Length of DFT and Number of Filters
One first suggestion for you is to implement DFT filter banks in some language (Octave, Python, Matlab) and play with them to get some insight. Then, 
let me provide a information source, and a few hints.  In  The DFT Filter Bank, you can find:


  In this section, we will show how the DFT can be computed exactly from
  a bank of $ N$ FIR bandpass filters, where each bandpass filter is
  implemented as a demodulator followed by a lowpass filter


The above website is really worth reading. You can see for the plot that you have two responses, one being obtained via a shift in frequency for the other. Hence you know that, from one of the Fourier modulation properties, that a shift in frequency corresponds to a modulation in the time domain. Let us now look at the low-pass filter only (in blue). A running low-pass filter has a frequency response related to the sinc function. More precisely, it is called a periodic or an aliased sinc, with frequency response:

\begin{eqnarray*}
H(e^{j\omega}) &amp;=&amp; \frac{1-e^{-j\omega N}}{1-e^{-j\omega }}
= \frac{e^{-j\omega N/2}}{e^{-j\omega /2}}
\frac{\sin(\omega N/2)}{\sin(\omega /2)}\\ 
&amp;= &amp;
Ne^{-j\omega(N-1)/2} \hbox{asinc}_N(\omega ).
\end{eqnarray*}
where $N$ is the length of the running sum. It can be inferred  from the number of ripples, corresponding to a number of zeroes of the aliased sinc.
The number of filters is potentially trickier, because of oversampled filter banks, but this may be outside the scope of your lecture. Look at how many shifted (modulated) versions of the low-pass can cover evenly the spectrum.

Then again, do not hesitate to verify via simulations.