Last visit was: 12 Jul 2024, 17:53 It is currently 12 Jul 2024, 17:53
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Request Expert Reply

# If xyz ≠ 0, xy > 0, and x2 + xy + xz < 0, then which of the following

SORT BY:
Tags:
Show Tags
Hide Tags
VP
Joined: 12 Feb 2015
Posts: 1060
Own Kudos [?]: 2163 [21]
Given Kudos: 77
Most Helpful Reply
Manhattan Prep Instructor
Joined: 04 Dec 2015
Posts: 932
Own Kudos [?]: 1556 [12]
Given Kudos: 115
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
General Discussion
Director
Joined: 09 Mar 2018
Posts: 776
Own Kudos [?]: 458 [1]
Given Kudos: 123
Location: India
Manager
Joined: 12 Jan 2019
Posts: 91
Own Kudos [?]: 56 [0]
Given Kudos: 211
Location: India
Concentration: Finance, Technology
If xyz ≠ 0, xy > 0, and x2 + xy + xz < 0, then which of the following [#permalink]
Can someone please simplify why it cannot be E

Aren't I II III independent statements?
If yes can we make use of the 3 of them to imply whether x is negative or no?
Manager
Joined: 18 Sep 2019
Posts: 50
Own Kudos [?]: 15 [0]
Given Kudos: 88
Re: If xyz ≠ 0, xy > 0, and x2 + xy + xz < 0, then which of the following [#permalink]
CAMANISHPARMAR wrote:
If xyz ≠ 0, xy > 0, and x^2 + xy + xz < 0, then which of the following must be true?

I. x(y + z) < 0

II. x + y + z < 0

III. If x < 0, then z > 0.

A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

Conditions:
a) xyz ≠ 0
b) xy > 0 (it means xy is either both positive or both negative)
c) x^2 + xy + xz < 0 (it means x^2 positive, xy must be positive from the second condition, and xz has to be negative)

I. x(y + z) < 0, => xy + xz <0, from condition c, we can see xz is negative and greater than positive x^2 + xy combined, so this statement is true
II. x + y + z < 0, we can not say this true. Maybe, maybe not.
III. If x < 0, then z > 0. Here given x is negative.

Condition c: x^2 + xy + xz < 0
x(x+y+z) <0, now to make x(x+y+z) negative/less than 0, we will need to make (x+y+z) positive. From condition b, we already know when x is negative, y has to be negative. So to make (x+y+z) positive, z has to be positive since x and y both are negative.

So this statement is true.

C) I and III only
Non-Human User
Joined: 09 Sep 2013
Posts: 33952
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: If xyz 0, xy > 0, and x2 + xy + xz < 0, then which of the following [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: If xyz 0, xy > 0, and x2 + xy + xz < 0, then which of the following [#permalink]
Moderator:
Math Expert
94302 posts