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## Official Guide Explanation:Data Sufficiency #115

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: 115
Page: 283
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Symbolism >
Category 2: Algebra > Functions > other

Explanation: As usual, when the GMAT introduces a complicated - sounding rule or function, it represents something quite simple. The two functions result in either the larger of the two numbers in parentheses (max) or the smaller (min). We're looking for min(10,w). If w is greater than 10, the result is 10. If w is less than 10, the result is w, and we'll need to know the value of w to answer the question.

Statement (1) is sufficient. In plain English, w is equal to the greater of 20 and z. If z is less than 20, the greater of 20 and z is 20. If z is greater, z must be larger than 20. In other words, w is either 20 or something greater than 20. Thus, min(10,w) = 10, because w must be greater than 10.

Statement (2) is also sufficient. Following the same reasoning as in (1), if w= max(10,w), w must be greater than 10. If w is greater than 10, min(10,w) = 10. Choice (D) is correct.

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