If the nine-digit number 708x6y8z9 is divisible by 99, then what is the value of x+y+z?
(a) 9
(b) 16
(c) 5
(d) 27
Sol:
It is given that 708x6y8z9 is divisible by 99.
Thus, 708x6y8z9 is divisible by both 11 and 9
For divisibility by 9, sum of digits is divisible by 9 (7+0+8+x+6+y+8+z+9 = 38+x+y+z. We
get 2 as remainder when 389. Thus, 2+x+y+z must be divisible by 9)
Possible values of (z+y+x) = 7,16,25, etc.
For divisibility by 11, the difference of sum of digits at odd and even place is divisible by
11 (i.e. in 708x6y8z9 : (9 + 8 + 6 + 8 + 7 ) – (z + y + x + 0) = 38 – ( z + y + x) is divisible by
11 ) Possible values of (z+y+x) =38,5,16 etc.
