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

Asked in: CSAT 2023

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