Question 1

Is the number x divisible by 12?
Statement I: x is divisible by 3 and x is divisible by 4.
Statement II: x is divisible by 2 and x is divisible by 6.

Accepted Answer

For a number to be divisible by 12, it must be divisible by both 3 and 4 (since 12 = 3 × 4 and 3, 4 are coprime). Statement I directly states x is divisible by both 3 and 4, so x is divisible by 12. Statement II says x is divisible by 2 and 6. Since 6 = 2 × 3, if x is divisible by 6, it is already divisible by both 2 and 3. However, this does not guarantee divisibility by 4. For example, x = 6 is divisible by 2 and 6, but not by 12. Therefore, only Statement I is sufficient.

Question 2

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 provide all three required variables, so we can calculate SI = (5,000 × 8 × 3) / 100 = Rs. 1,200. Therefore, both statements are necessary and sufficient.

Question 3

What is the cost price of an item if its selling price is Rs. 1,200?
Statement I: The profit percentage is 20%.
Statement II: The profit amount is Rs. 200.

Accepted Answer

The relationship is: Selling Price = Cost Price + Profit. We know SP = 1,200. Statement I tells us profit is 20% of CP. So, 1,200 = CP + 0.20 × CP = 1.20 × CP, giving CP = 1,000. Statement II tells us profit = 200. So, 1,200 = CP + 200, giving CP = 1,000. Both statements individually are sufficient to find CP. Therefore, either statement alone is sufficient.

Question 4

How many students passed the exam in a class?
Statement I: There are 50 students in the class.
Statement II: 70% of the students passed the exam.

Accepted Answer

To find the number of students who passed, we need both the total number of students and the pass percentage (or pass rate). Statement I gives us the total = 50 students. Statement II gives us the pass percentage = 70%. Together: Number passed = 50 × (70/100) = 35 students. Neither statement alone is sufficient; both are required. Therefore, both statements together are necessary and sufficient.

Question 5

What is the average age of three friends A, B, and C?
Statement I: A's age is 24 years and B's age is 26 years.
Statement II: The sum of all three ages is 75 years.

Accepted Answer

To find the average age, we need the sum of all three ages divided by 3. Statement I gives us A = 24 and B = 26, but we do not know C's age. Statement II directly gives us the sum of all three ages = 75. Using Statement II alone, average = 75 / 3 = 25 years. Statement I alone is insufficient because we lack C's age. Therefore, Statement II alone is sufficient.

Question 6

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

Statement I alone is sufficient. From Statement I: If profit = 25%, then SP = CP × 1.25. Given SP = ₹500, we get CP = 500/1.25 = ₹400. Statement II alone is insufficient because it only gives a relationship (CP = SP - 100) without knowing the actual SP value. Together they are also sufficient, but Statement I alone answers the question.

Question 7

What is the average age of three friends A, B, and C?
Statement I: A's age is 5 years more than B's age, and B's age is 3 years more than C's age.
Statement II: The sum of A's and C's ages is 40 years.

Accepted Answer

Statement I alone is insufficient—it only provides relationships, not absolute values. Statement II alone is insufficient—it gives one equation with two unknowns. Together: From I, A = B + 5 and B = C + 3, so A = C + 8. From II, A + C = 40. Substituting: (C + 8) + C = 40, so 2C = 32, C = 16. Then A = 24, B = 19. Average = (24 + 19 + 16)/3 = 59/3 ≈ 19.67. Both statements together are necessary and sufficient.

Question 8

A shopkeeper sells two types of items: pens and notebooks. The cost price of a pen is Rs. 5 and the cost price of a notebook is Rs. 8. The shopkeeper sells pens at a profit of P% and notebooks at a profit of Q%. On a particular day, the shopkeeper sold a total of 100 items and made a total profit of Rs. 240.

Statement I: The shopkeeper sold 60 pens and 40 notebooks.
Statement II: The average profit per item sold was Rs. 2.40.

Which of the following statements is/are sufficient to find the individual profit percentages P and Q?

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) Neither statement alone nor both together are sufficient.

Accepted Answer

This question tests whether students can distinguish between having sufficient information to solve for two unknowns versus merely having consistent constraints.

Question 9

A container has a mixture of milk and water. The ratio of milk to water is m:w. The container is filled to capacity V liters.

Statement I: The container has 15 liters of milk and 10 liters of water.
Statement II: The ratio of milk to water is 3:2, and the container's capacity is 25 liters.

Can we determine the ratio m:w and the volume of milk in the container?

(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

From Statement I: Milk = 15 liters, Water = 10 liters. Ratio m:w = 15:10 = 3:2. Total volume = 25 liters. Both the ratio and the volume of milk are determined. Statement I alone is sufficient.

From Statement II: Ratio m:w = 3:2, Capacity V = 25 liters. This tells us the ratio, but not the actual volume of milk. The container could be partially filled. For example, if filled to 20 liters, milk = 12 liters; if filled to 25 liters, milk = 15 liters. The volume of milk is indeterminate. Statement II alone is insufficient.

Question 10

A rectangular tank has length L, width W, and height H (all in meters). Water is filled to a height h meters. A pipe fills the tank at rate r cubic meters per hour, and a drain empties it at rate d cubic meters per hour.

Statement I: The tank's volume is 120 cubic meters, and the net filling rate is 2 cubic meters per hour.
Statement II: The current water volume is 60 cubic meters, and it will take 30 hours to fill the tank completely.

Can we determine the individual values of r and d?

(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

From Statement I: Tank volume = 120 m³, net rate = r - d = 2 m³/hr. This gives one equation with two unknowns (r and d). Insufficient.

From Statement II: Current volume = 60 m³, remaining volume = 120 - 60 = 60 m³. Time to fill = 30 hours. So net rate = 60/30 = 2 m³/hr, meaning r - d = 2. Again, one equation with two unknowns. Insufficient.

Combining both: We get r - d = 2 from both statements (same information). We still cannot determine r and d individually. We need either r or d explicitly.

Question 11

A company has two projects, X and Y. The profit from project X is p% of its investment, and the profit from project Y is q% of its investment. The total investment is Rs. 10 lakhs.

Statement I: The profit from project X is Rs. 2 lakhs, and the profit from project Y is Rs. 1.5 lakhs.
Statement II: The investment in project X is Rs. 5 lakhs, and the investment in project Y is Rs. 5 lakhs.

Can we determine the individual values of p and q?

(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

From Statement I: Profit(X) = 2 lakhs, Profit(Y) = 1.5 lakhs. Total investment = 10 lakhs. Let investment in X = I_X, investment in Y = I_Y. Then I_X + I_Y = 10. Also, p = (2/I_X) × 100 and q = (1.5/I_Y) × 100. We have two unknowns (I_X, I_Y) and one equation (I_X + I_Y = 10). Insufficient to find p and q uniquely.

From Statement II: I_X = 5 lakhs, I_Y = 5 lakhs. This satisfies I_X + I_Y = 10. But we don't know the profits, so we cannot calculate p and q. Insufficient.

Combining both: I_X = 5, I_Y = 5, Profit(X) = 2, Profit(Y) = 1.5. Then p = (2/5) × 100 = 40% and q = (1.5/5) × 100 = 30%. Both statements together are sufficient.

Question 12

A train travels from City P to City Q. The distance is d kilometers. The train travels the first half of the distance at speed s₁ km/hr and the second half at speed s₂ km/hr.

Statement I: The average speed for the entire journey is 48 km/hr, and s₁ = 40 km/hr.
Statement II: The time taken for the first half is 2.5 hours, and the time taken for the second half is 3 hours.

Can we determine the value of s₂?

(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

From Statement I: Average speed = 48 km/hr, s₁ = 40 km/hr. For equal distances, average speed = 2s₁s₂/(s₁ + s₂). So 48 = 2(40)s₂/(40 + s₂) → 48(40 + s₂) = 80s₂ → 1920 + 48s₂ = 80s₂ → s₂ = 60 km/hr. Statement I alone is sufficient.

From Statement II: Time for first half = 2.5 hrs, time for second half = 3 hrs. Distance in first half = s₁ × 2.5, distance in second half = s₂ × 3. Since distances are equal: s₁ × 2.5 = s₂ × 3 → s₁/s₂ = 3/2.5 = 6/5. This gives a ratio, not the individual value of s₂. Insufficient.

IBPS RRB PO Data Sufficiency — Maths

Data Sufficiency — Maths— Rules & Concept

Key Points to Remember

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Data Sufficiency — Maths — Practice Questions

60-Second Revision — Data Sufficiency — Maths