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# If w, x, y, and z are all positive numbers, then what is the value of

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Math Expert
Joined: 02 Sep 2009
Posts: 60627
If w, x, y, and z are all positive numbers, then what is the value of  [#permalink]

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04 Nov 2019, 03:17
00:00

Difficulty:

95% (hard)

Question Stats:

32% (02:04) correct 68% (02:13) wrong based on 44 sessions

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If w, x, y, and z are all positive numbers, then what is the value of (z - w)?

(1) $$z*y + w*x - y*w - x*z = 0$$

(2) $$y*w - x*z - z*y + w*x = 0$$

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Re: If w, x, y, and z are all positive numbers, then what is the value of  [#permalink]

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04 Nov 2019, 05:29
If w, x, y, and z are all positive numbers, then what is the value of (z - w)?

STATEMENT (1) z∗y + w∗x − y∗w − x∗z = 0
z∗y − y∗w − x∗z + w∗x = 0
y(z−w) − x(z−w) = 0
(y−x)(z−w) = 0
either (y−x) = 0 or (z−w) = 0
we cant get definite value of (z−w)
so, INSUFFICIENT

STATEMENT (2) y∗w − x∗z − z∗y + w∗x = 0
x∗z − w∗x + z∗y − y∗w = 0
x(z−w) + y(z−w) = 0
(x+y)(z−w) = 0

since x and y are positive integers so (x+y) cant be = 0
so, (z−w) = 0
what is the value of (z - w)? --- 0
SUFFICIENT

Re: If w, x, y, and z are all positive numbers, then what is the value of   [#permalink] 04 Nov 2019, 05:29
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