This is an expectation problem:

The problem does not specify how many choices there are for the answer
to the question. So I will suppose there are n choices for the answer.
Then the probability of guessing correctly is  and the 
probability of guessing incorrectly is 1 - .

Possibility              x (points)    P(x)     Expectation = x*P(x)
 
Answering correctly          3         1/n           3/n
Answering incorrectly       -1        1-1/n        -1(1-1/n)

So the total expectation on guessing is





Since 0 points are gotten if the problem is left blank, we
want to know how many choices n must be in order for the
expection to be greater than 0.  So we set that > 0



Multiply through by n





So if there are less than 4 choices for the answer to each question,
it is to the student's advantage to guess.  If there are exactly 4
choices per question, then the expectation will be 0 either way.
However if there are more than 4 choices for each question, it is
better to leave the question unanswered.

Edwin