It's hard to say if the signal will be received at purple due to diffraction or not.
This is a very qualitative analysis and that is usually not good.
It depends a lot on the actual distances involved and the wavelength of the wave. More importantly, Cell Phone towers do not emmit 1 wavelength, they do so in a band.
You might want to look into something called fading in wireless communication, more specifically large scale fading. But only if you are in the later stages of your undergraduate degree or postgrad.
If you are in school, you just want to look at the formulas for the diffraction pattern. If you are given the actual lengths and properties of the wave, you should be able to figure out why purple receives a signal.
Edit - It would be more helpful if you could show the actual question itself instead of your interpretation and where it was asked as it usually helps with people helping you out.