Official Guide Explanation:
Problem Solving #D18




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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.


Solution and Metadata

Question: D18
Page: 22
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: n is equal to (1)(2)(3)(4)(5)(6)(7)(8). Don't multiply all those numbers! The largest possible prime factor of the product must be no larger than 8. There's no way for, say, 11 to be a prime factor unless 11 (or a multiple of 11) is one of the numbers multiplied to get the product.

Thus, the only possible prime factors are 2, 3, 5, and 7, the primes less than 8. Since all four of those numbers are present in the list of numbers to be multiplied, all are factors of the product. Thus, there are 4 different prime factors of n, choice (A).

Click here for the full list of GMAT OG12 explanations.


You should follow me on Twitter. While you're at it, take a moment to subscribe to GMAT Hacks via RSS or Email.

Total GMAT Math

The comprehensive guide to the GMAT Quant section. It's "far and away the best study material available," including over 300 realistic practice questions and more than 500 exercises!
Click to read more.