Question 1

What is the area of a rectangle?
Statement I: The length is 12 cm.
Statement II: The perimeter is 40 cm.

Accepted Answer

Area = length × width. Statement I gives only length (12 cm), not width. Statement II: Perimeter = 2(l + w) = 40 → l + w = 20. With l = 12, we get w = 8. But Statement II alone doesn't give us the length. Together: l = 12 and w = 8, so Area = 96 cm². Both statements together are necessary.

Question 2

Is x greater than 10?
Statement I: x + 5 = 18.
Statement II: x - 3 > 7.

Accepted Answer

Statement I: x + 5 = 18 → x = 13. Since 13 > 10, the answer is YES. This alone is sufficient. Statement II: x - 3 > 7 → x > 10. This directly answers the question as YES. Either statement alone is sufficient to answer the question.

Question 3

A shopkeeper sells pens at a profit. What is the profit percentage?
Statement I: The cost price of each pen is ₹5.
Statement II: The selling price of each pen is ₹7.

Accepted Answer

To find profit percentage, we need both cost price and selling price. Statement I alone gives only cost price (₹5). Statement II alone gives only selling price (₹7). Together: Profit = 7 - 5 = ₹2. Profit % = (2/5) × 100 = 40%. Both statements together are necessary.

Question 4

What is the average of five consecutive even numbers?
Statement I: The smallest number is 12.
Statement II: The largest number is 20.

Accepted Answer

Both statements independently provide sufficient information to find the average of five consecutive even numbers. Statement I: If smallest is 12, the numbers are 12, 14, 16, 18, 20, and average = (12+20)/2 = 16. Statement II: If largest is 20, the numbers are 12, 14, 16, 18, 20, and average = 16. Either statement alone is sufficient.

Question 5

How many students passed the exam?
Statement I: 60% of the students passed.
Statement II: 120 students failed the exam.

Accepted Answer

Statement I: 60% passed means 40% failed, but we don't know the total number of students. Statement II: 120 students failed, but we don't know what percentage this represents. Together: If 40% = 120 students, then total = 300, and 60% passed = 180 students. Both statements together are necessary.

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