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## Official Guide Explanation:Problem Solving #61

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: 61
Page: 160
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Ratio and Proportion >
Category 2: Word Problems > Mixture Problems >

Explanation: This question boils down to a simple ratio. If a glucose solution consists of 15 grams of glucose per 100, we can write that as a fraction: (15/100). However, we're interested in how much glucose is in 45 cubic centimeters of the solution: ((x)/45). Since the ratio of glucose to total solution will always be the same, we can set the fractions equal to each other: (15/100) = ((x)/45). Simplify by multiplying both sides by 45: ((15(45))/100) = x. Instead of multiplying 15 and 45, look for factors that can cancel: ((5(3)(5)(9))/(5(5)(4))) = (27/4) = 6(3/4) = 6.75, choice (E).

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