There are 16 total questions and each wrong answer is worth -0.25 points, every correct answer is 1 point. An unanswered question is worth 0.
Is it better to guess 5 questions rather than 4 assuming that the other questions are left blank? Is it better to guess 6 questions rather than 7? What is the best number of questions to guess if there are 10 questions unanswered?
Our friends are having a debate.
If you pick the answer at complete random, you will (on average) gain $$ \frac14\cdot1+\frac34 \cdot\left(-\frac14\right)=\frac{1}{16}$$ points with each answer you guess ("gain" meaning compared to not answering the question at all).
Hence, the more answers you guess (instead of not answering at all), the better. Of course, this is only on average. If you are unlucky at least four times as often as you are lucky, you will obviously lose. Staying with 16 questions, this means the probability of losing points in total despite the good odds is
$$ \sum_{k=0}^3\begin{pmatrix} 16 \\ k \end{pmatrix} \left(\frac14\right)^k\left(\frac34\right)^{16-k}\approx0.4.$$