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## Official Guide Explanation:Problem Solving #28

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: 28
Page: 156
Difficulty: 6 (Moderately Difficult)
Category 1: Word Problems > Measurement Problems >

Explanation: This is a tricky measurement question, but you can solve it with the same techniques you'd use on any question involve unit conversion. We're told that 1 kilometer is the same as 3.9 * 104 inches. All we need to do is use that conversion to turn 2.3 * 1014 inches into kilometers.

To do so, we'll multiply that distance by 1. Since 1 km is the same as 3.9 * 104 inches, a fraction with one of those in the numerator and the other in the denominator equals 1. Our math should look like this:

2.3 * 1014 inches * ((1\text{ km})/(3.9 * 104\text{ inches}))

The "inches" cancel out, so we're left with:

((2.3 * 1014)/(3.9 * 104))km

To simplify, first deal with the exponents:

((2.3)/(3.9)) * ((1014)/(104)) = ((2.3)/(3.9)) * 1010

((2.3)/(3.9)) is about the same as (24/40), or 0.6, so we can approximate as:

0.6 * 1010

= 6 * 109, which is very close to choice (B).

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