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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 ## If x and y are unknown positive integers, is the mean of the tagged by: AAPL ##### This topic has 2 expert replies and 0 member replies ### Top Member ## If x and y are unknown positive integers, is the mean of the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Manhattan Prep If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set? 1) x + y = 7. 2) x - y = 3. OA A. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15313 messages Followed by: 1863 members Upvotes: 13060 GMAT Score: 790 AAPL wrote: Manhattan Prep If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set? 1) x + y = 7. 2) x - y = 3. Known values, in ascending order: 1, 5, 6, 7 Statement 1: x+y = 7 Mean = sum/quantity = (1+5+6+7+x+y)/6 = (1+5+6+7+7)/6 = 26/6 = 13/3 = 4.33. Text EXTREMES. Case 1: x and y are far from each other If x=1 and y=6, we get: 1, 1. 5, 6, 6, 7 Median = (5+6)/2 = 11/2 = 5.5 Case 2: x and y are near each other If x=3 and y=4, we get: 1, 3, 4, 5, 6, 7 Median = (4+5)/2 = 9/2 = 4.5 In both cases, the mean is LESS than the median, so the answer to the question stem is NO. SUFFICIENT. Statement 2: x-y = 3 Again, test EXTREMES. Case 1: x and y are as small as possible. If x=4 and y=1, we get: 1, 1, 4, 5, 6, 7 Mean = (1+1+4+5+6+7)/6 = 24/6 = 4 Median = (4+5)/2 = 9/2 = 4.5. In this case, the mean is LESS than the median, so the answer to the question stem is NO. Case 2: x and y are large If x=100 and y=97, we get: 1, 5, 6, 7, 97, 100 Mean = (1+5+6+7+97+100)/6 = 216/6 = 108/3 = 36. Median = (6+7)/2 = 13/2 = 6.5. In this case, the mean is GREATER than the median, so the answer to the question stem is YES. Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT. The correct answer is A. _________________ 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 22 Aug 2016 Posted: 1952 messages Followed by: 30 members Upvotes: 470 AAPL wrote: Manhattan Prep If x and y are unknown positive integers, is the mean of the set {6, 7, 1, 5, x, y} greater than the median of the set? 1) x + y = 7. 2) x - y = 3. OA A. Let's take each statement one by one. 1) x + y = 7. Mean = (1 + 5 + 6 + 7 + x + y)/6 = (19 + x + y)/6 = (19 + 7)/6 = 4.33 To find out median, we must first arrange terms in an ascending order. The terms, excluding x and y are: 1, 5, 6, 7. Median, excluding x and y: 5.5 If one of the terms (x and y) is less than equal to 5 and the other term is greater than or equal 6, i.e. one is added to the left of 5.5 and the other is added to its right, the median would not change. Given x + y = 7, the pairs of x and y are: (1, 6); (2, 5); and (3, 4) Needless to state that if the pair (1, 6) is added, the median would not change. Or, Median = 5.5 . Mean = 4.33. The answer is No. It will be interesting to see how would median change when we add (2, 5) and (3, 4). Since for both the pairs, the maximum values (5 and 4) are less than the median value (5.5), the new median would be less than 5.5. But will the median be greater than 4.33? Let's see. Again, since for the pair (2, 5), the maximum value (5) is greater than mean (4.33), the new median, would though be less than 5.33, it would be greater than mean 4.33. The answer is No. So, we are left with the last pair (3, 4). The set would be 1, 3, 4, 5, 6, 7 and its median would be (4 + 5)/2 = 4.5 > Mean 4.33. The answer is still No. Unique answer. Sufficient. 2) x - y = 3. If x and y both are very big, then both of them added to the right of median, 5.5, Mean = Mean = (19 + x + y)/6 = a very big number The set would be 1, 5, 6, 7, x, y and its median would be (6 + 7)/2 = 6.5 < Very big Mean. The answer is Yes. However, given x - y = 3, we can have x and y as: (4, 1); (5, 2); etc. Let's see the pair (4, 1). Mean = Mean = (19 + x + y)/6 = (19 + 4 + 1)/6 = 4 The set would be 1, 1, 4, 5, 6, 7 and its median would be (4 + 5)/2 = 4.5 > Mean 4. The answer is No. No unique answer. Insufficient. The correct answer: A Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review Himayatnagar | Hyderabad GMAT Prep | Bangalore GMAT Courses | Kukatpally GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! 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