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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 ## Problem solving: Difficulty level: 700, Source: Princeton tagged by: aishwaryav12 ##### This topic has 3 expert replies and 0 member replies ## Problem solving: Difficulty level: 700, Source: Princeton ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers? A. 49 B. 70 C. 140 D. 215 E. 525 ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15260 messages Followed by: 1862 members Upvotes: 13060 GMAT Score: 790 aishwaryav12 wrote: Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers? A. 49 B. 70 C. 140 D. 215 E. 525 For any evenly spaced set: sum = (number)(median) We can PLUG IN THE ANSWERS, which represent the sum. Since the number of integers can be 5 or 7, the sum must be a multiple of both 5 and 7. Eliminate A, which is not divisible by 5. Eliminate D, which is not divisible by 7. The equation in blue can be rephrased as follows: median = sum/number Since all of the integers must be odd, the correct answer must yield an odd value for the median. If B is the sum of 7 consecutive odd integers, we get: median = sum/number = 70/7 = 10. Since the yielded median is not odd, eliminate B. If D is the sum of 7 consecutive odd integers, we get: median = sum/number = 140/7 = 20. Since the yielded median is not odd, eliminate D. The correct answer is E. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 aishwaryav12 wrote: Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers? A. 49 B. 70 C. 140 D. 215 E. 525 $$?\,\,\,:\,\,\,\,\sum\nolimits_5 {\,{\rm{consecutive}}\,\,{\rm{odd}}\,\,{\rm{integers}}\,\,\,\, = \,} \,\,\,\,\sum\nolimits_7 {\,\,{\rm{consecutive}}\,\,{\rm{odd}}\,\,{\rm{integers}}}$$ > 5 consecutive odd integers are members of a finite arithmetic sequence, hence the middle term (one of them) is an odd integer and equal to their average. (A) average 49/5 is not an integer, hence cannot be the middle term. Refuted. (B) average 70/5 = 14 is not odd, hence cannot be the middle term. Refuted. (C) average 140/5 = 28 is not odd, hence cannot be the middle term. Refuted. > 7 consecutive odd integers are members of a finite arithmetic sequence, hence the middle term (one of them) is an odd integer and equal to their average. (D) average 215/7 is not a multiple of 7 (210 is), hence cannot be the middle term. Refuted. (E) is the answer by exclusion. This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2456 messages Followed by: 18 members Upvotes: 43 aishwaryav12 wrote: Which of the following integers can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers? A. 49 B. 70 C. 140 D. 215 E. 525 If a number can be written as both the sum of 5 consecutive odd integers and 7 consecutive odd integers, then itâ€™s a multiple of both 5 and 7. This eliminates choice A, 49 (since itâ€™s only a multiple of 7) and choice D, 215 (since itâ€™s only a multiple of 5). So we are left with 70, 140 and 525 to consider. Not only must the sum be both a multiple of 5 and 7, but the sum also has to be odd (since the sum of five odd numbers must also be odd). This eliminates answer choices B and C and we are left with E. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Award-winning private GMAT tutoring Register now and save up to$200

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