.Let XYZ be a three-digit number, where (x + y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by

XYZ is a 3-digit number not divisible by 3.

We know that expanded form of XYZ will be 100 X + 10Y + Z. (basic decimal number system)

So, XYZ + YZX + ZXY = (100 X + 10Y + Z) + (100 Y + 10Z + X) + (100 Z + 10X + Y)

= 111X + 111Y + 111Z = 111 (X + Y + Z)

(note 3 and 37 are prime numbers and X + Y + Z is not a multiple of 3 (given), so it will not be multiple of 9 too)

So, the correct option is (b).