We already know that John didn't take any vacation time last week, and that's the only span of time that we care about for this argument. John's vacation habits outside of this week aren't necessary either way.

This isn't necessary because the conclusion is simply that John worked in the insurance company on those days; it doesn’t matter how long the workday was.

Like (A), it's not necessary to assume anything about John's vacation habits, because the support establishes that he had neither holidays nor vacation days last week. And that's the only week we care about!

This is required for the conclusion to follow, which we can see by using negation. If (D) weren’t true, then John could have worked in the insurance company on the weekend instead of every day between Monday and Thursday. The only way the conclusion follows is if we assume (D) is true.

The conclusion is simply that John worked in the insurance company from Monday through Thursday. This could still be true if he also worked as a blacksmith on any of those days—nothing tells us John only worked in insurance those days.

If (E) were phrased differently, and specifically said that John didn't also work in the insurance company on Friday, then it might be necessary. After all, a Friday working in insurance would take away from one of the Monday through Thursday days. But as written, (E) is too broad, making it unnecessary—John could have pulled double duty on any non-Friday weekday without harming the argument.