# Write a 4-digit number abcd as 1000a + 100b + 10c + d = (1001a + 99b + 11c) – (a – b + c – d) = 11(91a + 9b + c) + [(b + d) – (a + c)] If the number abcd is divisible by 11, then what can you say about [(b + d) – (a + c)]?

If the number abcd is divisible by 11 then [ (b + d) - (a + c) ] also must be divisible by 11.

let the number be 1089

here a = 1, b = 0, c = 8 and d = 9

1089 = 1000*1 + 100*0 + 10*8 + 9

= (1001*1 + 99*0 + 11*8) + [(0 + 9) - (1 + 8)]

= 11(91*1 + 9*0 + 8) + [ 9 - 9 ]

here  [ (b + d) - (a + c) ] = [9 - 9 ] = 0 which is divisible by 11.

hence If the number abcd is divisible by 11 then [ (b + d) - (a + c) ] also must be divisible by 11.

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