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## Official Guide Explanation:Data Sufficiency #57

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: 57
Page: 277
Difficulty: 4 (Moderately Easy)
Category 1: Word Problems > Other >
Category 2: Arithmetic > Properties of Integers > Other

Explanation: If Max has a total of \$125 in 20's and 5's, he could have anywhere from 0 to 6 20's. He must have at least one 5, and could have as many as 25 5's.

Statement (1) is sufficient. He could have one 5, in which case the \$125 consists of \$5 in 5's and \$120 in 20's. If he has only \$100 in 20's, he must have \$25 in 5's -- that's five 5 - dollar bills. Since the statement tells us he has fewer than five 5's, he must have exactly 1.

Statement (2) is also sufficient. If he has more than 5 20's, he must have 6, for a total of \$120. That leaves \$5 in 5's. Choice (D) is correct.

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