Question

The HCF of two numbers is 11 and their sum is 132. If poth the numbers are greater than 42, then the difference between the two numbers is :

• A. 18
• B. 22
• C. 26
• D. 11

Answer 1

Answer:

B. 22

Let the two numbers be 11x and 11y (since HCF = 11).

$Sum = 132$

$11x + 11y = 132 \Rightarrow x + y = 12$
Both numbers are greater than 42

11x > 42 \Rightarrow x \ge 4,\quad 11y > 42 \Rightarrow y \ge 4

(x) and (y) must be coprime (because HCF is exactly 11)

Possible coprime pairs with sum 12:

• (1, 11) (too small)

• (5, 7) ✅

• (7, 5)

$11 \times 5 = 55,\quad 11 \times 7 = 77$
Difference:

$77 - 55 = \boxed{22}$