The solution is unique, and can be found by progressive elimination of impossible answer choices (or by trial and error). Post the solution in the combox.
1) The number of questions whose answer is a vowel is:
a) 4
b) 1
c) 3
d) 5
e) 2
2) The answer to question 5 is:
a) B
b) C
c) D
d) E
e) A
3) The most number of times the same answer occurs on this test is:
a) 2
b) 1
c) 4
d) 3
e) None of the above
4) The first question whose answer is B is:
a) 3
b) 4
c) 5
d) 1
e) 2
5) The only adjacent pairs of questions whose answers are also adjacent in the alphabet are:
a) 1 & 2
b) 1 & 2 and 3 & 4
c) 4 & 5
d) 2 & 3 and 3 & 4
e) 3 & 4