If xyz 0, which of the following must be positi

Question

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)

johnwesley · Answer

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

KarishmaB · Answer

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.

Bunuel · Answer

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.

Carcass · Answer

Nice question

Thank you guys

ydmuley · Answer

Given:

xyz < 0 and
yz > 0 ======> This means that either x and y both are positive or both are negative.

So x can has to be negative, only answer choice which gives us a positive option will be the choice which squares x.

Hence, answer is C - (x^2)yz

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions