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

1. **Identify the Pattern**: The number is given as **XYZXYZ**. This immediately reminds us of the **ABCABC** pattern from the 2015 CSAT paper [1].\n\n2. **Decompose the Number**: Just like in the previous year's analysis, we can break this number down:\n $XYZXYZ = (XYZ \\times 1000) + (XYZ \\times 1)$\n $XYZXYZ = XYZ \\times (1000 + 1)$\n $XYZXYZ = XYZ \\times 1001$ [37].\n\n3. **Analyze the Constant**: The number is essentially some variable ($XYZ$) multiplied by the fixed number **1001**. This means the number will always be divisible by the factors of 1001.\n\n4. **Factorize 1001**: We need to find what divides 1001. As highlighted in standard divisibility rules for CSAT:\n - $1001 \\div 7 = 143$\n - $143 \\div 11 = 13$\n - So, $1001 = 7 \\times 11 \\times 13$ [42].\n\n5. **Conclusion**: Since the number is a multiple of 1001, it is automatically divisible by all its factors: **7, 11, and 13**. \n\n6. **Final Verification**: Option (D) lists all three primes, which matches our finding perfectly.