Question

50 bells B1 , B2 , B3 ,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively. Bells $B_{11}$ , $B_{22}$, $B_{33}$ and $B_{44}$ ring together in $2^2.a^1.b^1$ sec sec.Which of the following is always true about a and b ?

• A. LCM of a and b is 22
• B. a = 11 and b = 5
• C. HCF of a and b = 1
• D. HCF of a and b = 2

Answer 1

The correct option is C

HCF of a and b = 1

Bells $B_{11}$ , $B_{22}$, $B_{33}$ and $B_{44}$ will ring together at the LCM of 11, 22, 33 and 44. All the four numbers have a common factor of 11. Now the LCM will be 11 x LCM of 1, 2, 3, 4, i.e. 11 x 12 = 132. 132 can be written as 2².3¹.11¹. So a = 3 and b = 11.