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If x, y, and z are integers, and x < y < z, is z y = y

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If x, y, and z are integers, and x < y < z, is z y = y [#permalink] New post 02 Nov 2009, 04:18
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A
B
C
D
E

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If x, y, and z are integers, and x < y < z, is z – y = y – x?

(1) The mean of the set {x, y, z, 4} is greater than the mean of the set {x, y, z}.
(2) The median of the set {x, y, z, 4} is less than the median of the set {x, y, z}.
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Re: Mean & Median [#permalink] New post 02 Nov 2009, 05:05
I'd go with C

A.
(x+y+z+4)/4>(x+y+z)/3
=> x+y+z<12
Cannot prove z-y=y-x
Not sufficient

B.
Median{x,y,z,4}<Median{x,y,z}

Consider x=0, y=5, z=6
4.5<5 => Satisfies this condition; but z-y <> y-x

Consider x=0, y=5, z=10
4.5<5 => Satisfies this condition; and z-y=y-x
Not Sufficient

Combining (A) and (B)
pick numbers which add up to less than 12 and satisfy B
x=0, y=5, z=6; but z-y <> y-x
in other words, we have to pick y > 4. The minimum seq. 4,5,6 (1,5,7) adds up to >12 hence wrong!
So the answer is NO.
Sufficient

Is this the OA? There must be a better and efficient way to do this!
Re: Mean & Median   [#permalink] 02 Nov 2009, 05:05
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If x, y, and z are integers, and x < y < z, is z y = y

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