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For a certain set of n numbers, where n > 1, is the average [#permalink]
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11 Mar 2009, 18:24
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For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median? (1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. (2) The range of n numbers in the set is 2(n  1). OPEN DISCUSSION OF THIS QUESTION IS HERE: foracertainsetofnnumberswheren1istheaverage167948.html
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Last edited by Bunuel on 16 May 2014, 02:27, edited 2 times in total.
Renamed the topic, edited the question and added the OA.



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Re: DS gmatprep1  set of n numbers [#permalink]
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11 Mar 2009, 20:17
ugimba wrote: For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
2) The range of n numbers in the set is 2(n1).
Please explain 1. it's clear it is a set with consecutive even numbers => median will always equal to the mean. sufficient 2. range can be equal to 2(n1) only if it's a set with consecutive even numbers. Therefore, same as 1)  sufficient D.



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Re: DS gmatprep1  set of n numbers [#permalink]
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11 Mar 2009, 20:47
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ugimba wrote: For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
2) The range of n numbers in the set is 2(n1).
Please explain 1) n=3 x,x+2,x+4 mean = x+2 median =x+2 say n=2 x,x+2 mean = x+1 median = x+1 Sufficient 2) range 2 (n1) n=3 range = 2(n1) = 4 e.g 0,1,4 > median = 1 and mean = 5/3 median<>mean 2,4,6 > range=62 = 4 median =4 and mean = 4 Not sufficient A.
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Re: DS gmatprep1  set of n numbers [#permalink]
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11 Mar 2009, 21:14
x2suresh wrote: ugimba wrote: For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2.
2) The range of n numbers in the set is 2(n1).
Please explain 1) n=3 x,x+2,x+4 mean = x+2 median =x+2 say n=2 x,x+2 mean = x+1 median = x+1 Sufficient 2) range 2 (n1) n=3 range = 2(n1) = 4 e.g 0,1,4 > median = 1 and mean = 5/3 median<>mean 2,4,6 > range=62 = 4 median =4 and mean = 4 Not sufficient A. You are right, the 2) is insufficient. The answer is A.



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Re: DS gmatprep1  set of n numbers [#permalink]
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11 Oct 2011, 03:12
Thanks x2suresh, the official guide made the explanation of the answer for this question so complex.



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Re: For a certain set of n numbers, where n > 1, is the [#permalink]
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05 Oct 2013, 07:08
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Hello Can someone please help me in finding my mistake. Given: The range is 2(n1) Now we know that: last term = first term +(n1)d last term  first term = range = (n1)d Comparing we get d = 2 This means that the sequence is AP. However, going by number putting techinque, I can see that the above result is not necessary true. Can someone please explain my mistake.
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Re: For a certain set of n numbers, where n > 1, is the [#permalink]
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05 Oct 2013, 07:22
imhimanshu wrote: Hello Can someone please help me in finding my mistake.
Given: The range is 2(n1)
Now we know that:
last term = first term +(n1)d
last term  first term = range = (n1)d
Comparing we get d = 2
This means that the sequence is AP.
However, going by number putting techinque, I can see that the above result is not necessary true. Can someone please explain my mistake. for a series in AP MEAN = MEDIAN ==>this is always true. but IF MEAN = MEDIAN ===>then it is not necessary that series is in AP. for statement 2 We are not sure that series is AP so we cant use the formula nth term = first term+(n1)d. hope it helps
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Re: For a certain set of n numbers, where n > 1, is the average [#permalink]
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15 May 2014, 11:50
ugimba wrote: For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. (2) The range of n numbers in the set is 2(n  1). I thought that 2(n1) was the range for both n consecutive even/odd integers Therefore, we still have an evenly spaced set Thus, 2 was sufficient Could someone please advice where am I going wrong here? Thanks! Cheers J



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Re: For a certain set of n numbers, where n > 1, is the average [#permalink]
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16 May 2014, 02:26
jlgdr wrote: ugimba wrote: For a certain set of n numbers, where n > 1, is the average (arithmetic mean) equal to the median?
(1) If the n numbers in the set are listed in increasing order, then the difference between any pair of successive numbers in the set is 2. (2) The range of n numbers in the set is 2(n  1). I thought that 2(n1) was the range for both n consecutive even/odd integers Therefore, we still have an evenly spaced set Thus, 2 was sufficient Could someone please advice where am I going wrong here? Thanks! Cheers J But the reverse is not necessarily true: not all nelement sets which have the range equal to 2(n  1) are consecutive odd or consecutive even integers. For example, {2, 3, 6} has the range equal to 2(n  1) but this set is not of that type.
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Re: For a certain set of n numbers, where n > 1, is the average [#permalink]
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