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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.
Solved.