• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## In any sequence of n nonzero numbers, a pair of consecutive tagged by: AbeNeedsAnswers ##### This topic has 1 expert reply and 0 member replies ### Top Member ## In any sequence of n nonzero numbers, a pair of consecutive ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In any sequence of n nonzero numbers, a pair of consecutive terms with opposite signs represents a sign change. For example, the sequence -2, 3, -4, 5 has three sign changes. Does the sequence of nonzero numbers s1, s2, s3, . . . , sn have an even number of sign changes? (1) sk = (-1)^k for all positive integers k from 1 to n. (2) n is odd. C Source: Official Guide 2020 ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10184 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that in any sequence of N NON-ZERO numbers, a pair of consecutive terms with opposite signs represents a sign change (for example, the sequence -2, 3, -4, 5 has three sign changes). We're asked if the sequence of nonzero numbers s1, s2, s3, . . . , sn has an EVEN number of sign changes. This is a YES/NO question. This question can be solved with a bit of Arithmetic and TESTing VALUES. (1) sk = (-1)^k for all positive integers k from 1 to N. While the information in Fact 1 might look complex, it actually defines how the sequence 'works.' The initial terms - and the pattern behind the sequence - are... 1st term = (-1)^1 = -1 2nd term = (-1)^2 = +1 3rd term = (-1)^3 = -1 4th term = (-1)^4 = +1 Etc. We know how the sequence repeats, but we DON'T know how many terms are in it, so we don't know exactly how many sign changes there are (and thus, we don't know if the total number of changes is even OR odd). IF.... There are 3 terms, then we have -1, +1, -1 and two sign changes - so the answer to the question is YES. There are 4 terms, then we have -1, +1, -1, +1 and three sign changes - so the answer to the question is NO. Fact 1 is INSUFFICIENT (2) N is ODD. Fact 2 tells us the number of terms in the sequence, but we know nothing about any of their values, so we don't know how many sign changes occur. Fact 2 is INSUFFICIENT Combined, we know... sk = (-1)^k for all positive integers k from 1 to N. N is ODD. We know exactly how the sequence 'works' and that there are an ODD number of terms. IF There are 3 terms, then we have -1, +1, -1 and two sign changes - so the answer to the question is YES. There are 5 terms, then we have -1, +1, -1, +1, -1 and four sign changes - so the answer to the question is YES. There are 7 terms, then we have -1, +1, -1, +1, -1, +1, -1 and six sign changes - so the answer to the question is YES. Etc. Whenever there are an odd number of terms, the answer to the question is YES. Combined, SUFFICIENT Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

### Top First Responders*

1 Ian Stewart 59 first replies
2 Brent@GMATPrepNow 59 first replies
3 Jay@ManhattanReview 53 first replies
4 GMATGuruNY 30 first replies
5 ceilidh.erickson 20 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

188 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

88 posts
4 Ian Stewart

GMATiX Teacher

68 posts
5 Jay@ManhattanReview

Manhattan Review

61 posts
See More Top Beat The GMAT Experts