Question

if x represents sum of all the positive 3 digit nos that can be constructed using each of the distinct non zero digits a b c exactly once what is the largest integer by which x must be divisible

Answer 1

There should be a total of 9x8x7 numbers to sum up. Do you agree?

Answer 2

In each of the 3 columns, the numbers 1-9 are equally represented.

Answer 3

see,,6 nos can be formed using a,b,c

now , out of these 6 ,
a comes 2 times in the first place , 2 times in the 2nd , 2 times in the 3rd
same with b and c

if we add em all ,,
100(a+b+c)*2 + 10(a+b+c)*2 + (a+b+c)*2
=222(a+b+c)

so is the ans 222 ?

Answer 4

So, taking the units column, you can sum 1 x (8x7) + 2 x (8x7) + 3 x (8x7) + ... to 9 x (8x7). Get that sum and add to that a similar treatment for the other 2 columns.

Answer 5

dats rite

Answer 6

@shubhamsrg can u explain y did u pic 100 10.. was lil confuse der

Answer 7

in base 10 notation,
suppose 123,
we write it as 100(1) + 10(2) + 3

same for abc
100a + 10b +c

Answer 8

k

Answer 9

in all those 6 nos.
100a will be there 2 times,,100 b 2 times and 100 c 2 times
adding em all,, you get what was written above..