Question

the sum of the all number formed by the digits x, y and z of the following number xyz is divisible by
a. 11
b. 3
c.5
choose the correct answer...​

Answer 1

$All \: possible \: numbers \: formed \: by \: the \: digits x,y and z are : xyz,yxz and zxy.</p><p></p><p></p><p>∴xyz+yxz+zxy=(100x+10y+z)+(100y+10z+x)+(100z+10x+y)</p><p></p><p>=100x+10x+x+10y+100y+y+z+100z+10z</p><p></p><p>=111x+111y+111z</p><p></p><p>=111(x+y+z)</p><p></p><p>=3×37(x+y+z)</p><p></p><p></p><p>Therefore, xyz+yzx+zxy is \: divisible \: by \:  37.</p><p></p><p>Hence, \: option \: (C) \: is \: correct.</p><p></p><p>$