Take a 2-digit number xy and reverse its digits. Add them so that their sum becomes a 3-digit number zxz.

  • Is zxz a multiple of 11?
  • Is zxz less than 198?  

Dear Student,

Please find below the solution to the asked query:

Given : Take a 2 - digit number xy and reverse its digits. Add them so that their sum becomes a 3 - digit number zxz.

So ,

1 ) xyyx  =  zxz

10 x  _  y +  10 y  +  x  =  zxz 

11 x  +  11 y  =  zxz 

11 ( x + y ) =  zxz

Yes zxz is multiple of 11 

2 ) We know greatest two digit number  =   99  and  99 + 99 =  198 

But , Here we get x  =  y =   9 

But We take x and y  as different digits , So

Yes zxz is less than 198 . 


Hope this information will clear your doubts about Playing with Numbers.

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