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

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

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29 Jan 2017, 23:17
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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. $$M + 1$$

Thanks,
Saquib
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[Reveal] Spoiler: OA

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Last edited by EgmatQuantExpert on 29 Jan 2017, 23:26, 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]

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29 Jan 2017, 23:19
The official solution has been posted. Looking forward to a healthy discussion..
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Last edited by EgmatQuantExpert on 07 Feb 2017, 10:29, 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]

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30 Jan 2017, 07:11
C. Sum of all the elements is same as original set. Hence mean is M
Manager
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink]

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30 Jan 2017, 10:03
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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Posts: 806
Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink]

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07 Feb 2017, 10:28
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 $$= M$$

Thanks,
Saquib
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Senior Manager
Joined: 24 Oct 2016
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Re: A set X: {a1, a2, a3, a4, a5} with non-zero elements have mean M. [#permalink]

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02 Mar 2017, 04:05
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]

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03 Apr 2017, 04:14
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, 04:14
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