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

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 5

In a Data Sufficiency question, we need to determine: 'How many students in a class scored above 75 marks?'

Statement I: There are 40 students in the class, and 60% of them scored above 75 marks.
Statement II: 24 students scored above 75 marks, and 16 students scored 75 marks or below.

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

Accepted Answer

To answer 'How many students scored above 75 marks?', we need a definite numerical value.

Statement I: 60% of 40 = 0.60 × 40 = 24 students scored above 75 marks. This gives a definite answer.

Statement II: Directly states that 24 students scored above 75 marks. This also gives a definite answer.

Both statements independently provide the same definite answer (24 students). Therefore, either statement 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

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 7

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 8

Five friends—Arun, Bhavna, Chitra, Deepak, and Esha—sit in a row facing North. Bhavna sits third from the left. Deepak sits immediately to the right of Bhavna. Arun sits to the left of Bhavna but not at the extreme left. Chitra sits at one of the ends. Is it possible to determine the exact seating arrangement?
Statement I: Esha sits at the extreme left.
Statement II: Arun sits second from the left.

Accepted Answer

This question tests whether given constraints are sufficient to uniquely determine a linear arrangement.

Question 9

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 10

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 11

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 12

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 13

In a coding system, each letter is replaced by a digit such that the same letter always gets the same digit, and different letters get different digits. In the code, MATH + MATH = GAMES. What is the value of M?
Statement I: G = 1.
Statement II: A = 9.

Accepted Answer

Cryptarithmetic problem testing whether given digit assignments are sufficient to uniquely determine another digit.

Question 14

Six people—P, Q, R, S, T, U—have different ages. R is older than Q. S is younger than T. U is the oldest. Can we determine whether P is older than Q?
Statement I: P is older than R.
Statement II: T is older than Q.

Accepted Answer

Comparative reasoning problem testing whether given age relationships are sufficient to establish a specific comparison.

Question 15

In a family, there are five members: A, B, C, D, and E. A is the father of B. C is the mother of D. B and D are siblings. Is E male or female?
Statement I: E is the spouse of A.
Statement II: E is the mother of B.

Accepted Answer

Blood relation problem testing logical deduction about family relationships and gender inference.

Question 16

A shopkeeper has a total of 100 items consisting of pens, pencils, and erasers. The number of pens is twice the number of pencils. Is it possible to determine the exact number of erasers?
Statement I: The number of pens is 40.
Statement II: The number of pencils and erasers combined is 60.

Accepted Answer

Quantitative reasoning problem testing whether given constraints are sufficient to uniquely determine an unknown quantity.

Question 17

Five people—A, B, C, D, E—sit in a row. Statement I: B sits immediately to the right of A. Statement II: D sits at one end and C sits immediately to the right of D. Is Statement I alone sufficient to determine the exact seating arrangement?

Accepted Answer

This is a data sufficiency question where we must evaluate whether given statements are sufficient to uniquely determine the arrangement. Statement I only tells us B is right of A, but leaves 3 other people (C, D, E) with multiple possible positions. Statement II adds constraints but doesn't fix A and B's position relative to D and C. Neither statement alone, nor both together, uniquely determines the arrangement because we don't know the relative positions of the A-B pair versus the D-C pair, nor where E fits.

Question 18

A shopkeeper sells three types of items: X, Y, Z. Statement I: The ratio of X sold to Y sold is 3:2. Statement II: The total items sold is 100, and Z accounts for 20% of total sales. What is the number of X items sold? Determine sufficiency.

Accepted Answer

Statement I gives the ratio X:Y = 3:2, but doesn't tell us the absolute quantities or how many Z items exist. Statement II tells us total is 100 and Z = 20 items, so X + Y = 80. Combined: X:Y = 3:2 means X = 3k, Y = 2k for some k. Then 3k + 2k = 80 → 5k = 80 → k = 16 → X = 48. Both statements together are necessary and sufficient.

Question 19

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.

Question 20

Six boxes are arranged in a circle. Statement I: Box P is directly opposite Box Q. Statement II: Box R is two positions clockwise from Box P. Is the position of Box R uniquely determined relative to Box Q?

Accepted Answer

In a circle of 6 boxes, 'directly opposite' means 3 positions away. If P is at position 1, Q is at position 4. 'Two positions clockwise from P' means R is at position 3 (1 + 2 = 3). Relative to Q at position 4, R at position 3 is one position counter-clockwise. However, we don't know the absolute starting position of P—it could be any of the 6 positions. But the relative position of R to Q is always the same: one position counter-clockwise. Both statements together determine R's position relative to Q uniquely.

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