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## Official Guide Explanation:Problem Solving #131

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: 131
Page: 78
Difficulty: 6 (Moderately Difficult)
Category 1: Algebra > Functions > Sequences

Explanation: The sequence notation gets complicated, but in short, it tells us that for the first k terms, each term in the set is 3 greater than the previous one. After that, each term is 3 less than the previous one. Clearly, the numbers increase for a while, then decrease at the same rate.

We know that x0 = xn = 0, so the sequence starts and ends at zero. xk = 15, so since the numbers increase by 3 up to xk, the sequence starts:

(0, 3, 6, 9, 12, 15)

0 is the 0th number in the set (x0) so 3 is the 1st and 15 is the 5th. It will take 5 more numbers to decrease back to zero:

(0, 3, 6, 9,12, 15, 12, 9, 6, 3, 0)

There are 11 numbers in the set, but since the index numbers start counting at zero, the final number is the 10th. Thus, xn is the same as x10 , so n = 10, choice (D).

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