If xyz < 0 and yz > 0, which of the following must be positi

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If xyz < 0 and yz > 0, which of the following must be positi [#permalink]

20 Feb 2013, 16:41

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If xyz < 0 and yz > 0, which of the following must be positive?

(A) xy
(B) xz
(C) (x^2)yz
(D) x(y^2)z
(E) xy(z^2)

[Reveal] Spoiler: OA

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Re: If xyz < 0 and yz > 0, which of the following must be positi [#permalink]

20 Feb 2013, 17:17

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If yz>0 and xyz<0, lets get first yz>0:

a) or y is + and z is +

If this is true, we get xyz<0 and we know: x has to be -

b) or y is - and z is -

If this is true, we get xyz<0 and we know: x has to be -

Therefore, we have OR option A: y+ z+ x- ; OR option B: y- z- x- . Which is positive?

(A) xy: is positive only in option B
(B) xz: is positive only in option B
(C) (x^2)yz: is positive for both option A and B
(D) x(y^2)z: is positive only in option B
(E) xy(z^2): is positive only in option B

Solution MUST be C
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Re: If xyz < 0 and yz > 0, which of the following must be positi [#permalink]

20 Feb 2013, 21:06

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carcass wrote:

If xyz < 0 and yz > 0, which of the following must be positive?
(A) xy
(B) xz
(C) (x^2)yz
(D) x(y^2)z
(E) xy(z^2)

Given that yz is positive and xyz is negative, you can say that x MUST be negative. As for y and z either they are both positive or both negative.

Option (C) has x^2 which is positive and yz which is positive. So (C) must be positive.
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Re: If xyz < 0 and yz > 0, which of the following must be positi [#permalink]

21 Feb 2013, 03:01

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carcass wrote:

If xyz < 0 and yz > 0, which of the following must be positive?

(A) xy
(B) xz
(C) (x^2)yz
(D) x(y^2)z
(E) xy(z^2)

Similar questions to practice:
if-x-y-z-but-x-2-y-2-z-2-0-which-142225.html
if-a-b-c-and-d-are-integers-and-ab2c3d4-0-which-of-the-136450.html

Hope it helps.
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Re: If xyz < 0 and yz > 0, which of the following must be positi [#permalink]

21 Feb 2013, 07:28

Nice question

Thank you guys
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Re: If xyz < 0 and yz > 0, which of the following must be positi [#permalink] 21 Feb 2013, 07:28

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