For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by:
- A7 and 11 only
- B11 and 13 only
- C7 and 13 only
- D7, 11 and 13Correct
Explanation
Any 6-digit number of the form XYZXYZ can be written as XYZ multiplied by 1001. For example, if the number is 123123, it is 123 multiplied by 1001.
The number 1001 is the product of three prime numbers: 7, 11, and 13. Specifically, 7 multiplied by 11 multiplied by 13 equals 1001.
Since 1001 is exactly divisible by 7, 11, and 13, any number in the form XYZXYZ must also be divisible by all three. Therefore, the correct option is D.
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