It's hard to rephrase this one, so I wouldn't bother.
Clearly, neither statement alone is sufficient. You at least need to know something about each variable. We go straight to combination. (Don't take that step lightly -- but if you're sure that neither statement can be sufficient on its own, then go ahead and move on.)
It's helpful to know your decimal equivalents. 8/9 is .888888888888 repeating. 1/8 is .125. If X is less than 8/9, then x could be .8880 (that's less than .8888888 repeating). Y could be .124. Add those up and you get 1.012, which is greater than 1.
However, since both X and Y just have to be LESS than those benchmarks, either could be as small as 0, in which case their sum would be less than 1.
So it's possible for it to be greater than 1 and possible for it to be less than 1. Insufficient.
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Source: Beat The GMAT — Data Sufficiency |
Together you have that:
x < 64/72 (multiply by 8/8 to get a common denominator)
y < 9/72 (multiply by 9/9 to get a common denominator)
x + y < 73/72
Could be either 72/72 (equal to 1, so NO, and you could still be smaller than 73/72 and be greater than 1 too like Laura says) or 71/72 (less than 1, so YES) --> answer has to be E.
x < 64/72 (multiply by 8/8 to get a common denominator)
y < 9/72 (multiply by 9/9 to get a common denominator)
x + y < 73/72
Could be either 72/72 (equal to 1, so NO, and you could still be smaller than 73/72 and be greater than 1 too like Laura says) or 71/72 (less than 1, so YES) --> answer has to be E.
