Person 2 always consumers along the 45 degree crossed line. (Since he has min preferences)
Now, given endowment e and a price vector >1, person 1 would prefer to consume at point A while 2 likes to consume at point B. Hence we have an excess demand of good 'x'. And by the definition of a competitive equilibrium, there should be no excess demand of any good and each person should be maximising utility given the price vector.
Similarly for a price vector<1, person 1 chooses point C while 2 chooses point D.
In fact this will arise for any positive price vector.
So answer is "d"