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## Official Guide Explanation:Data Sufficiency #112

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

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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