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A set X: {a1, a2, a3, a4, a5} with nonzero 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 nonzero 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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A set X: {a1, a2, a3, a4, a5} with nonzero 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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Re: A set X: {a1, a2, a3, a4, a5} with nonzero 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



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Re: A set X: {a1, a2, a3, a4, a5} with nonzero 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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Re: A set X: {a1, a2, a3, a4, a5} with nonzero elements have mean M. [#permalink]
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07 Feb 2017, 10:28
Hey, PFB the official solution. To Find: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 DThanks, Saquib Quant Expert eGMATRegister for our Free Session on Number Properties (held every 3rd week) to solve exciting 700+ Level Questions in a classroom environment under the realtime guidance of our Experts
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Re: A set X: {a1, a2, a3, a4, a5} with nonzero 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 nonzero 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 5M123+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 nonzero elements have mean M.
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