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## Official Guide Explanation:Problem Solving #85

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: 85
Page: 72
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Geometry > Triangles > other

Explanation: The area of a triangle is (1/2)bh, and the base and height must be perpendicular. The base of this triangle is RT, so b is the distance between R and T, (1,0) and (c,0), respectively. Since c is the larger number (further to the right on the x - axis), the distance is c - 1, so b = c - 1. The height is a line parallel to the y - axis that you can draw between the x - axis and point S. That point on the x - axis has the coordinates (a,0). The distance between S and that point is b - 0, so h = b. (Note that we've used b in its conventional sense to stand for base, and also for the variable called b in this problem. Be careful, and realize that the GMAT does this on purpose!)

So, we can plug these values into the equation for area of a triangle: (1/2)(c - 1)(b) = ((b(c - 1))/2), choice (B).

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