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## Official Guide Explanation:

Problem Solving #214

**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****: 214**

Page: 183

Difficulty: **7** (Very Difficult)

Category 1: Arithmetic > Discrete Probability >

Category 2: Word Problems > Sets >

Category 3: Arithmetic > Fractions >

**Explanation:** If Xavier and Yvonne, but not Zelda, solve the problem, there are three events that must occur, each of which have their own probability. The probability that Xavier sovles the problem is (1/4) , that Yvonne solves the problem, (1/2), and that Zelda doesn't solve the problem, 1 - (5/8) = (3/8). The probability of multiple independent events occuring is the product of the individual probabilities, so we're looking for ((1/4))((1/2))((3/8)) = ((1(1)(3))/((4)(2)(8))) = (3/64) , choice (E).

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