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## Official Guide Explanation:

Problem Solving #123

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 123**

Page: 77

Difficulty: **5** (Moderate)

Category 1: Geometry > Coordinate Geometry > Other

Category 2: Algebra > Inequalities > other

Category 3: Arithmetic > Real Numbers >

**Explanation:** Before trying sets of coordinates to see if they work in the equation 2x - 3y ≤ -6, think a bit about what values of x and y would result in a value less than -6. For two numbers to add up to a negative, one or both of them has to be negative, so either 2x, -3y, or both must be negative. Put another way, either x must be negative, y must be positive, or both. So, either of the quadrants in which x values are negative (II and III) are possible, as are the quadrants in which y must be positive (I and II). IV, then, is impossible: if x is positive and y is negative, 2x will be positive and -3y will be positive, which cannot sum to a number less than -6.

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