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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 ## Median ##### This topic has 6 member replies ## Median ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median. (2) The sum of the 3 numbers is equal to 3 times one of the numbers. D Legendary Member Joined 01 Jun 2008 Posted: 708 messages Followed by: 1 members Upvotes: 13 D for mean = median, the sequence must be evenly spaced. II) lets take 1 2 3 1+2+3 = 6, which is also 3*2. now lets take 1 4 5 can't replicate that. so II is sufficient I) Hi - Low = 2(Hi - Median) lets take 1 2 3 again. 3-1 = 2 (3 - 1), which is equal to 2. works. lets take 1 4 5. can't replicate that. so I is also sufficient. Newbie | Next Rank: 10 Posts Joined 17 Nov 2008 Posted: 4 messages a, b, c are the numbers where a < b < c median = b and average is (a+b+c)/3 Is b = (a+b+c)/3 ? 3b = a + c +b 2b = a + c 1: (c-a) = 2(c-b) c-a = 2c - 2b 2b=c +a So, Statement 1 is true. 2: a+b+c=3a or 3b or 3c 2 does not lead to statement above. Answer: A Master | Next Rank: 500 Posts Joined 11 Aug 2008 Posted: 248 messages Upvotes: 13 i go with A as well, as a+b+c cud be equal to 3a,3b or 3c ! Last edited by earth@work on Fri Dec 12, 2008 10:02 am; edited 1 time in total Legendary Member Joined 28 Aug 2008 Posted: 2467 messages Followed by: 11 members Upvotes: 331 It is D) Stmt I Let h be the highest number Let the median be the middle number Let l be the lowest number h-l = 2(h-median) h-l = 2h-2median 2median = h+l median = (h+l)/2 (1) mean = l+median+h/3 3 mean = l+h+median 3mean = l+ h + (l+h)/2 6 mean = 3(l+h) mean = l+h/2 (2) From (1) and (2) mean and median are the same SUFF Stmt II Let 3 numbers be x,y,z 3x= x+y+z i.e 2x = y+z i.e x = y+z/2 (Or) y = x+z/2 (similar to above) (or) z = x+y/2 Again this is telling us that there is a common difference between one number to the next number and is is the same SINCE ONE OF THE NUMBERS THAT FALLS EXACTLY BETWEEN 2 OTHERS NUMBERS IS THE AVERAGE OF THE 2 NUMBERS Mean = Median (for consecutive numbers or for numbers where the common difference is the same from one number to thenext after arranging them in ascending order) SUFF Choose D) Senior | Next Rank: 100 Posts Joined 03 Nov 2008 Posted: 33 messages Upvotes: 3 Target GMAT Score: 750 You can think about statement 2 conceptually. The sum of three different numbers cannot equal 3 times the smallest one, because the sum will be more than 3 times the smallest since the other two are greater, by definition, than the smallest. The sum of the numbers cannot be 3x the biggest for the opposite reason. Therefore, if the sum equals 3x a number, it must be the middle number. But if you know that the sum is 3 times the middle, and you also know that is equal to the sum of all three, the larger and smaller must be equidistant from the middle number, and then the middle would therefore be the average as well as the median. Last edited by GMATters1001 on Fri Dec 12, 2008 6:43 am; edited 1 time in total Legendary Member Joined 16 Nov 2008 Posted: 546 messages Upvotes: 13 Test Date: 29th jan Target GMAT Score: 780+ GMAT Score: NA IMO D Nice question! _________________ Admission champion, Hauz khaz 011-27565856 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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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