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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 ## Question of the Week - 3 (The value of the variable E is...) tagged by: e-GMAT ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## Question of the Week - 3 (The value of the variable E is...) ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers. Which of the following can be a possible value of the reciprocal of E? A. 0.154 B. 0.1818 C. 0.667 D. 2 E. 3.03 To access all questions: Consolidated list of Questions of the Week ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12831 messages Followed by: 1247 members Upvotes: 5254 GMAT Score: 770 e-GMAT wrote: The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers. Which of the following can be a possible value of the reciprocal of E? A. 0.154 B. 0.1818 C. 0.667 D. 2 E. 3.03 A fast approach is to use some estimation. E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 â‰ˆ 0.5 + 0.25 + 0.15 + 0.1 + 0.1 + 0.1 + 0.05 + 0.05 + 0.05 + 0.05 â‰ˆ1.4 Which of the following can be a possible value of the reciprocal of E? The reciprocal of E â‰ˆ1/1.4 â‰ˆ0.7 Check the answer choices . . . answer = C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 26 Jul 2010 Posted: 645 messages Followed by: 225 members Upvotes: 527 Solution Given: In this question, we are given that â€¢ The value of the variable E is determined by adding the reciprocals of the first 10 even natural numbers. To find: We need to determine â€¢ Among the given options, which one can be a possible value of the reciprocal of E. Approach and Working: As E equals the sum of the reciprocals of the first 10 even natural numbers, we can write E in the following manner: â€¢ E = 1/2 + 1/4 + 1/6 + 1/8 + 1/10 + 1/12 + 1/14 + 1/16 + 1/18 + 1/20 Or, E = 1/2 (1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10) Now, if we observe the terms within the bracket carefully, we can see that 1 is the largest among all the 10 terms and 1/10 is the smallest among all the 10 terms. â€¢ If all 10 terms were equal to 1/10, then E would be 1/2 x 10 x 1/10 = 1/2. o But since the actual terms are more, we can say that the value of E is greater than 1/2. â€¢ Similarly, if all 10 terms were equal to 1, then E would be 1/2 x 10 x 1 = 5. o But since the actual terms are less, we can say that the value of E is less than 5. Combining the above results, we can say â€¢ 1/2 < E < 5 Or, 2 > 1/E > 1/5 Or, 2 > 1/E > 0.2 From the given options, only 0.667 falls in the given range. Hence, the correct answer is option C. Answer: C • 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 • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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