 75
Profit on notebooks + Profit on pens = 75
Let profit on notebooks = 15 × 20 × (P/100) = 3P
Let profit on pens = 40 × 5 × (Q/100) = 2Q
3P + 2Q = 75
This is one equation with two unknowns. We cannot find Q uniquely.
Statement II alone is NOT sufficient.

Therefore, Statement I alone is sufficient.

Question 8

A train travels from City X to City Y. The distance between the cities is unknown. The train travels at a constant speed for the entire journey.

Statement I: The train takes 5 hours to complete the journey and covers 80 km in the first hour.
Statement II: The train covers 320 km in the first 4 hours of the journey.

What is the total distance between City X and City Y?

Accepted Answer

To find total distance, we need: distance = speed × time. Statement I tells us the time (5 hours) and the speed (80 km/h from 'covers 80 km in the first hour'). This gives distance = 80 × 5 = 400 km. Statement II tells us 320 km in 4 hours, which means speed = 320/4 = 80 km/h. Combined with the time from Statement I, we get 400 km. However, Statement II alone doesn't provide the total time. Statement I alone is sufficient.

Question 9

A shopkeeper sells two types of items. The cost price of item A is ₹x per unit and item B is ₹y per unit. He sells item A at 25% profit and item B at 20% loss. In a particular transaction, he sells 40 units of A and 60 units of B, earning a net profit of ₹800.

Statement I: The cost price of item A is ₹100 per unit.
Statement II: The cost price of item B is ₹80 per unit.

Which statement(s) is/are sufficient to find the net profit percentage on the total transaction?

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 net profit percentage, we need: (Net Profit / Total Cost Price) × 100.

Total Cost Price = 40x + 60y
Net Profit = 40x(0.25) + 60y(-0.20) = 10x - 12y = 800

From the profit equation: 10x - 12y = 800, or 5x - 6y = 400

Statement I alone: If x = 100, then 5(100) - 6y = 400 → 500 - 6y = 400 → y = 16.67. We can now calculate total cost price and net profit percentage. SUFFICIENT.

Statement II alone: If y = 80, then 5x - 6(80) = 400 → 5x - 480 = 400 → x = 176. We can now calculate total cost price and net profit percentage. SUFFICIENT.

However, the question asks which statement(s) is/are sufficient. Both individually provide enough information. But the answer structure requires checking if ONE statement alone works.

Using Statement I: Total CP = 40(100) + 60(16.67) = 4000 + 1000 = 5000. Net Profit % = (800/5000) × 100 = 16%.

Using Statement II: Total CP = 40(176) + 60(80) = 7040 + 4800 = 11840. Net Profit % = (800/11840) × 100 ≈ 6.76%.

Both statements alone are sufficient to answer the question independently.

Question 10

A cylindrical tank has a base radius of r meters and height h meters. Water flows into the tank at a rate of A cubic meters per hour and flows out at a rate of B cubic meters per hour. The tank starts empty and reaches 75% capacity in exactly T hours.

Statement I: The radius is 2 meters, height is 5 meters, and the net inflow rate is 3 cubic meters per hour.
Statement II: The tank's volume is 60π cubic meters and the net inflow rate is 3 cubic meters per hour.

Which statement(s) is/are sufficient to determine the time T?

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

Volume of cylinder = πr²h
75% of tank volume = 0.75 × πr²h
Time T = (0.75 × πr²h) / (net inflow rate) = (0.75 × πr²h) / (A - B)

To find T, we need: (1) the tank's volume πr²h, and (2) the net inflow rate (A - B).

Statement I: r = 2, h = 5, net rate = 3 m³/hr
Volume = π(2)²(5) = 20π cubic meters
75% volume = 0.75 × 20π = 15π cubic meters
T = 15π / 3 = 5π hours ≈ 15.7 hours
Statement I alone is SUFFICIENT.

Statement II: Volume = 60π cubic meters, net rate = 3 m³/hr
75% volume = 0.75 × 60π = 45π cubic meters
T = 45π / 3 = 15π hours ≈ 47.1 hours
Statement II alone is SUFFICIENT.

Both statements independently provide the required information.

Question 11

A rectangular plot of land has length L meters and width W meters. A fence is built around the perimeter. The cost of fencing is ₹p per meter. Additionally, a diagonal path is laid across the plot at a cost of ₹q per meter. The total cost of fencing and the diagonal path is ₹12,000.

Statement I: The perimeter is 200 meters and the diagonal is 50√2 meters, with p = 40 and q = 60.
Statement II: The length is 60 meters, the width is 40 meters, and the total cost is ₹12,000.

Which statement(s) is/are sufficient to determine the individual costs of fencing and the diagonal path?

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

Total cost = (Perimeter × p) + (Diagonal × q) = 12,000

Perimeter = 2(L + W)
Diagonal = √(L² + W²)

Statement I: Perimeter = 200m, Diagonal = 50√2 m, p = 40, q = 60
Cost of fencing = 200 × 40 = ₹8,000
Cost of diagonal = 50√2 × 60 = 3000√2 ≈ ₹4,242.64
Total = 8,000 + 4,242.64 ≈ ₹12,242.64 (approximately ₹12,000 with rounding)
Statement I is SUFFICIENT to determine individual costs.

Statement II: L = 60m, W = 40m, total cost = ₹12,000
Perimeter = 2(60 + 40) = 200m
Diagonal = √(60² + 40²) = √(3600 + 1600) = √5200 = 20√13 m
We have: 200p + 20√13 × q = 12,000
This is one equation with two unknowns (p and q). NOT SUFFICIENT to determine individual costs.

Only Statement I is sufficient.

Question 12

A train travels from City P to City Q. The distance between P and Q is d kilometers. The train travels the first half of the distance at speed s₁ km/h and the second half at speed s₂ km/h. The average speed for the entire journey is 48 km/h.

Statement I: The first half is covered at 40 km/h and the second half at 60 km/h.
Statement II: The harmonic mean of the two speeds is 48 km/h.

Which statement(s) is/are sufficient to verify that the average speed is indeed 48 km/h?

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

For a journey where equal distances are covered at different speeds, average speed = 2s₁s₂ / (s₁ + s₂) (harmonic mean formula).

Given: Average speed = 48 km/h
So: 2s₁s₂ / (s₁ + s₂) = 48

Statement I: s₁ = 40, s₂ = 60
Average speed = 2(40)(60) / (40 + 60) = 4800 / 100 = 48 km/h ✓
Statement I is SUFFICIENT to verify.

Statement II: "The harmonic mean of the two speeds is 48 km/h"
This directly states that 2s₁s₂ / (s₁ + s₂) = 48, which is exactly the formula for average speed in this scenario.
Statement II is SUFFICIENT to verify (it's essentially the definition of what we need to verify).

Both statements independently verify the condition.

Question 13

A company manufactures two products: X and Y. The profit on product X is ₹m per unit and on product Y is ₹n per unit. In a given month, the company sells a units of X and b units of Y, generating a total profit of ₹50,000. The profit margin (profit as a percentage of cost price) on X is 25% and on Y is 20%.

Statement I: 25a + 20b = 50,000 and the cost price of X is ₹100 per unit.
Statement II: The selling price of X is ₹125 per unit and the selling price of Y is ₹120 per unit.

Which statement(s) is/are sufficient to determine the number of units of X sold (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

Profit margin = (Profit / Cost Price) × 100

For product X: 25% margin means Profit = 0.25 × Cost Price
If cost price of X = C_X, then profit per unit m = 0.25 × C_X

For product Y: 20% margin means Profit = 0.20 × Cost Price
If cost price of Y = C_Y, then profit per unit n = 0.20 × C_Y

Total profit equation: m × a + n × b = 50,000

Statement I: Equation 25a + 20b = 50,000 and cost price of X = ₹100
From cost price of X = ₹100 and 25% margin: m = 0.25 × 100 = ₹25 per unit
But the equation given is 25a + 20b = 50,000, which suggests m = 25 and n = 20.
If m = 25 and n = 20, we have one equation with two unknowns (a and b). NOT SUFFICIENT to find a uniquely.

Statement II: Selling price of X = ₹125, selling price of Y = ₹120
From SP of X = ₹125 and 25% margin: CP_X = 125/1.25 = ₹100, so m = 25
From SP of Y = ₹120 and 20% margin: CP_Y = 120/1.20 = ₹100, so n = 20
Total profit equation: 25a + 20b = 50,000
Again, one equation with two unknowns (a and b). NOT SUFFICIENT to find a uniquely.

Both statements together: We have 25a + 20b = 50,000 with two unknowns. Even combined, we cannot determine a unique value for a without additional information (like the value of b or another constraint).

Neither statement alone nor together is sufficient.

Question 14

A shopkeeper sells two types of items: Type A and Type B. The profit margin on Type A is 25% and on Type B is 40%. Last month, the shopkeeper sold a total of 500 items and earned a total profit of ₹4,500.

Statement I: The cost price of Type A is ₹100 per item.
Statement II: The shopkeeper sold 200 items of Type B.

Which of the following is necessary to determine the number of Type A items sold?

(A) Statement I alone is sufficient, but Statement II alone is not sufficient.
(B) Statement II alone is sufficient, but Statement I alone is not sufficient.
(C) Both statements together are sufficient, but neither alone is sufficient.
(D) Both statements together are not sufficient to answer the question.

Accepted Answer

Let x = number of Type A items sold, y = number of Type B items sold.

Given constraints:
- x + y = 500 (total items)
- Profit from Type A: 0.25 × CP_A × x
- Profit from Type B: 0.40 × CP_B × y
- Total profit: 0.25 × CP_A × x + 0.40 × CP_B × y = 4,500

Statement I alone: CP_A = ₹100
This gives: 0.25(100)x + 0.40 × CP_B × y = 4,500
→ 25x + 0.40 × CP_B × y = 4,500
We have two unknowns (x and CP_B) and two equations, but CP_B is still unknown. We cannot determine x uniquely. Statement I alone is INSUFFICIENT.

Statement II alone: y = 200
This gives: x = 300 (from x + y = 500)
But we need to verify if this is consistent:
0.25 × CP_A × 300 + 0.40 × CP_B × 200 = 4,500
→ 75 × CP_A + 80 × CP_B = 4,500
This equation has infinite solutions for different values of CP_A and CP_B. Statement II alone is INSUFFICIENT.

Both statements together:
- CP_A = ₹100
- y = 200, so x = 300
- Verify: 0.25(100)(300) + 0.40 × CP_B × 200 = 4,500
- 7,500 + 80 × CP_B = 4,500
- 80 × CP_B = -3,000
- CP_B = -₹37.50 (impossible—negative cost price)

This reveals the system is inconsistent. However, the question asks what is "necessary to determine" the number of Type A items. With Statement II, we can directly determine x = 300 from the constraint x + y = 500, regardless of whether the profit data is consistent. The number of Type A items is determinable from Statement II alone.

Answer: (B) Statement II alone is sufficient, but Statement I alone is not sufficient.

SBI PO Data Sufficiency — Maths

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Data Sufficiency — Maths — Practice Questions

60-Second Revision — Data Sufficiency — Maths