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Is the average of n consecutive integers equal to 1

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by sachin_yadav » Wed Mar 23, 2011 1:44 am
Source:- "MGMAT - Number properties"

Hi all,

Please help

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

Answer is D
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Source: — Data Sufficiency |
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by HSPA » Wed Mar 23, 2011 3:00 am
I took 5 consecutive number (5 is odd) -1,0,1,2,3
and average is 1.

How is option A sufficient here... n is even but I am getting n as odd
How is option B sufficient here... only if n= S we can get 1. But S is less than n.

Combined:
0,1 here n = 2 and S= 1
S is btw 0 and n
I am not able to solve this kindly help
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by sachin_yadav » Wed Mar 23, 2011 10:22 am
HSPA wrote:I took 5 consecutive number (5 is odd) -1,0,1,2,3
and average is 1.

How is option A sufficient here... n is even but I am getting n as odd
How is option B sufficient here... only if n= S we can get 1. But S is less than n.

Combined:
0,1 here n = 2 and S= 1
S is btw 0 and n
I am not able to solve this kindly help

Hi All,

please help. Does the first option means the following:-

In option A, if we take out the average of even consecutive integers then result will be odd, for instance

0 + 2/2 =1 {-4, -2, 0, 2, 4, 6}

4 + 6/2 =5 {2, 4, 6, 8 }

6 + 8/2 = 14/2 =7 {4, 6, 8, 10}

So, in this case it is insufficient

or

option A means the following:-

the average of an even number of consecutive integers will never be an integer.

1 + 2 + 3 + 4 = 2 + 3/ 2 = 5/2

Therefore, the average of the n consecutive integers cannot equal 1. SUFFICIENT

Regards
Sachin
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by GMATGuruNY » Wed Mar 23, 2011 3:13 pm
sachin_yadav wrote:Source:- "MGMAT - Number properties"

Hi all,

Please help

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

Answer is D
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.
Is S < n, then S/n cannot be equal to 1.
Sufficient.

The correct answer is D.
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by sachin_yadav » Fri Mar 25, 2011 3:26 am
GMATGuruNY wrote:
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.
Is S < n, then S/n cannot be equal to 1.
Sufficient.

The correct answer is D.
Thank you so much Mitch for this great explanation. I was confused between "consecutive even integers" and "even consecutive integers" and thought that they both mean the same thing i.e (2, 4, 6, 8......)

So, consecutive even integers mean {2,4,6,8,......n} and even consecutive integers mean "even number of consecutive integers" (1 + 2 + 3 + 4) , (5 + 6 + 7 + 8).

Thank you once again

Regards
Sachin
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