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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 ## Consecutiveness of n ##### This topic has 8 expert replies and 8 member replies Goto page • 1, • 2 ## Consecutiveness of n Hi! This was from one of the MGMAT CATs. Can some one please explain? A list contains n distinct integers. Are all n integers consecutive? (1) The average (arithmetic mean) of the list with the lowest number removed is 1 more than the average (arithmetic mean) of the list with the highest number removed. (2) The positive difference between any two numbers in the list is always less than n. OA is D Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 N = A, B,C,D,E,F Statement 1: (B+C+D+E+F)/5 = 1 + (A+B+C+D+E)/5 B+C+D+E+F = 5 + A+B+C+D+E F-A = 5 Only consecutive number series is possible to give such a result Hence, consecutive. SUFFICIENT Statement 2: F-A < 6 Since, numbers are different.. Only consecutive number series is possible to give such a result SUFFICIENT Answer {D} _________________ R A H U L ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1500 members Upvotes: 2256 GMAT Score: 800 ^^ The post above shows that the statements are sufficient for n = 6, but they don't necessarily represent all values of n. (There's no reason to assume that n is 6.) If you're going to take the "plug in numbers" approach, then, good -- it's an effective approach -- but you should definitely try more than one value of n! _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi -- Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 lunarpower wrote: ^^ The post above shows that the statements are sufficient for n = 6, but they don't necessarily represent all values of n. (There's no reason to assume that n is 6.) If you're going to take the "plug in numbers" approach, then, good -- it's an effective approach -- but you should definitely try more than one value of n! Ron, from the result of statement one F-A = 5 [A,B,C,D,E & F are integer values] it's pretty much clear that RHS would always be one less than the value of "n" I could think of.. Hence, trying multiple values of "n" would be merely waste of time that I could have saved for next questions..That's why i din't try more values. .. _________________ R A H U L ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1500 members Upvotes: 2256 GMAT Score: 800 theCodeToGMAT wrote: Ron, from the result of statement one F-A = 5 [A,B,C,D,E & F are integer values] it's pretty much clear that RHS would always be one less than the value of "n" I could think of.. Hence, trying multiple values of "n" would be merely waste of time that I could have saved for next questions..That's why i din't try more values. :) .. Fair enough. If you see the seeds of a strong pattern, then, great. Nicely done. I guess my point is that, since you're going to the trouble of posting these things on a public forum, you may as well lay out that part of the reasoning more explicitly. E.g., "I can tell that the same thing will happen for other n's." Or something like that. In other words, even if your solution is awesome, there's little point in posting it without that kind of explanatory detail. (Maybe I misunderstand the point of view of people on the forum, though. For instance, there are tons and tons of posts on every thread that say things like "I choose B", with no explanation whatsoever. Such posts add zero value to the discussion -- and are frustrating to scroll through, if there are lots of them -- but people still post them.) _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi -- Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Legendary Member Joined 14 Aug 2012 Posted: 1556 messages Followed by: 34 members Upvotes: 448 Target GMAT Score: 750 GMAT Score: 650 Thanks Ron. Yeah, I agree with you .. I will try my best to post "Sound" solutions _________________ R A H U L Senior | Next Rank: 100 Posts Joined 01 Jun 2012 Posted: 89 messages Followed by: 2 members Upvotes: 6 Hi Ron and theCodeToGMAT, I am extremely sorry I lost track of this thread while I was checking my other posts and posts by others in this forum. I kinda got the first statement. But still confused with the second. What does 'positive' difference mean in the first place? Can you please explain statement II once again? Again, apologies for missing this thread. Thanks ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1500 members Upvotes: 2256 GMAT Score: 800 sidceg wrote: Hi Ron and theCodeToGMAT, I am extremely sorry I lost track of this thread while I was checking my other posts and posts by others in this forum. I kinda got the first statement. But still confused with the second. What does 'positive' difference mean in the first place? Can you please explain statement II once again? Again, apologies for missing this thread. Thanks "Positive difference" is exactly what it says. It's the difference between two numbers, expressed as a positive number. E.g., the positive difference between 3 and 7 is 4. The positive difference between 7 and 3 is also 4. For statement 2, the only thing you really need to think about is the difference between the biggest and smallest values in the set. (If you don't see why that is so, think about it for a bit.) Try making any set, at all, that doesn't consist entirely of consecutive integers. See whether you can get that difference to be less than N. _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi -- Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Senior | Next Rank: 100 Posts Joined 01 Jun 2012 Posted: 89 messages Followed by: 2 members Upvotes: 6 lunarpower wrote: sidceg wrote: Hi Ron and theCodeToGMAT, I am extremely sorry I lost track of this thread while I was checking my other posts and posts by others in this forum. I kinda got the first statement. But still confused with the second. What does 'positive' difference mean in the first place? Can you please explain statement II once again? Again, apologies for missing this thread. Thanks "Positive difference" is exactly what it says. It's the difference between two numbers, expressed as a positive number. E.g., the positive difference between 3 and 7 is 4. The positive difference between 7 and 3 is also 4. For statement 2, the only thing you really need to think about is the difference between the biggest and smallest values in the set. (If you don't see why that is so, think about it for a bit.) Try making any set, at all, that doesn't consist entirely of consecutive integers. See whether you can get that difference to be less than N. I tried the following cases. 1,2,3: 3-2<3 --> Yes 4,5,6,7: 7-4<4 --> Yes -3,-2,-1,0,1: 1-(-3)<5 --> Yes But what about [-5,0,5,10]? Are these integers consecutive? ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1500 members Upvotes: 2256 GMAT Score: 800 "Consecutive" means "next to each other in sequence, without skipping anything". The difference between any two consecutive integers is 1. 5, 10, 15, 20, ... would be consecutive multiples of 5. But they're not consecutive integers, since there are other integers between them. -- More importantly, those values are irrelevant to the problem at hand, because they don't satisfy statement 2. Statement 2 says that the difference between any 2 integers in the set is LESS than N. Try getting that to happen with anything other than a set of consecutive integers. Not gonna happen. _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi -- Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Senior | Next Rank: 100 Posts Joined 01 Jun 2012 Posted: 89 messages Followed by: 2 members Upvotes: 6 lunarpower wrote: "Consecutive" means "next to each other in sequence, without skipping anything". The difference between any two consecutive integers is 1. 5, 10, 15, 20, ... would be consecutive multiples of 5. But they're not consecutive integers, since there are other integers between them. Okay I often got confused between the consecutive numbers as numbers spaced equally. lunarpower wrote: More importantly, those values are irrelevant to the problem at hand, because they don't satisfy statement 2. Statement 2 says that the difference between any 2 integers in the set is LESS than N. Try getting that to happen with anything other than a set of consecutive integers. Not gonna happen. Since I had considered consecutive numbers as numbers equally spaced, I tried the above numbers also which yielded a NO. So with all other cases YES and this one case NO, I concluded that statement II is not sufficient. ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1500 members Upvotes: 2256 GMAT Score: 800 Ah, I see. But, no, that's not what "consecutive integers" means. There's a different name for that sort of thing -- I think it's "arithmetic progression" or "arithmetic sequence", or something like that -- but you won't need to know that name for the gmat exam. _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi -- Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Senior | Next Rank: 100 Posts Joined 01 Jun 2012 Posted: 89 messages Followed by: 2 members Upvotes: 6 Alright! Thanks Ron Newbie | Next Rank: 10 Posts Joined 04 Jan 2014 Posted: 7 messages sidceg wrote: Hi! This was from one of the MGMAT CATs. Can some one please explain? A list contains n distinct integers. Are all n integers consecutive? (1) The average (arithmetic mean) of the list with the lowest number removed is 1 more than the average (arithmetic mean) of the list with the highest number removed. (2) The positive difference between any two numbers in the list is always less than n. OA is D Statement I is sufficient Let us say n = 4 and the numbers are 4, 5, 6 and 7 If we remove 4 then the average is 6 If we remove 7 then the average is 5 which satisfies with the statement Now lets go algebra: If the numbers are {x, x+1, x+2.....x+n-1} with average (2x + n - 1)/2 (First + last)/2 If we remove x then the average will become (x + 1 + x + n - 1)/2 = (2x + n)/2 increasing by 1/2 If we remove x + n - 1 the average will become (x + x + n -2)/2 = (2x + n -2)/2 decreasing by 1/2 Hence the difference will always be the 1 between them. Statement II is sufficient: If the numbers are {x, x+1, x+2.....x+n-1} If we subtract the first and the last we will get = |x + n - 1 - x| = n - 1 which is always less than n. Now is there any other set which can have that. Since the members of the set are distinct it is not possible to have that. Answer is D. _________________ Perfect Scores If you think our post was valuable then please encourage us with Kudos To learn GMAT for free visit: https://Perfect-Scores.com https://Youtube.com/PerfectScores https://Facebook.com/PerfectScores ### GMAT/MBA Expert GMAT Instructor Joined 03 Mar 2008 Posted: 3380 messages Followed by: 1500 members Upvotes: 2256 GMAT Score: 800 PerfectScores wrote: Statement I is sufficient Let us say n = 4 and the numbers are 4, 5, 6 and 7 If we remove 4 then the average is 6 If we remove 7 then the average is 5 which satisfies with the statement Now lets go algebra: If the numbers are {x, x+1, x+2.....x+n-1} with average (2x + n - 1)/2 (First + last)/2 If we remove x then the average will become (x + 1 + x + n - 1)/2 = (2x + n)/2 increasing by 1/2 If we remove x + n - 1 the average will become (x + x + n -2)/2 = (2x + n -2)/2 decreasing by 1/2 Hence the difference will always be the 1 between them. ^^ It appears here that you're starting with a set of consecutive integers, and trying to prove statement 1. That's not the way it works, although you'll get lucky with the answer here. If you want to take an approach like this one, then you must also prove that starting with any other set (i.e., a set that doesn't consist entirely of consecutive integers) won't give a difference of 1. _________________ Ron has been teaching various standardized tests for 20 years. -- Pueden hacerle preguntas a Ron en castellano Potete chiedere domande a Ron in italiano On peut poser des questions Ã Ron en franÃ§ais Voit esittÃ¤Ã¤ kysymyksiÃ¤ Ron:lle myÃ¶s suomeksi -- Quand on se sent bien dans un vÃªtement, tout peut arriver. Un bon vÃªtement, c'est un passeport pour le bonheur. Yves Saint-Laurent -- Learn more about ron Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. 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