M3 - When are two Tensions the same??

I am on Edexcel.

As the title says, I am wondering in what situations tensions would be the same? For example, in the question below the tensions are the same (I only know this from the Mark Scheme), but I'm unsure why and in what situations this occurs.

Thanks in advance for any responses.

When the particle is threaded, so one string. then tensions are the same
When the particle is is attached to 2 different strings, then tensions are not the same

So if it were firmly attached, as mentioned in part c), you now assume it is two separate strings, thus the answer being "could not assume tensions same"?

correct if I understand your question well

Okay, thanks so much for the help!