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## Official Guide Explanation:

Data Sufficiency #68

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 68**

Page: 278

Difficulty: **6** (Moderately Difficult)

Category 1: Word Problems > Work Problems > 3+ inputs

Category 2: Word Problems > Work Problems > 2 inputs

**Explanation:** This question looks fairly complicated, discussing simultaneous and combined rate for three machines. Most GMAT questions only ask you to consider two machines in scenarios like these.

Statement (1) is sufficient. As it turns out, the question is simpler than it looked. Instead of finding the individual rates of all three machines, we can treat M and P as one machine. If we know M and P's combined rate, and we know the combined rate of all three machines, we can find K's individual rate. We don't need to consider M and P as separate, because nowhere up to this point in the question are they treated as such.

Statement (2) is insufficient. As in (1), this gives us the combined rate of two of the three machines. However, it doesn't give us the information we're looking for. Knowing the combined rate of K and P, we can find the rate of M. But since K and P are treated as one unit, we can't separate their individual rates. Choice (A) is correct.

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