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## Official Guide Explanation:

Problem Solving #112

**Background**

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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****: 112**

Page: 76

Difficulty: **6** (Moderately Difficult)

Category 1: Word Problems > Other >

Category 2: Arithmetic > Properties of Integers > Factors and Multiples

**Explanation:** Whenever you see a phrase like "none left out," the question is probably about factors and multiples. The factors of 21 are 1, 3, 7, and 21, so if no white tulips are to be left out, there must be 1, 3, 7, or 21 bouquets. Similarly, since the factors of 91 are 1, 7, 13, and 91, there must be 1, 7, 13, or 91 bouquets if no red tulips are to be left out. Since both must be considered, the only possible numbers of bouquets are 1 or 7. We're looking for the greatest possible number, so 7 is the answer. Choice (E) is correct.

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