Official Guide Explanation:
Data Sufficiency #156

 

 

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.

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

 

Solution and Metadata

Question: 156
Page: 287
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Exponents >
Category 2: Arithmetic > Powers and Roots of Numbers > Powers
Category 3: Algebra > Inequalities > other

Explanation: Statement (1) is insufficient: 5k + 1 = 5k51, so we can simplify the inequality:

5k51 > 3,000

5k > ((3,000)/5)

5k > 600

If 5k is greater than 600, it is unknown whether it is less than 1,000.

Statement (2) is sufficient: even without manipulating the equation, you can recognize that it is an equation with one variable, so you can solve for that variable. Regardless of what that variable is, you can find the value of 5k and determine whether it is less than 1,000. Choice (B) is correct.

For those interested, here's how to solve the equation in (2) for 5k:

5k - 1 = 5k-500

500 = 5k-5k - 1

500 = 5k-5k5-1

500 = 5k(1 - 5-1)

500 = 5k(1 - (1/5))

500 = 5k((4/5))

5k = 500((5/4)) = (2500/4) = 625

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.