Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3

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

Answer: B

XYZ is a three-digit number.

So, you can write this as: 100X + 10Y + Z (as X is at hundreds place and Y is at tens place)

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

= 111(X + Y + Z)

Hence, it is divisible by (X + Y + Z).

Also, 111 is divisible by 3, as well as 37.

So, the expression XYZ + YZX + ZXY is not divisible by 9.