Easy question but missed out on something

Is x+y<1 ?

(1)x<8/9

(2)y<1/8

Ans E

I chose C

My approach : Each statement cannot be sufficient with differing values for x and y . (1) says x<8/9 or x< 0.88 and (2) says y<1/8 or y<0.12 so lets say x is 0.87 and y is 0.11 then for all values x+y will be less than 1.

Where did I go wrong ?