So we know that 2/3 full equals to a kg, so when the bucket is completely full it will weigh (in terms of a) = 3a/2 kg
Similarly, since we know that 1/2 full equals to b kg, when the bucket is completely full it will weigh (in terms of b now) = 2b kg
So 3a/2 = 2b <=> 3a = 4b
By substituting in E, we see that it is indeed 3a-2b since 3a-2b=4b-2b=2b, which is the total weight in terms of b.
P.S. Since we have calculated that the TOTAL weight in terms of a is "3a/2", all answer choices that have this term plus or minus something, will be incorrect. This leaves us only A and E. E is the correct.
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- GMAT Prep #1 CAT (Apr 2019) : 640 (Q48, V31)
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