For what value of*, the number 588*01be perfectly divisible by 11?
Answers
A number is divisible by 11 if the difference of sums of the alternate digits in the numbers is also divisible by 11.
As an example, a six digit number 100000a + 10000b + 1000c + 100d + 10e + f is divisible by 11 if (a + c + e) - (b + d + f) is also divisible by 11.
Consider the given number 588x01. (Taking * as x)
Sum of alternate digits
⇒ 5 + 8 + 0 = 13
⇒ 8 + x + 1 = x + 9
Difference of the sums
⇒ 13 - (x + 9) = 13 - x - 9 = 4 - x.
4 - x thus obtained shall be a multiple of 4 if 588x01 is divisible by 11.
As x is a digit of the number 588x01, x can only be a one-digit whole number. Means x has only the values of natural numbers from 0 to 9.
The difference of the sums can be 0. If 4 - x is taken as 0, then the value of x will be 4.
If 4 - x is taken as 11, then x will be -7. But x can't be -7.
If 4 - x is taken as -11, then x will be 15. But x can't be 15 too.
Thus the one and only possible value for x is 4.