This looks like an overlapping set problem, and ETS does love to use tables for overlapping sets, but we really don't need to worry about making an overlapping sets table here. Just count up all the males, count up all the juniors, and be careful not to double count the male juniors, because that is of course one of the trap answer choices (D).

Conveniently, all the males have already been added up for us and they total 860. So we just need to add the juniors who aren't males, otherwise known as females, and add them. They represent another 88 students. Since 860 + 88 = 948, C is the answer.
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I am not following either solution, as I am a visual person, I think I would benefit if someone would post a picture with a venn diagram that leads to the solution. Thank you!

Or someone can tell me what is wrong in my solution.

The way I learned to solve overlapping set problems is to use

total = set A + set B - both + neither

But when I use it, I don't get the right answer.
total = 860 + 270 - 182 + 452 = 1430

You lost me at the bolded portion, my mind's reasoning is telling me that the number of juniors is the 182+88, which is in contrast to the "182 or 88" you mentioned. Can you please explain this portion? Thanks.

I don't understand what you mean. Are you talking about the grammar? The way I read the question is like this:

"How many students are either juniors, or males, or both?"

Edit: I added the commas, it won't show the underline for some reason.

I had no idea what you were saying lol, I just tried guessing what you were trying to convey. I think the grammar structure of your sentence was off which made it hard to interpret. You mentioned 'stem', 'either', 'or', perhaps that made me infer you were trying to talk about the grammar of the question.

I understand the answer now by rereading kruttikaaggarwal's answer and drawing the Venn diagram myself, and it clicked.