question_answer

If 756 x is divisible by 11, where x is a digit find the value of x.

Answer:

Sum of digits of odd place = 7 + 6 = 13

Sum of digit of even place = 5 + x

Difference   \[\left( x+5 \right)-13=\text{ }x-8~\]    (i)

Now \[\left( x-8 \right)\]should be equal 0 or a multiple of 11 (i.e., 11, 22, 33,... etc)

\[x-8=0\]

\[\Rightarrow \]   \[x=8\text{ }or\text{ }x-8=11\]

x = 11 + 8 = 19

Since, x is a digit, so it can take value from 0-9

Hence,    x = 8

Required number is 7568.