Question

Both the ends of a 99 digit number n are 2. N is divisible by 11, then all the middle digits are

Answer 1

Answer:

FOUR (4)

Step-by-step explanation:

A number is divisible by 11

If the difference of the sum of digits at odd and even places be either zero or multiple of 11. If the middle digit be 4, then 244 ...442 are divisible by 11

Answer 2

All the middle elements of number are 4

1) Given the number is 99 digit.

2) Both the ends of number are 2 and number is divisible by 11.

3) A number N is divisible by 11 only when the difference of sum of numbers at even and odd places is either 0 or 11.

4) Let the number be 2a₁a₂a₃...........a₉₆a₉₇2

5)  Even placed numbers are : a₉₇,a₉₅,a₉₃,........a₃,a₁

Odd placed numbers are : 2, a₉₆,a₉₄,a₉₂,.........a₄,a₂,2

6) Since all the middle elements are same:

Sum of even placed numbers would be 49a₁

Sum of odd placed numbers would be 4 + 48a₂

7) To be divisible by 11, 49a₁ = 4+48a₂

And , a₁=a₂. So, a₁=4

8) Hence, all the middle elements are 4.