Question 1

Is the number X divisible by 6? Statement 1: X is divisible by both 2 and 3. Statement 2: X is an even number greater than 10.

Accepted Answer

A number is divisible by 6 if and only if it is divisible by both 2 and 3; Statement 1 directly confirms this condition, while Statement 2 only confirms divisibility by 2.

Question 2

What is the age of Rahul? Statement 1: Rahul's age is 5 years more than Priya's age. Statement 2: The sum of Rahul's and Priya's ages is 35 years.

Accepted Answer

Statement 1 gives a relationship but not exact ages; Statement 2 gives a sum but not individual values; together they form two equations (R = P + 5 and R + P = 35) that uniquely determine R = 20.

Question 3

Is the area of a rectangle greater than 50 square cm? Statement I: The length of the rectangle is 10 cm. Statement II: The perimeter of the rectangle is 30 cm.

Accepted Answer

From Statement I, length = 10 cm; from Statement II, perimeter = 30 cm, so 2(10 + width) = 30, giving width = 5 cm; therefore area = 10 × 5 = 50 cm², which is not greater than 50, and both statements are needed to answer.

Question 4

What is the value of x? Statement I: 3x + 5 = 20. Statement II: x is a positive integer less than 10.

Accepted Answer

From Statement I alone: 3x + 5 = 20 gives 3x = 15, so x = 5; Statement II is not needed as it only narrows the range but does not uniquely determine x.

Question 5

What is the age of Ravi? Statement I: Ravi is 5 years older than Priya. Statement II: Priya's age is 12 years.

Accepted Answer

Statement I provides the relationship between their ages and Statement II provides Priya's exact age; together they determine Ravi's age as 17 years.

Question 6

Is the sum of three consecutive integers divisible by 3? Statement I: The first integer is 5. Statement II: The middle integer is even.

Accepted Answer

The sum of any three consecutive integers is always divisible by 3 regardless of the starting point, so neither statement is needed to answer the question.

Question 7

Is triangle ABC a right-angled triangle? Statement I: One angle of the triangle is 90°. Statement II: Two sides of the triangle are 3 cm and 4 cm.

Accepted Answer

A triangle with one angle of 90° is, by definition, a right-angled triangle; Statement I alone is sufficient.

Question 8

A shopkeeper bought some items at a cost price. What is the profit percentage?
Statement I: The selling price is 25% more than the cost price.
Statement II: The cost price is ₹400 and the selling price is ₹500.
Which statement(s) is/are sufficient to answer the question?

Accepted Answer

Profit percentage = [(SP - CP) / CP] × 100, and Statement I directly gives SP = CP + 25% of CP, which is sufficient to calculate 25% profit; Statement II provides specific values but is redundant.

Question 9

A rectangular plot has a perimeter of 60 metres. Is the length of the plot greater than 20 metres?
Statement I: The width of the plot is 10 metres.
Statement II: The area of the plot is 200 square metres.
Which statement(s) is/are sufficient to answer the question?

Accepted Answer

From perimeter = 60 and width = 10, we get length = (60/2) - 10 = 20 metres, so length is NOT greater than 20; Statement I alone is sufficient, while Statement II alone cannot uniquely determine length.

Question 10

Two numbers have a sum of 50. What is the larger number?
Statement I: The difference between the two numbers is 10.
Statement II: One number is 3 times the other.
Which statement(s) is/are sufficient to answer the question?

Accepted Answer

From Statement I: x + y = 50 and x - y = 10 gives x = 30 (larger number); from Statement II: x + 3x = 50 gives x = 12.5 and 3x = 37.5 (larger number); both statements independently provide a unique answer.

Question 11

A shopkeeper sells three types of items: pens, notebooks, and erasers. To determine the total profit percentage on all items sold, which of the following information is sufficient?

Statement I: The cost price and selling price of pens is ₹5 and ₹7 respectively, and 100 pens were sold.

Statement II: The cost price and selling price of notebooks is ₹20 and ₹25 respectively, and 50 notebooks were sold. The cost price and selling price of erasers is ₹2 and ₹3 respectively, and 200 erasers were sold.

(A) Statement I alone is sufficient
(B) Statement II alone is sufficient
(C) Both statements I and II together are necessary
(D) Neither statement alone nor both together are sufficient

Accepted Answer

Total profit percentage requires combined cost price and selling price of ALL three items; Statement I gives only pens data while Statement II gives notebooks and erasers data, so both statements together are necessary to calculate overall profit percentage.

Question 12

A shopkeeper sells two types of items: pens and notebooks. Is the total revenue from selling pens greater than the total revenue from selling notebooks?
Statement I: The selling price of a pen is ₹5 and the selling price of a notebook is ₹15.
Statement II: The shopkeeper sold 120 pens and 40 notebooks.

Accepted Answer

Both statements are needed: Statement I provides unit prices (₹5 per pen, ₹15 per notebook) and Statement II provides quantities (120 pens, 40 notebooks), allowing us to calculate revenues (₹600 vs ₹600) to answer whether pen revenue is greater.

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