Tom has two pens. One is red. The other is black.
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What about in sentences in exam questions (like math, logic, etc.) or in academic research papers?
Yes, you can. But these short choppy sentences sound like a 5-year old child wrote them.
How do you write when a group is divided into two, but the exact number of each subgroup is not known (i.e. indefinite)? Say, about 60-70
Not logical, because "the others" (or "the rest") means "the ones not yet mentioned." "Some" is indefinite, so you can't logically combine "some" with "the others". Tom has five pens; one is red and the others are blue or black.