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## Official Guide Explanation:Problem Solving #106

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.

Solution and Metadata

Question: 106
Page: 167
Difficulty: 7 (Very Difficult)
Category 1: Arithmetic > Properties of Integers > Remainder
Category 2: Arithmetic > Decimals >

Explanation: When x is divided by y, the result will contain an integer quotient (call it q) and a remainder (call it r). These will always relate in the following way:

((x)/(y)) = q + ((r)/(y))

Since ((x)/(y)) = 96.12, we know that q = 96, and that ((r)/(y)) = 0.12. We know the remainder is 9, so we can solve for y:

(9/(y)) = 0.12

9 = 0.12y

y = (9/(0.12)) = (900/12) = (300/4) = 75, choice (B).

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