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## Official Guide Explanation:Problem Solving #144

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: 144
Page: 81
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Symbolism >
Category 2: Arithmetic > Properties of Integers > Primes

Explanation: The symbol is equivalent to factorial notation, so the question is interested in the range from (6! + 2) to (6! + 6). A prime number is an integer with no factors aside from 1 and itself, so if you can find another factor, you can show that a number is not prime. For instance:

(6! + 2) = 6(5)(4)(3)(2)(1) + 2 = 2((6)(5)(4)(3)(1) + 1) Since 2 is a factor of this number, it is not prime.

Note that the same manipulation can be done to any number between (6! + 2) to (6! + 6). As long as the constant is between 2 and 6, it can be factored out of both itself and the factorial. Therefore, there are no prime numbers in this range, choice (A).

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