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# For a certain set of n numbers, where n > 1, is the average

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Director
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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: for-a-certain-set-of-n-numbers-where-n-1-is-the-average-167948.html
[Reveal] Spoiler: OA

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(n-1).

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(n-1) 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(n-1).

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 (n-1)
n=3
range = 2(n-1) = 4
e.g
0,1,4 --> median = 1 and mean = 5/3
median<>mean

2,4,6 --> range=6-2 = 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(n-1).

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 (n-1)
n=3
range = 2(n-1) = 4
e.g
0,1,4 --> median = 1 and mean = 5/3
median<>mean

2,4,6 --> range=6-2 = 4

median =4 and mean = 4

Not sufficient

A.

You are right, the 2) is insufficient.

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Manager
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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

Given: The range is 2(n-1)

Now we know that:

last term = first term +(n-1)d

last term - first term = range = (n-1)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

Given: The range is 2(n-1)

Now we know that:

last term = first term +(n-1)d

last term - first term = range = (n-1)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+(n-1)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(n-1) was the range for both n consecutive even/odd integers
Therefore, we still have an evenly spaced set
Thus, 2 was sufficient

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
1
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Expert's post
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(n-1) was the range for both n consecutive even/odd integers
Therefore, we still have an evenly spaced set
Thus, 2 was sufficient

Thanks!
Cheers
J

But the reverse is not necessarily true: not all n-element 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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16 May 2014, 02:27
Expert's post
3
This post was
BOOKMARKED
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. This implies that the set is even;y spaced. In any evenly spaced set the mean (average) is equal to the median. Sufficient.

(2) The range of the n numbers in the set is 2(n- 1). This is completely useless. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: for-a-certain-set-of-n-numbers-where-n-1-is-the-average-167948.html
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Re: For a certain set of n numbers, where n > 1, is the average   [#permalink] 16 May 2014, 02:27
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