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A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M.

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EgmatQuantExpert
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A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   Updated on: 30 Jan 2017, 00:26
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A set X: {\(a_1, a_2, a_3, a_4, a_5\)} with non-zero elements have mean \(M\). What is the mean of the set Y: {\(a_1 - 1, a_2 - 2, a_3 - 3, a_4 + 5, a_5 + 1\)}?


    A. \(M - 3\)
    B. \(M - 2\)
    C. \(M - 1\)
    D. \(M\)
    E. \(M + 1\)

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D

Originally posted by EgmatQuantExpert on 30 Jan 2017, 00:17.
Last edited by EgmatQuantExpert on 30 Jan 2017, 00:26, edited 1 time in total.
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A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   Updated on: 07 Feb 2017, 11:29
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The official solution has been posted. Looking forward to a healthy discussion..:)

Originally posted by EgmatQuantExpert on 30 Jan 2017, 00:19.
Last edited by EgmatQuantExpert on 07 Feb 2017, 11:29, edited 1 time in total.
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   30 Jan 2017, 08:11
C. Sum of all the elements is same as original set. Hence mean is M
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   30 Jan 2017, 11:03
ohmr wrote:
ankujgupta wrote:
C. Sum of all the elements is same as original set. Hence mean is M

I think you mean D

My bad. Yes it should be D .
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   07 Feb 2017, 11:28
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Hey,

PFB the official solution. :)


To Find:

    • Mean of set Y

Working Out:

In Set X: {\(a_1, a_2, a_3, a_4, a_5\)}

    • Mean of Set X with 5 elements = \(M\)
    • Sum = Mean * Number of elements
    • \(a_1 + a_2 + a_3 + a_4 + a_5 = 5M\) (1)

In Set Y: {\(a_1 - 1, a_2 - 2, a_3 - 3, a_4 + 5, a_5 + 1\)}

    • Sum of elements \(= (a_1 – 1) + (a_2 – 2) + (a_3 – 3) + (a_4 + 5) + (a_5 + 1)\)
Rearranging, we get
    • Sum \(= a_1 + a_2 + a_3 + a_4 + a_5 + (-1 + -2 + -3 + 5 + 1)\)
    • Sum \(= a_1 + a_2 + a_3 + a_4 + a_5 + 0\)
    • Sum \(= 5M\) From(1)
    • Mean\(= \frac{(Sum)}{(Number of elements)}\)
    • Mean \(= \frac{5M}{5}\)
    • Mean \(= M\)

Correct Answer: Option D


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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   02 Mar 2017, 05:05
choose simple no such as 1,2,3,4,5 so average will be 3 now follow the process you will get 0+0+0+9+6=15/5=3 so answer would be D
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink] New post   03 Apr 2017, 05:14
Set X:
Mean=M= (a1+a2+a3+a4+a5)/5
Sum of these values= 5M

Set Y:
We see similar elements a1, a2, ...........
Combine them together and we know that their sum is equal to 5M.

Therefore
5M-1-2-3+5+1
=5M+0
=5M

The mean of set Y= 5M/5=M

Mean of set X=Mean of set Y
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink]
03 Apr 2017, 05:14
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