Question

Two consecutive natural numbers each of which is multiple of 3 and with their product = 108.

Statement (1): The required natural numbers are 9 and 12.

Statement (2): If two natural numbers are 3x and 3x + 3; 3x(3x + 3) = 108

Options

• Both the statements are true.

• Both the statements are false.

• Statement 1 is true, and statement 2 is false.

• Statement 1 is false, and statement 2 is true.

Answer 1

Both the statements are true.

Explanation:

Let the two consecutive natural numbers each of which is multiple of 3 be 3x and 3(x + 1).

Product = 108

⇒ 3x × 3(x + 1) = 108

⇒ 3x × (3x + 3) = 108

⇒ 9x² + 9x = 108

⇒ 9x² + 9x − 108 = 0

⇒ 9(x² + x − 12) = 0

⇒ x² + x − 12 = 0

⇒ x² + 4x − 3x − 12 = 0

⇒ x(x + 4) − 3(x + 4) = 0

⇒ (x + 4)(x − 3) = 0

⇒ (x + 4) = 0 or (x − 3) = 0

⇒ x = −4 or x = 3

Since, number are two natural numbers. So, x = 3.

And, when x = 3, two consecutive numbers = 3 × 3 = 9 and 3 × (3 + 1) = 3 × 4 = 12

So, both statements are true.