Eight people Ax, Bx, Cx, Dx, Ex, Fx, Gx and Hx are

Solution

 Since four persons sit between Hx and Dx, Hx could be at the 2nd place from extreme left and Dx at the 2nd place from extreme right.  Since two people sit between Hx and Bx, Bx must be three places away from Hx.  Bx sits to the immediate left of Ax, means Ax is sitting between Bx and Dx.  Gx sits third to the left of Ax.  Ex is the neighbor of Dx, means Ex is sitting at the extreme right end.  Fx sits third to the right of Cx. Final arrangement is shown as below: From the above, it is clear that, Cx and Ex sit at the extreme ends. So, statement I is true. However, statement II is false because there are 3 persons sitting between Bx and Cx. Hence, the correct answer is (A).