Question

The sum of two 2 - digit numbers is 132. If their HCF is 11, the numbers are <br />a) 55, 77<br />b) 44, 88<br />c) 33, 99<br />d) 22, 110​

Answer 1

Answer:

$\huge\underline\bold {Answer:}$

Since the HCF is 11, the numbers must be of the form 11a and 11b, where a and b are prime to each other.

11a + 11b = 132

=> a + b = 12

The possible pairs of numbers whose sum is 12 are 1, 11; 2, 10; 3, 9; 4,8; 5, 7; 6,6.

Out of these pairs, the pairs of numbers that are prime to each other are 1, 11 and 5, 7. The pairs which satisfies the given condition is 5, 7. The pairs which satisfies the given condition is 5, 7.

Hence the numbers are 11 × 5 and 11 × 7, i.e., 55 and 77.