SSC GD 2023 PYQ — Question 43

The correct answer is Option 1 i.e 9.

We know that,

(a - b)² = a² + b² - 2ab             ----- (1)

(a + b)² = a² + b² + 2ab            ----- (2)

Let the two numbers be a and b.

Now, we have

⇒ a - b = 9 and ab = 2430

Using equation (1);

⇒ 9² = a² + b² - 4860

⇒ a² + b² = 4941

Now, using equation (2);

⇒ (a + b)² = 4941 + 4860

⇒ (a + b)² = 9801

⇒ (a + b) = 99

Now adding (a + b) and (a - b), we get

⇒ 2a = 108

⇒ a = 54 and b = 45

Prime factorization of a and b;

⇒ a = 54 = 3³ × 2

⇒ b = 45 = 3² × 5

Hence, the HCF = 3² = 9