For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by

(UPSC CSAT – 2023)

1. 7 and 11 only
2. 11 and 13 only
3. 7 and 13 only
4. 7,11 and 13

Solution: Ans.(4)

XYZXYZ = XYZ×1000 + XYZ

                  = XYZ × (1000 + 1)

                  = XYZ × 1001

                  = XYZ × 7×11×13

Hence XYZXYZ is divisible by 7, 11 and 13 all.