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# A list of 18 numbers is arranged from the least to the

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CEO
Joined: 15 Aug 2003
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A list of 18 numbers is arranged from the least to the [#permalink]

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01 Oct 2003, 23:36
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2. A list of 18 numbers is arranged from the least to
the greatest. The average of the first n numbers in the list is x
and the average of the remaining numbers is y. If the average of x
and y is equal to the average of all 18 numbers, which of the following
msut be true:

A) n = 1
B) n = 9
C) n = 17
D) 1 < n < 9
E) 9 < n < 17
Intern
Joined: 12 Sep 2003
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05 Oct 2003, 20:42
E.
Both sets must sum the same number, and as the remaining set has greater numbers, n must have more than half of the 18 numbers.
Senior Manager
Joined: 19 May 2004
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06 Aug 2004, 07:40
Nice question. The answer should be B.
I will post my complete solution after a few more people try.
CIO
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06 Aug 2004, 09:58
i admit that i'm having a hard time wrapping my brain around this.

Of course, if they are 18 consecutive numbers, then the average of all would be the one in the middle, and the average of the first 9 would be the middle of the first 9, and the average of the second 9 would be the middle of the second 9, and the average of those two would be the middle of everything, since consecutives just always work out so nicely like that.

My problem to understand is what if they aren't consecutive. Would this still be possible?

But it doesn't matter, because I've just shown that it is true that this could come up 9, and there's only one answer in the whole list that includes 9, and that's B. D and E both exclude 9.

So I'm going with B, having not tried the non-consecutive option.
Director
Joined: 16 Jun 2004
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06 Aug 2004, 10:26
sum of n no.s = nx
sum of remaining no.s = (18-n)y

Avg of the above no.s = [nx + (18-n)y]/18 = (x+y)/2

==> 9x + 9y = nx + y(18-n)
==> 9x + 9y = nx + 18y - ny
==> 9x - nx = 9y - ny
==> x(9-n) = y(9-n)
==> (9-n) (x-y) = 0
==> n=9

B it is..
Senior Manager
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06 Aug 2004, 14:18
I got the same equation as venksune.
It's important to note that x can not equal to y,
And that from this reason, the only solution is x=9.
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