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tough problem:

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by \'manpreet singh » Mon Nov 05, 2012 9:42 am
Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 <S <n.
Last edited by \'manpreet singh on Tue Nov 06, 2012 12:46 am, edited 1 time in total.
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Source: — Data Sufficiency |
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by GMATGuruNY » Mon Nov 05, 2012 1:04 pm
'manpreet singh wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 < S < n.
Average of consecutive integers = median.
Question rephrased: Does the median = 1?

Statement 1: n is even.
It is not possible for 1 to be the median of an even number of consecutive integers:
0,1,2 = 3 integers
-1,0,1,2,3 = 5 integers
-2,-1,0,1,2,3,4 = 7 integers.
The lists above illustrate that an odd number of integers is required for the median to be 1.
Thus, if n is even, the median cannot be 1.
SUFFICIENT.

Average = Sum/Number of Integers
Question rephrased: Does Sum/n = 1?

Statement 2: If S is the sum of the n consecutive integers, then 0 < S < n.
If S < n, then S/n cannot be equal to 1.
SUFFICIENT.

The correct answer is D.
Last edited by GMATGuruNY on Mon Nov 05, 2012 8:35 pm, edited 1 time in total.
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by \'manpreet singh » Mon Nov 05, 2012 8:27 pm
Thanks Mitch! :)
I guess i need to rephrase the question more properly to avoid getting stuck.

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by FLUID » Mon Nov 05, 2012 11:36 pm
'manpreet singh wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If 5 is the sum of the n consecutive integers, then 0 <5 <n.
Does not make sense if we don't post right question.
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by \'manpreet singh » Tue Nov 06, 2012 12:48 am
FLUID wrote:
'manpreet singh wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If 5 is the sum of the n consecutive integers, then 0 <5 <n.
Does not make sense if we don't post right question.
I have corrected the the minor error but guys above have got the question correctly.

Manpreet
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by Brent@GMATPrepNow » Tue Nov 06, 2012 7:24 am
'manpreet singh wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 <S <n.
Here's a slightly different approach.

Target question: Is the average of n consecutive integers equal to 1?

Statement 1: n is even.
IMPORTANT: In a set of consecutive integers, the mean and the median will be equal.
So, let's see if we have enough information to find the median of this set.
When we have an even number of integers, the median will equal the mean (average) of the two middlemost values.
Now notice that the mean of two consecutive numbers can never be an integer.
For example, the mean of 3 and 4 is 3.5, the mean of 0 and 1 is 0.5, and the mean of -5 and -4 is -4.5
So, from statement 1, we can conclude that the average of the n consecutive integers cannot equal 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If S is the sum of the n consecutive integers, then 0 <S <n.
This tells us that the average of the n values must equal S/n
Can S/n = 1?
No. If S<n, then S/n cannot equal 1.
In other words, the average of the n consecutive integers cannot equal 1
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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