Question

If 119xy is divisible by 99 than find the value of x+y

Answer 1

Answer:

x+y= 16

Step-by-step explanation:

for 119xy to be divisible by 99, the number 119xy must be divisible by both 9 and 11. (as 9 and 11 are multiples of 99)

for a number to be multiple of 9 , sum of its digits should either be 9 or a multiple of 9.

now, 1+1+9+x+y = 11+x+y

sum should be 18, 27, ....

therefore, x+y can be 7, 16, .....

now x+y=7 can take values of x and y as

0+7

1+6

2+5

3+4

and same digits in reverse order

again for a number to be multiple of 11, sum of digits at the even places-sum of digits at the odd places = either 0, 11 or multiple of 11.

now, using x+y = 7

we can not find the number which is multiple of 11

so we take x+y = 16

then x and y can have values as

7+9

8+8

9+7

now taking x as 7 and y as 9 we found the number to be 11979

which is divible by clearly divisible by 9

sum of digits at even place =1+9+9 =19

sum of digits at odd place = 1+7= 8

now, 19-8=11

hence the above number is also divisible by 11.

hence, x+y = 16

Answer 2

Answer:

Step-by-step explanation: