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## Official Guide Explanation:Problem Solving #98

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: 98
Page: 166
Difficulty: 5 (Moderate)
Category 1: Word Problems > Rate Problems > other
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: When working with a sequence (a series of numbers that change in a given pattern), it's useful to assign a value or a variable to one term in the sequence and apply the pattern. The idea is this: say that the "intensity corresponding to a reading of 3" is x. If a reading of n + 1 has 10 times the intensity o fa reading of n, that means a reading of 4 (one greater than 3) has ten times the intensity of a reading of 3, or 10x . Similarly, a reading of 5 has an intensity of 10(10x). See a pattern emerging? Every time 1 is added to the reading, the intensity is multiplied by ten. So, the difference between readings of 8 and 3--1 is added five times--is 10(10)(10)(10)(10), or 105, choice (C).

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