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## Official Guide Explanation:Data Sufficiency #104

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: 104
Page: 160
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Powers and Roots of Numbers > Powers
Category 2: Arithmetic > Properties of Integers > Other

Explanation: Statement (1) is insufficient. Consider the range of 3 - digit integers: 100 to 999. To make things simpler, think of the endpoints as 102 and 103, just remember that 103 is a bit greater than 999. If that's the range for m, the endpoints for m3 are:

(102)3 = 106 = 1,000,000

(103)3 = 109 = 1,000,000,000

Really, the upper limit it a bit less--say 900,000,000. Regardless, we don't know the number of digits of m3.

Statement (2) is also insufficient. Five digits puts m2 between 10,000 and 99,999, or 104 and (approximately) 105. Use the same approach:

If m2 = 104, then m = 102 and m3 = 106.

If m2 = 105, then m = 105/2 and m3 = 1015/2

Again, m3 can be as little as 1,000,000. It can be greater than 107 = 10,000,000, though, so it can have either seven or eight digits.

Taken together, the statements are still insufficient. In either statement, both seven or eight digits is possible. Choice (E) is correct.

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