Minimum Channel Bandwidth for PCM
I don't think the exam question is stated properly, unless there is additional context that the student is supposed to know.

First, the bandwidth depends on the encoding. The question seems to assume binary encoding, but PCM does not specify this.

Second, the bandwidth depends on the pulse shape. Usually one assumes rectangular unless otherwise specified, but this information should bave been included in the question.

In general, the PCM signal can be written as a pulse train:

$$s_{\text{PCM}}(t) = \sum_{k=-\infty}^\infty a_k p(t-kT_p),$$

where $T_p$ is the pulse rate and $a_k$ is the encoded PCM data. In general, the bandwidth of $s_{\text{PCM}}(t)$ is equal to the bandwidth of $p(t)$.

As an example, let's say we want to transmit the bits $1010$ using a bipolar, non-return to zero binary encoding with $a_k \in \lbrace 1, -1 \rbrace$. The pulse shape is rectangular with duration $T_p = 1/(nf_s)$. Assuming $n$ starts at $n=1$, the PCM signal can be written as:

$$s_{\text{PCM}}(t) = p(t-T_p)-p(t-2T_p)+p(t-3T_p)-p(t-4T_p).$$

The problem is, what is the bandwidth of this signal? Theoretically, it's equal to the bandwidth of the rectangular pulse $p(t)$ with duration $T_p$. However, there are several ways to measure that bandwidth.

For instance, if you use the "absolute bandwidth" definition, then the bandwidth is infinite. There are ten or more engineering definitions of bandwidth, and each gives you a different number. Note, however, that transmitting $s_{\text{PCM}}(t)$ over any channel with less than infinite bandwidth will result in some amount of distortion.

Now let's say that $p(t)$ is a sinc pulse of appropriate width. The expression for the signal doesn't change. Theoretically, now the signal has infinite time duration, but its bandwidth is finite and equal to $1/(2T_p)=nf_s/2$.