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D
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Difficulty:
95%
(hard)
Question Stats:
42% (02:18) correct
58%
(02:10)
wrong
based on 510
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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
(1) n is even
(2) if S is the sum of the n consecutive integers, then 0 < S < n
Show SpoilerMy approach
Correct answer D
Hello Fluke and Everyone in this forum - can you please explain the conceptual way of to solve this and improve my understanding ?
My approach to solve this:
Statement 1: Sufficient, because the average of the even number of consecutive integers can never be an integer.
Statement 2: I understand what the statement means, but I am struggling to understand the concept.
My understanding is
Average = Sum/Number of terms
Therefore, Sum = Average * Number of Terms
Therefore S=Average/n. But what can we conclude from this? The book says that this is sufficient as well.
So the answer is D. But I don't understand the Statement 2.
Hello Fluke and Everyone in this forum - can you please explain the conceptual way of to solve this and improve my understanding ?
My approach to solve this:
Statement 1: Sufficient, because the average of the even number of consecutive integers can never be an integer.
Statement 2: I understand what the statement means, but I am struggling to understand the concept.
My understanding is
Average = Sum/Number of terms
Therefore, Sum = Average * Number of Terms
Therefore S=Average/n. But what can we conclude from this? The book says that this is sufficient as well.
So the answer is D. But I don't understand the Statement 2.
20 Dec 2016, 17:55
Kudos
Bookmarks
Great Question.
Here is what i did in this one ->
We are asked if the mean of n consecutive is an integer or not.
N consecutive integer => Evenly spaced set =>Mean = Median =Average of the first and the last term
Mean for N consecutive integers can take only 2 forms =>
x => For N = odd
x.5=> for N=even
for some integer x
Statement 1-->
N is even
So mean will never be an integer(Because median will never be an integer)
Hence mean can never be "one".
Hence Sufficient
Statement 2-->
Sum=> S
And 0<S<N
\(Mean = \frac{Sum}{#}\)
Mean = \(\frac{S}{N}\)
As \(0<S<N\)=>
\(\frac{S}{N}\) will be a decimal between (0,1)
Hence mean will never be one.
Hence Sufficient
Hence D
Here is what i did in this one ->
We are asked if the mean of n consecutive is an integer or not.
N consecutive integer => Evenly spaced set =>Mean = Median =Average of the first and the last term
Mean for N consecutive integers can take only 2 forms =>
x => For N = odd
x.5=> for N=even
for some integer x
Statement 1-->
N is even
So mean will never be an integer(Because median will never be an integer)
Hence mean can never be "one".
Hence Sufficient
Statement 2-->
Sum=> S
And 0<S<N
\(Mean = \frac{Sum}{#}\)
Mean = \(\frac{S}{N}\)
As \(0<S<N\)=>
\(\frac{S}{N}\) will be a decimal between (0,1)
Hence mean will never be one.
Hence Sufficient
Hence D
General Discussion
02 Jul 2011, 14:55
Kudos
Bookmarks
enigma123
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 \(0<S>n\).
1) \(n\) is even
2) If \(S\) is the sum of the \(n\) consecutive integers then \(0<S>n\).
2) To get an average=1; the Sum of elements must be equal to number of elements.
\(If S=n; \frac{S}{n}=1\);
If S is NOT equal to n, the average can not be 1.
Sum=100; n=100; S/n=100/100=1
Sum=1; n=1; S/n=1/1=1
Sum=10; n=9; S/n=10/9=1.##(NOT EQUAL TO 1)
Sufficient.
