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## Official Guide Explanation:Problem Solving #93

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 93
Page: 73
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Decimals >
Category 2: Arithmetic > Fractions >

Explanation: This wouldn't be too arduous if you chose to multiply (-1.5)(1.2) and (4.5)(0.4), but it's good to get in other habits. 4.5 is three times 1.5, so the numerator can be factored as follows:

(-1.5)(1.2) - (4.5)(0.4) = (1.5)(-1.2 - (3)(0.4))

Similarly, 0.4 can be factored out as well:

(1.5)(-1.2 - (3)(0.4)) = (1.5)(0.4)(-3 - 3) = (1.5)(0.4)(-6)

Now, that makes the fraction easier to work with:

(((1.5)(0.4)(-6))/30) = ((-(1.5)(0.4))/5) = ((-0.6)/5) = ((-6)/50) = ((-12)/100)= - 0.12, choice (B).

This method may involve more steps, but each step is faster, and since it avoids decimal multiplication whenever possible, it avoids many chances for careless mistakes.

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