Official Guide Explanation:
Problem Solving #D03

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: D03
Page: 20
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: First, make sure that you understand how the sequence works. In more language, each term (a_n) is the average of the previous two terms (a_{n - 1} and a_{n - 2}). So, to determine the third term, we'd need to know the first and second terms, then find the average of those two terms.

To find the sixth term, we need to know the fifth term and the fourth term. The question gives us the fifth term, but not the fourth term. However, we're given the third term. Since the fifth term is the average of the third and fourth terms, we can use the two given terms to find the fourth term:

a₅ = ((a₄ + a₃)/2)

20 = ((a₄ + 4)/2)

40 = a₄ + 4

a₄ = 36

Now that we know the fourth term, we can calculate the sixth term:

a₆ = ((a₅ + a₄)/2) = ((20 + 36)/2) = (56/2) = 28

Choice (E) is correct.

Click here for the full list of GMAT OG12 explanations.

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.