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## Official Guide Explanation:Data Sufficiency #164

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: 164
Page: 288
Difficulty: 7 (Very Difficult)
Category 1: Geometry > Coordinate Geometry > Distance
Category 2: Word Problems > Geometry Problems >
Category 3: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: Statement (1) is insufficient: it includes nothing about u or v. Statement (2) is also insufficient. It may be easier to work with these equations (at least for now) in the form u + r = 1 and v + s = 1. If u and s are 1 and r and v are 0, yes, the points are equidistant from the origin. There are plenty of counterexamples, though: for instance if u and v are 0 and r and s are 1.

Taken together, the statements are sufficient. Note that the equation in (1) can be rewritten in two ways:

r = 1 - s

s = 1 - r

The first indicates that, since v = 1 - s, r = v. The second indicates that, since u = 1 - r, s = u. Therefore, the two sets of coordinates are equal, though the x and y coordinates are reversed. If the distance of each individual coordinate is equal to a coordinate in the other point, the distance of the points from the origin is the same. Choice (C) is correct.

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