i think of it in a different way.
if ab=1 there can be two cases a=b=1 or a=1/b.
S1) aba=a -------> with a=b=1 ------> 1x1x1=1 true. -------> with a=1/b---------> (1/b)b(1/b)=1/b -------> (1/b)=(1/b) true. sufficient
S2) bab=b -------> with a=b=1 ------> 1x1x1=1 true. -------> with a=1/b---------> b(1/b)b=b --------------> b=b true sufficient
Ans should be D
What you've done above is assumed that the answer to the question is 'yes', and you have then tried to prove that the statements are true. That is backwards
. The statements are facts
; they cannot be wrong, so you should never be trying to prove that they're true. They are. The question, on the other hand, is a question
; you don't know what the answer to the question is without more information, and that's the whole point of Data Sufficiency. You can't just assume the answer to the question is 'yes', because then you're assuming what you should be trying to prove. That's the logical fallacy known as 'begging the question'. It's crucially important to be clear about the approach to DS questions, because if you approach them backwards, you'll answer many DS questions incorrectly, including this one.
Here the answer is E, since even knowing both statements, we might have a=b=1 or a=b=0.
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