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. 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 (a, b) = 1
• D. HCF (a, b) = 2

Answer 1

The correct option is C

HCF (a, 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. 11x 12. Therefore the LCM of 11, 22, 33, 44 = 11 x 12 = 132.

132 can be prime factorised as $132=2\times 2\times 3\times 11$ i.e $2^2{.3}^1.{11}^1$

So a = 3 and b = 11.

HCF of 3 and 11 is 1.