If 500 is the multiple of 100 that is closest to X and 400 is the multiple of 100 that is closest to Y, then which multiple of 100 is closest to X+Y

1) X'<'500
2) Y'<'400





"500 is the multiple of 100 that is closest to X"
means
"500 is closer to X than is any other multiple of 100"
which means
450 '<' X '< '550

"400 is the multiple of 100 that is closest to Y"
means
"400 is closer to Y than is any other multiple of 100"
which means
350 '< 'Y '<' 450

let's look at both statements together:
if both statements are true, then we have 450 '<' X '<' 500 and 350 '<' Y '<' 400.
in order to investigate the range of possibilities, look near the low end of the range and then look near the high end of the range.
low end:
if X = 451 and Y = 351, then X + Y = 802, which is closer to 800 than to other multiples of 100.
if X = 499 and Y = 399, then X + Y = 898, which is closer to 900 than to other multiples of 100.
(notice that if you're slow at arithmetic, you needn't calculate these exact values; 451 + 351 is approx 450 + 350, which is obviously closer to 800 than to other hundreds, and 499 + 399 ~ 500 + 400, which is obviously close to 900)

this gives two different answers to the problem, so both statements together are still insufficient.

answer = e