Let x be the total number of problems in the test.


Alice solved more than 0.6x problems, but less than 0.65x problems.


From the condition, you have this compound inequality


    0.6x < 35 < 0.65x


It implies   


    x <  = 58.3 (rounded)   and   x >  = 53.8 (rounded).


So, the integer values of x are among the values  54, 55, 56, 57 and 58.


Of them, only the value of 56 is a multiple of 4.


ANSWER.  The number of questions in the test was 56.