A, B, C, and E are wrong.
Originally Posted by SeRCaN
I'd normally ask you to try to solve this sort of thing first; but in this case I don't want to encourage this use of 'such that'!
In maths/physics questions, it's common to use 'such that' to start a specification [with the meaning 'of such a kind that']: "ABCD is a square such that A and B form the base of an equilateral triangle ABE."
In your example, the same meaning could apply: 'Alaska is a ... state of such a kind that....' But as you've already said it's sparsely populated, your sentence needs some other expression or punctuation to announce that the rest of the sentence gives evidence of that sparseness. You're not giving the specifications of Alaska, you're giving figures to support the statement that it's a very large state with very few people. I'd use a simple colon:
Alaska is a very large state with very few people: on average, only 0.42 people live on every square kilometre.
But if you're looking for an answer to the multiple choice question, I'm afraid it has to be D.