decoding the question stem:

"500 is the multiple of 100 that's closest to x": this means that, of all multiples of 100, 500 is closest to x.
in other words, x is closer to 500 than to 400 or 600 (or to any other multiple of 100, for that matter). what does this mean?
it means that 450 < x < 550. (note that this is almost the same thing as "x rounded to the nearest hundred produces 500", except for the piddling exception of 450.)

the second half of the problem statement, similarly interpreted, gives the following: 350 < y < 450.

(1)
in combination with the question stem, this means that 450 < x < 500 (and we still know that 350 < y < 450).
therefore, 800 < x + y < 950.
this isn't good enough to answer the question; the numbers between 800 and 850 are closer to 800, the numbers between 850 and 950 are closer to 900, and 850 is equidistant from 800 and 900.
insufficient.

(2)
in combination with the question stem, this means that 350 < y < 400 (and we still know that 450 < x < 550).
therefore, 800 < x + y < 950, exactly the same inequality that holds for statement (1).
insufficient.

(together)
now we know that 450 < x < 500 and 350 < y < 400.
this means that 800 < x + y < 900.
still not good enough to answer the question; the numbers between 800 and 850 are closer to 800, the numbers between 850 and 900 are closer to 900, and 850 is equidistant from 800 and 900.
insufficient.

ans = e