Study the following information carefully and answer the questions given below:
An uncertain number of persons sit in a linear row and face north.
Five persons sit between F and M. D sits third to the right of M. A sits four places away from D. More than four persons sit between A and F. K sits second to the right of A and third from one of the extreme ends of the row. Six persons sit between K and G. E sits fifth to the left of G. E sits fourth from one of the extreme ends of the row. As many persons sits to the left of E as to the right of H.

How many persons sit between E and K?

The correct answer is Eleven.

Let us determine the relative positions of E, G, and K step-by-step from the given conditions:
1. Six persons sit between K and G: This means the distance between K and G is 7 positions (either G is 7 positions to the right of K, or 7 positions to the left of K).
2. E sits fifth to the left of G: This means E is located exactly 5 positions to the left of G.

Now, let us analyze the two possible cases for the relative positions of K, G, and E:

Case 1: G sits to the right of K
If we assign position 0 to K:
- G is 7 positions to the right of K, so G is at position 7.
- E sits 5 positions to the left of G, so E is at position: 7 - 5 = 2.
In this arrangement (K _ E _ _ _ _ G), only 1 person sits between E and K, which does not match the given options.

Case 2: G sits to the left of K
If we assign position 0 to E:
- Since E sits fifth to the left of G, G must be 5 positions to the right of E, placing G at position 5.
- Since six persons sit between K and G, and G is to the left of K, K must be 7 positions to the right of G, placing K at position: 5 + 7 = 12.
Thus, the seating order from left to right is:
E (at index 0) _ _ _ _ G (at index 5) _ _ _ _ _ _ K (at index 12).

The number of persons sitting between E and K is:
12 - 0 - 1 = 11 persons.