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## Official Guide Explanation:

Data Sufficiency #101

**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.

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**Solution and Metadata**

**Question****: 101**

Page: 281

Difficulty: **5** (Moderate)

Category 1: Word Problems > Mixture Problems >

**Explanation:** It takes a bit of analysis to recognize this, but it's essentially a weighted average question. The 10 kilograms of Material K consists of some A (x kg) and some B (y kg). If it were all A, the cost would be $30--10 kg at $3 each. It it were all B, the cost would be $50. If it were half and half, the cost would be $40, right in the middle.

Statement (1) is insufficient. If y > 4, then x < 6, since their sum must be 10. However, we don't know that the amounts are integer values. The mix could consist of 4.1 kg of B, in which case the answer is "yes." If the mix consisted of 6 kg of B, the answer is "no."

Statement (2) is sufficient. As described a moment ago, the price of a half - and - half mix of the two materials would be $40. If the price is less than $40, that means that more than half of the mix is of the cheaper variety--that is, Material A, which is $3 per kg. Since there is more A than B, x > y. Choice (B) is correct.

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