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Official Guide Explanation:Problem Solving #11

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: 11
Page: 153
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Powers and Roots of Numbers > Roots other than 2
Category 2: Arithmetic > Powers and Roots of Numbers > Roots

Explanation: When dealing with very small decimals, like 0.000064, it is often easier to rewrite them using scientific notation. 0.000064 = 64 * 10-6, so we can think of the question as rt[ 3rt[64 * 10-6]]. Start from the inside, and to make things simpler, think of 64 as 26. Thus, the first step is simplifying 3rt[26 * 10-6], which is equivalent to (26 * 10-6)1/3. Distributing the exponent, we get (26)1/3 * (10-6)1/3, or 22 * 10-2. The next step is keep working our way out of the radical signs: rt[22 * 10-2] = (22)1/2 * (10-2)1/2 = 2 * 10-1 = 0.2, which is choice (E).

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