Correct option is (A) 114345
A number is divisible by 99 if it is divisible by both 11 & 9.
A number is divisible by 9 if sum of its all digits is divisible by 9 and a number is divisible by 11 if difference of the sum of odd digits and the sum of even digits is either 0 or multiple of 11.
(A) 114345
Sum of digits = 1+1+4+3+4+5 = 18 is divisible by 9.
\(\therefore\) 114345 is divisible by 9.
Sum of digits at odd places = 1+4+4 = 9.
Sum of digits at even places = 1+3+5 = 9.
Difference = 9 - 9 = 0
\(\therefore\) 114345 is divisible by 11.
\(\because\) 114345 is divisible by both 9 & 11.
\(\therefore\) 114345 is divisible by 99.
(B) 3572406
Sum of digits at odd places = 3+7+4+6 = 20.
Sum of digits at even places = 5+2+0 = 7.
Difference = 20 - 7 = 13 not divisible by 11.
\(\therefore\) 3572406 is not divisible by 11.
\(\therefore\) 3572406 is not divisible by 99.
(C) 913462
Sum of digits = 9+1+3+4+6+2 = 25 is not divisible by 9.
\(\therefore\) 913462 is not divisible by 9.
\(\therefore\) 913462 is not divisible by 99.
(D) 135792
Sum of digits at odd places = 1+5+9 = 15.
Sum of digits at even places = 3+7+2 = 12.
Difference = 15 - 12 = 3 is not divisible by 11.
\(\therefore\) 135792 is not divisible by 11.
\(\Rightarrow\) 135792 is not divisible by 99.
