Let the Set P be (10, 4, 7, 18) and Set Q be (x, 10, 4, 7, 18, 25).

To calculate the median, the values in the set have to be arranged in ascending order.

Elements of set P can be arranged as 4,7,10,18. The median is the average of 7 and 10. Median of set P = 8.5

Elements of set Q can be arranged as 4,7,10,18, 25. Note that we need to decide the location of x depending on the median.
We know that the median of set Q is 4 more than the median of set P. Therefore, median of set Q = 12.5.

Set Q has 6 elements, hence the median will be the average of the 3rd and 4th value in the set.
If x<4 OR x>25, 3rd value = 10 and 4th value = 18. Median ≠ 12.5. Therefore, x is neither less than 4 nor greater than 25.
If 4<x<10 OR 18<x<25, a similar conclusion may be drawn.

Therefore, x has to be between 10 and 18 and hence Median = \(\frac{10 + x }{ 2}\) = 12.5.

Simplifying, we get x = 15. The correct answer option is D.

Hope that helps!

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