For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by:
For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by:
7 and 11 only
11 and 13 only
7 and 13 only
7, 11 and 13
Solution
A number of the form XYZXYZ equals $\overline{XYZ} \times 1001$. Since $1001 = 7 \times 11 \times 13$, the number XYZXYZ is always divisible by 7, 11 and 13.