Official Guide Explanation:
Data Sufficiency #112




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Solution and Metadata

Question: 112
Page: 282
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Work Problems > 2 inputs

Explanation: While we're given two different times, we can't yet determine rates. The two machines each filled part of the lot, but we don't know how much of the lot each machine filled.

Statement (1) is insufficient. This doesn't help us find rates--we don't know how "30 bottles" relates to the size of the entire lot. X's total of 30 * 60 bottles per hour could represent 20% of the lot, 10% of the lot, or an infinite number of other possibilities.

Statement (2) is sufficient. This tells us how much each machine accomplished in the time they spent filling the lot. If X produced twice as many bottles as Y, that means X filled (2/3) of the order and Y filled the remaining (1/3). Thus, if X filled (2/3) of the order in 4 hours, it would've taken X 6 hours to fill the entire order. Choice (B) is correct.

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