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A certain list consists of 3 different members. Does the med

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Manager
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Joined: 23 Nov 2008
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A certain list consists of 3 different members. Does the med [#permalink]

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New post 27 Nov 2008, 01:39
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A certain list consists of 3 different members. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median
(2) The sum of the 3 numbers is equal to 3 times one of the numbers
[Reveal] Spoiler: OA

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Re: DS: Median [#permalink]

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New post 27 Nov 2008, 02:04
D.
the ques asks if the nos are consecutive or the no.s are equidistant from each other in which case we'll have mean=median.
(1)if nos. are A,B,C with B as median, C-A=2(C-B)
or C-B=B-A ---suff
(2)Tricky . we can have A+B+C=3A or A+B+C=3B or A+B+C=3C.
in each case, however A,B &C will be the medians and hence suffice.
(since all nos. are different)

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Re: DS: Median [#permalink]

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New post 28 Nov 2008, 21:20
A certain list consists of 3 different members. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?
1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median
2) The sum of the 3 numbers is equal to 3 times one of the numbers

here is my approach,

let the numbers be x,y,z
is mean = median? basically we have to prove weather all the numbers are same or consecutive, OK letz prove it,

assuming x,y,x in ascending order,

1) z-x = 2(z-y)

y = (z+x)/2 -- median ---- 1

mean = (x+y+z)/3 -- 2

sub 1 in 2 we get mean == median

2) x+y+z = 3y ( since all are diff numbers, only y is eligible)

so it just repeats the above soln.

SO D

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Re: DS: Median   [#permalink] 28 Nov 2008, 21:20
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