I had the exact same exact instincts as you and I've been trying to think through the logic of what makes something more or less effective.
From the instructions we know that our responses to the SJT should be "based only on the information provided" and that we "should not assume any prior knowledge of the scenarios described." Finally, it is mentioned that "scenarios are unrelated to each other," and therefore we "should not use the information in one scenario to respond to another."
What my takeaway is from the instructions is that I should think about the effect each answer has and not make assumptions about what you would do beyond what is written. For example, as a trainee my first course of action would be to ask my colleagues to see if they have helped the associate because with that information I would THEN proceed to help out (if I'm still needed) or offer to help later (if the work has been completed). In the STJ, I don't think you are able to make such assumptions.
I recommend analysing the effects of each answer and thinking of what makes them different:
(1) "Speak to the Associate and explain that you are very busy this week. However, offer to help them next week when you have more availability."
This response shows that you are proactive at communicating with the associate, that you are mindful and realistic about your workflow and can independently judge how much availability you have, and most importantly, offer to help the associate (even though this is at a later time).
(2) "Speak to the Associate to get a better understanding of how long the task would take, then consult with your supervisor."
In comparison to the first response, although you communicate with the Associate, you do not make an offer to help them out. You also show that you need to consult with your supervisor to figure out your workload, whereas in the first response you made a judgement of your availability. So between these first two responses, the first one is stronger.
(3) "Ask some of your colleagues who were on the original request and see whether they have already helped the Associate."
In this response, you do not communicate with the Associate. This by itself is not disqualifying (I think), because you do talk to others and as HSF's quiz shows "colleagues are [often] pressed for time" so it might be better not to bother the Associate in the event you can't help immediately or promise to help later. However, notice how you do not offer to help the Associate. From a "doing things" perspective, you are not contributing or promising anything here because we are not allowed to assume what you do after getting an answer from colleagues. Looking at responses 1-3, this is the weakest one.
(4) "It is likely another colleague has replied, so make a note to check in with the Associate later in the week after you have finished a few more of your tasks."
In this response, you don't immediately speak to the Associate just like in the third response, however, unlike in that one, you do make a note to check in with the Associate and do, similarly to the first response, show awareness of having "a number of important tasks to complete by the end of the week."
What confused me about this response is the "it is likely another colleague has replied" part. While taking the practice test, I made my own assumptions, thinking, what if colleagues didn't reply?! This train of thinking was influenced by seeing response 3. However, I think you are meant to evaluate statements independently of each other and consider them as true.
Ultimately, I think it is the act of checking in later after finishing your important tasks is what makes this a stronger response over the third. Therefore, the third is the "least effective" response. And since we didn't identify anything stronger than the first response, that remains our "most effective."