Question 1

What is the average age of three friends?
Statement I: The sum of ages of the first two friends is 48 years.
Statement II: The age of the third friend is 24 years.

Accepted Answer

Average = Total sum / Number of items. We have the sum of two ages (48) and the third age (24), giving total = 72. Average = 72 / 3 = 24 years. Both statements together are 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.

(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 cost price, we need a relationship between cost price and selling price.

Statement I: Profit = 25%, Selling Price = ₹500
Using: 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
This gives a relationship but without knowing the actual SP value, we cannot find CP numerically.
For example: If SP = ₹600, then CP = ₹500. If SP = ₹700, then CP = ₹600.
Statement II ALONE is NOT sufficient.

The answer is (A) — Statement I alone is sufficient.

Question 3

What is the simple interest earned on a principal amount?
Statement I: The principal is ₹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 SI = (P × R × T) / 100. Statement I gives P and R. Statement II gives T. Both statements together are necessary and sufficient to calculate SI.

Question 4

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 = length × width. Statement I gives length only. Statement II gives perimeter = 2(length + width) = 40, so length + width = 20. With length = 12, we get width = 8. Both statements together are sufficient.

Question 5

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

Accepted Answer

Cost Price (CP) = Selling Price (SP) - Profit. Statement I gives SP = ₹500 and Profit = ₹100, so CP = 500 - 100 = ₹400. Statement I alone is sufficient. Statement II alone cannot determine CP without knowing either SP or profit amount.

Question 6

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, 3 are coprime). Statement I alone is insufficient. Statement II alone is insufficient. Together, they are sufficient.

Question 7

How many students passed in both Mathematics and Science?
Statement I: 60% of 150 students passed Mathematics, and 70% of 150 students passed Science.
Statement II: 20% of students failed both subjects.

Accepted Answer

Statement I alone is insufficient because it gives individual pass rates but not the overlap. Statement II alone is insufficient as it only tells us about failures in both. Together: 60% passed Math (90 students), 70% passed Science (105 students). 20% failed both (30 students), so 80% passed at least one subject (120 students). Using inclusion-exclusion: 90 + 105 - 120 = 75 students passed both. Both statements together are necessary.

Question 8

A shopkeeper sells two types of items: pens and notebooks. The cost price of a pen is ₹5 and the cost price of a notebook is ₹8. The shopkeeper sells all items at a markup. Statement I: The shopkeeper sells 40 pens and 30 notebooks, making a total profit of ₹290. Statement II: The markup percentage on pens is 50% and the markup percentage on notebooks is 25%. Is the total profit of ₹290 consistent with the markup percentages given in Statement II?

Accepted Answer

This is a Data Sufficiency question where we need to determine if Statement II alone is sufficient to verify the profit claim in Statement I. Using Statement II: Selling price of pen = 5 + (50% of 5) = ₹7.50. Selling price of notebook = 8 + (25% of 8) = ₹10. Profit from 40 pens = 40 × (7.50 - 5) = 40 × 2.50 = ₹100. Profit from 30 notebooks = 30 × (10 - 8) = 30 × 2 = ₹60. Total profit = ₹100 + ₹60 = ₹160, NOT ₹290. Therefore, Statement II alone is NOT sufficient to make the profit claim true. Both statements together show a contradiction, meaning the data is inconsistent. The answer is that Statement II is insufficient because it produces a different profit figure.

Question 9

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 SP = 500 and profit = 25%, we get CP = 500/1.25 = ₹400. Statement II alone is insufficient because it only tells us SP - CP = 100, which doesn't uniquely determine CP without knowing SP. Together they are also sufficient but Statement I alone suffices.

Question 10

What is the average age of five friends?
Statement I: The sum of ages of three friends is 45 years.
Statement II: The sum of ages of the other two friends is 30 years.

Accepted Answer

Statement I alone is insufficient (only 3 out of 5 friends). Statement II alone is insufficient (only 2 out of 5 friends). Together: Total sum = 45 + 30 = 75 years. Average = 75/5 = 15 years. Both statements together are necessary and sufficient.

Question 11

What is the speed of a train?
Statement I: The train covers 240 km in 4 hours.
Statement II: The train covers 180 km in 3 hours.

Accepted Answer

Statement I alone: Speed = 240/4 = 60 km/h. This is sufficient. Statement II alone: Speed = 180/3 = 60 km/h. This is also sufficient. Both statements give the same answer independently, so either statement alone is sufficient.

Question 12

What is the length of a rectangular field?
Statement I: The perimeter of the field is 100 meters.
Statement II: The breadth of the field is 15 meters.

Accepted Answer

Statement I alone is insufficient because perimeter = 2(L + B), which gives L + B = 50, but doesn't determine L uniquely. Statement II alone is insufficient because breadth alone doesn't determine length. Together: L + B = 50 and B = 15, so L = 35 meters. Both statements together are necessary.

Question 13

A shopkeeper sells two types of items. The cost price of item A is Rs. 40 per unit and item B is Rs. 60 per unit. He sells item A at 25% profit and item B at 20% profit. In a particular transaction, he sells a total of 100 units and earns a total profit of Rs. 2,200.

Statement I: He sold 60 units of item A and 40 units of item B.
Statement II: The ratio of units sold of item A to item B is 3:2.

Which statement(s) is/are sufficient to answer: How many units of item A were sold?

Accepted Answer

Testing whether students can identify that both statements provide the same information in different forms, and whether they can verify sufficiency through algebraic constraint-checking.

Question 14

A rectangular tank has length L meters, width W meters, and height H meters. Water is filled to a height of h meters. A pipe fills the tank at rate F cubic meters per hour, and a drain empties it at rate D cubic meters per hour.

Statement I: The tank's volume is 240 cubic meters, currently 60% full, and the net filling rate is 3 cubic meters per hour.
Statement II: The pipe fills at 8 cubic meters per hour, the drain empties at 5 cubic meters per hour, and the current water volume is 144 cubic meters.

Which statement(s) is/are sufficient to determine: How many hours will it take to fill the tank completely?

Accepted Answer

Testing whether students can identify that Statement II lacks information about total tank capacity, while Statement I provides it implicitly.

Question 15

A train travels from City X to City Y. The distance between the cities 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.

Statement I: The first half is covered in 4 hours and the second half in 6 hours.
Statement II: The average speed for the entire journey is 48 km/h and the ratio of S₁ to S₂ is 3:2.

Which statement(s) is/are sufficient to determine: What is the total distance D?

Accepted Answer

Testing whether students can recognize that average speed for distance-based halves requires harmonic mean, not arithmetic mean, and whether they can identify missing constraints.

Question 16

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 man receives equal amounts from both schemes.

Statement I: The principal invested in Scheme A is Rs. 10,000.
Statement II: The rate of interest in Scheme B is 10% per annum.

Is the data sufficient to determine the principal invested in Scheme B?

(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

This is a Data Sufficiency question testing whether given constraints can uniquely determine an unknown value. The key is recognizing that equal final amounts from two different interest mechanisms create a relationship between principals and rates, but we need specific numerical values to solve.

SBI Clerk Data Sufficiency — Maths

SBI 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