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radhika1306
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DS
Source: Beat The GMAT — Data Sufficiency |
Imagine x=8/9=64/72 and y=1/8=9/72.
In this case, x+y=73/72.
However, we know that x is strictly less than 8/9 and y is strictly less than 1/8. That's fine. Set it so that x+y=72.5/72. Because in the case of equality, the sum equals 73/72, you know that there is a case which satisfies both "less than" criteria which sums to 72.5/72 (it's not worth it to solve out the fraction, you just need to realize that one exists... i.e., if x=7.999999/9 and y=.99999999/8 ). This sum is greater than one.
On the other hand, if x=y=0, the sum is definitely less than 1.
In this case, x+y=73/72.
However, we know that x is strictly less than 8/9 and y is strictly less than 1/8. That's fine. Set it so that x+y=72.5/72. Because in the case of equality, the sum equals 73/72, you know that there is a case which satisfies both "less than" criteria which sums to 72.5/72 (it's not worth it to solve out the fraction, you just need to realize that one exists... i.e., if x=7.999999/9 and y=.99999999/8 ). This sum is greater than one.
On the other hand, if x=y=0, the sum is definitely less than 1.
