Question 1

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. SI = (5,000 × 8 × 3) / 100 = 1,200. The answer can be determined only when both statements are combined.

Question 2

What is the average age of three persons A, B, and C?
Statement I: A is 24 years old and B is 30 years old.
Statement II: The sum of ages of A, B, and C is 84 years.

Accepted Answer

To find the average age of three persons, we need the sum of their ages divided by 3. Statement I gives us ages of A and B (24 + 30 = 54), but not C. Statement II directly gives us the sum of all three ages = 84. Using Statement II alone: Average = 84 / 3 = 28 years. Statement II alone is sufficient.

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.

Accepted Answer

Area of rectangle = Length × Width. Statement I gives length = 12 cm, but not the width. Statement II gives perimeter = 40 cm. From perimeter: 2(L + W) = 40, so L + W = 20. If L = 12, then W = 8 cm. Using both statements: Area = 12 × 8 = 96 cm². Statement I alone is insufficient (no width). Statement II alone is insufficient (no length). Both statements together are necessary and sufficient.

Question 4

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: If profit = 25% and SP = ₹500, then CP = SP / (1 + profit%) = 500 / 1.25 = ₹400. This statement ALONE is sufficient.

Statement II: If CP = SP - 100, and we know SP = ₹500 (from Statement I), then CP = 500 - 100 = ₹400. However, Statement II alone does NOT give us the selling price, so we cannot find CP independently. But if we combine both statements, we get CP = ₹400.

Since Statement I alone gives us the answer (CP = ₹400), the answer is (A).

Question 5

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

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 and 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. When both statements are combined, we know x is divisible by both 2 and 3, which means x is divisible by 6. Both statements together are necessary and sufficient.

Question 6

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

Accepted Answer

We know Selling Price (SP) = Rs. 1,200. To find Cost Price (CP), we use: CP = SP / (1 + Profit%/100) or CP = SP - Profit Amount. Statement I gives profit% = 20%, so CP = 1,200 / 1.20 = Rs. 1,000. Statement II gives profit = Rs. 200, so CP = 1,200 - 200 = Rs. 1,000. Either statement alone is sufficient to find CP. Both statements are individually sufficient.

Question 7

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. The shopkeeper sells all items at a markup. In a particular day, the shopkeeper sold a total of 100 items and earned a total profit of Rs. 300.

Statement I: The selling price of a pen is Rs. 8, a notebook is Rs. 28, and an eraser is Rs. 3.

Statement II: The shopkeeper sold 40 pens, 30 notebooks, and 30 erasers.

Which of the following is sufficient to answer: What is the total revenue (selling price × quantity) for the day?

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 revenue, we need: (Selling Price × Quantity) for each item type.

From Statement I alone:
- We know selling prices: Pen Rs. 8, Notebook Rs. 28, Eraser Rs. 3
- We know 100 items were sold total and profit was Rs. 300
- But we do NOT know the quantity breakdown (how many pens, notebooks, erasers)
- Without quantities, we cannot calculate total revenue
- Statement I alone is INSUFFICIENT

From Statement II alone:
- We know quantities: 40 pens, 30 notebooks, 30 erasers
- We know cost prices: Pen Rs. 5, Notebook Rs. 20, Eraser Rs. 2
- Total cost price = (40 × 5) + (30 × 20) + (30 × 2) = 200 + 600 + 60 = Rs. 860
- Total profit given = Rs. 300
- Total revenue = Total cost price + Total profit = 860 + 300 = Rs. 1160
- Statement II alone is SUFFICIENT

Therefore, the answer is Statement II alone is sufficient.

Question 8

A train travels from City P to City Q. The distance between P and Q is unknown. The train travels at a constant speed for the entire journey.

Statement I: The train takes 6 hours to cover 360 km.
Statement II: The train covers 60 km in 1 hour.

What is the speed of the train?

Accepted Answer

Speed = Distance / Time. Statement I: Speed = 360/6 = 60 km/h. Statement II: Speed = 60 km/h directly. Both statements independently give the same answer: 60 km/h. Either statement alone is sufficient.

Question 9

A rectangular garden has an unknown length and width. The area of the garden is unknown.

Statement I: The perimeter of the garden is 60 meters.
Statement II: The length of the garden is 18 meters.

What is the area of the rectangular garden?

Accepted Answer

Area of rectangle = length × width. Statement I: Perimeter = 2(L + W) = 60, so L + W = 30. This gives a relationship but not unique values for L and W (e.g., L=20, W=10 or L=18, W=12). Statement II: L = 18. Combined: 18 + W = 30, so W = 12. Area = 18 × 12 = 216 m². Statement I alone is insufficient (infinite solutions). Statement II alone is insufficient (W unknown). Both statements together are necessary and sufficient.

Question 10

A shopkeeper has apples and oranges. The number of apples is unknown, and the number of oranges is unknown. The total number of fruits is unknown.

Statement I: The ratio of apples to oranges is 3:2.
Statement II: There are 15 more apples than oranges.

How many apples does the shopkeeper have?

Accepted Answer

Let apples = A, oranges = O. Statement I: A/O = 3/2, so A = 1.5O. This gives a relationship but not absolute values (e.g., A=3, O=2 or A=30, O=20). Statement II: A = O + 15. This also gives a relationship but not absolute values (e.g., A=16, O=1 or A=20, O=5). Combined: 1.5O = O + 15 → 0.5O = 15 → O = 30 → A = 45. Statement I alone is insufficient. Statement II alone is insufficient. Both statements together are necessary and sufficient.

Question 11

A person invests money in two schemes: Scheme A and Scheme B. Scheme A offers simple interest at a rate of r% per annum, and Scheme B offers compound interest at a rate of (r-2)% per annum, compounded annually.

Statement I: The person invests Rs. 10,000 in Scheme A and Rs. 15,000 in Scheme B. After 2 years, the total amount in both schemes is Rs. 27,500.
Statement II: The difference between the interest earned from Scheme A and Scheme B after 2 years is Rs. 200.

What is the rate of interest r?

Accepted Answer

This question tests whether students can set up and solve simultaneous equations involving simple and compound interest, and whether they can identify when statements provide redundant versus independent information.

Question 12

A company manufactures two products: Product X and Product Y. The profit margin on Product X is 30%, and on Product Y is 20%. In a given month, the company sold some units of each product.

Statement I: The total revenue from both products is Rs. 50,000, and the total cost price is Rs. 40,000.
Statement II: The number of units of Product X sold is twice the number of units of Product Y sold.

What is the cost price of one unit of Product X?

Accepted Answer

This question tests whether students can distinguish between aggregate profit data and individual product pricing, and whether they confuse total profit with individual unit costs.

Question 13

A train travels from Station X to Station Y. The distance between the two stations is unknown. The train's speed for the first half of the journey (by distance) is 60 km/h, and for the second half, it is 80 km/h.

Statement I: The total time taken for the journey is 7 hours.
Statement II: The average speed for the entire journey is approximately 68.57 km/h.

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

Accepted Answer

This question tests understanding of harmonic mean in average speed problems and whether students can work backwards from average speed to find distance.

IBPS Clerk Data Sufficiency — Maths

IBPS Clerk Data Sufficiency — Maths — Past Exam Questions

Data Sufficiency — Maths— Rules & Concept

Key Points to Remember

Exam-Specific Tips

60-Second Revision — Data Sufficiency — Maths