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# If w < x < y < z, is the product of four numbers

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Manager
Joined: 10 Feb 2011
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If w < x < y < z, is the product of four numbers [#permalink]  15 Feb 2011, 12:11
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177. If w < x < y < z, is the product of four numbers negative?
(1) z > 0.
(2) wx < 0.
[Reveal] Spoiler: OA
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Joined: 20 Dec 2010
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Kudos [?]: 1015 [0], given: 376

Re: 177. If w < x < y < z, is the product of four numbers negati [#permalink]  15 Feb 2011, 12:32
If w < x < y < z, is the product of four numbers negative?

(1) z > 0.
z=+ve
w,x,y can be -ve: product -ve
w,x,y can be +ve: product +ve
Not sufficient

(2) wx < 0.

w and x have opposite signs.
only w can be negative;

w=-ve; x=+ve; y,z can be +ve: product -ve

w can't be positive because that will make x +ve and wx > 0

Sufficient.

Ans: "B"
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~fluke

Manager
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Kudos [?]: 60 [0], given: 10

Re: 177. If w < x < y < z, is the product of four numbers negati [#permalink]  15 Feb 2011, 12:40
but i still don't get it...even if we know from statement (2) that w for example is negative and x is positive, we still don't know anything about y and z. if y or z is negative, so the whole product can be positive...
Math Forum Moderator
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Re: 177. If w < x < y < z, is the product of four numbers negati [#permalink]  15 Feb 2011, 12:46
banksy wrote:
but i still don't get it...even if we know from statement (2) that w for example is negative and x is positive, we still don't know anything about y and z. if y or z is negative, so the whole product can be positive...

y and z will never be negative: w<x<y<z

x is positive;
y is greater than x; y must be +ve and even z.
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~fluke

Manager
Joined: 10 Feb 2011
Posts: 115
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Kudos [?]: 60 [0], given: 10

Re: 177. If w < x < y < z, is the product of four numbers negati [#permalink]  15 Feb 2011, 12:52
oh, right!thanks a lot)
Manager
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Re: 177. If w < x < y < z, is the product of four numbers negati [#permalink]  15 Feb 2011, 20:49
B is sufficient as if the product of two numbers is less than zero, one must be negative and the other positive. Since w<x, and one is negative and one positive, x must be positive. Y and Z must therefore also be positive. +*+*+*- is negative.
CEO
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Re: If w < x < y < z, is the product of four numbers [#permalink]  16 Dec 2014, 08:55
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Re: If w < x < y < z, is the product of four numbers   [#permalink] 16 Dec 2014, 08:55
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