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# If w < x < y < z, is the average (arithmetic mean) of w, x, y, and z

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Joined: 02 Sep 2009
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If w < x < y < z, is the average (arithmetic mean) of w, x, y, and z  [#permalink]

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06 Dec 2019, 06:05
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Difficulty:

55% (hard)

Question Stats:

61% (01:42) correct 39% (02:14) wrong based on 42 sessions

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If $$w < x < y < z$$, is the average (arithmetic mean) of w, x, y, and z greater than y ?

(1) $$w + z = x + y$$

(2) $$w = 2$$ and $$z = 18$$

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If w < x < y < z, is the average (arithmetic mean) of w, x, y, and z  [#permalink]

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06 Dec 2019, 10:43
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If w<x<y<z, is the average (arithmetic mean) of w, x, y, and z greater than y ?
$$\frac{w + x+ y + z}{4} > y$$?

(1) w+z=x+y
Now adding x + y on both sides
w + x + y + z = x + y + x + y
$$\frac{w + x + y + z}{4} = \frac{x + y}{2}$$

As $$\frac{x + y}{2}$$ < y always
$$\frac{w + x + y + z}{4}$$ < y

SUFFICIENT.

(2) w=2 and z=18
Clearly, INSUFFICIENT.
As x = 3 y = 4 then $$\frac{w + x+ y + z}{4} = \frac{27}{4}$$ > y
OR
x = 3 y = 15 $$\frac{w + x+ y + z}{4} = \frac{38}{4}$$ < y

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If w < x < y < z, is the average (arithmetic mean) of w, x, y, and z   [#permalink] 06 Dec 2019, 10:43
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