It is currently 18 Oct 2017, 02:54

Close

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If xy > 0 and yz < 0, which of the following must be negativ

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
Joined: 14 Jul 2012
Posts: 8

Kudos [?]: 28 [0], given: 4

Location: Canada
Concentration: Marketing, Entrepreneurship
WE: Sales (Other)
If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 19 Mar 2013, 12:42
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

65% (01:04) correct 35% (00:50) wrong based on 510 sessions

HideShow timer Statistics

If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)
[Reveal] Spoiler: OA

Last edited by Bunuel on 19 Mar 2013, 12:54, edited 2 times in total.
Renamed the topic, edited the question and the tags.

Kudos [?]: 28 [0], given: 4

Expert Post
13 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [13], given: 12181

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

Show Tags

New post 19 Mar 2013, 12:57
13
This post received
KUDOS
Expert's post
4
This post was
BOOKMARKED
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)


Notice that option C is x(y^2)z = (xy)(yz) = positive*negative = negative.

Answer: C.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128668 [13], given: 12181

1 KUDOS received
Manager
Manager
User avatar
Joined: 04 Oct 2011
Posts: 217

Kudos [?]: 62 [1], given: 44

Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 440 Q33 V13
GPA: 3
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 19 Mar 2013, 18:05
1
This post received
KUDOS
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)


xy > 0
++ (or)
--
yz < 0
+- (or)
-+

Remember Square of any number is always +ve. so we can remove all squares

A. xyz there is a chance for --+ so may be +
B. xy ++ or --
C. xz if x is + then z should be - and vice versa
D. x may be + or -
E. +ve
_________________

GMAT - Practice, Patience, Persistence
Kudos if u like :)

Kudos [?]: 62 [1], given: 44

Intern
Intern
avatar
Joined: 14 Jul 2012
Posts: 8

Kudos [?]: 28 [0], given: 4

Location: Canada
Concentration: Marketing, Entrepreneurship
WE: Sales (Other)
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 20 Mar 2013, 06:39
Hi, sorry to bother again, but I still didn't understand either of the explanations.....

I saw a long way in the book to solve it but I didn't get how both of you were able to solve it quick in that manner.

Thanks.

Kudos [?]: 28 [0], given: 4

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41886

Kudos [?]: 128668 [1], given: 12181

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

Show Tags

New post 20 Mar 2013, 06:43
1
This post received
KUDOS
Expert's post
GMAThirst wrote:
Hi, sorry to bother again, but I still didn't understand either of the explanations.....

I saw a long way in the book to solve it but I didn't get how both of you were able to solve it quick in that manner.

Thanks.


xy > 0 means that xy is positive.
yz < 0 means that yz is negative.

x(y^2)z = (xy)(yz) = positive*negative = negative. Thus option C is always negative.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128668 [1], given: 12181

Intern
Intern
avatar
Joined: 14 Jul 2012
Posts: 8

Kudos [?]: 28 [0], given: 4

Location: Canada
Concentration: Marketing, Entrepreneurship
WE: Sales (Other)
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 20 Mar 2013, 06:48
Hey Banuel,

Thanks it's much clearer now. Also, I'll make sure to follow the GMAT Rules for posting

Kudos [?]: 28 [0], given: 4

Director
Director
avatar
Joined: 03 Aug 2012
Posts: 899

Kudos [?]: 885 [0], given: 322

Concentration: General Management, General Management
GMAT 1: 630 Q47 V29
GMAT 2: 680 Q50 V32
GPA: 3.7
WE: Information Technology (Investment Banking)
Premium Member
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 25 Jul 2013, 21:20
I follow the tables for these types of questions

XY>0 => Both must be -ve or both must be +ve.

YZ<0 =>Both must be of opposite signs.

X | Y | Z

+ + -
- - +

Evaluate all the options by this you will arrive at (C).

Rgds,
TGC !
_________________

Rgds,
TGC!
_____________________________________________________________________
I Assisted You => KUDOS Please
_____________________________________________________________________________

Kudos [?]: 885 [0], given: 322

Intern
Intern
avatar
Joined: 06 Jan 2013
Posts: 11

Kudos [?]: 27 [0], given: 24

Location: United States
Concentration: Finance, Economics
GMAT Date: 11-15-2013
GPA: 3.5
WE: Education (Education)
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 29 Aug 2013, 05:36
I also follow the table approach for these types of questions, as per the attached file. I set up the columns for x, y, and z, and check which combination of positive and negative values I need to satisfy the conditions given (xy>0 and yz<0), then I check each answer choice in turn. When actually doing these questions I wouldn't fill in the whole table (since the answer is C there is no point checking D and E), but for the sake of completeness I added them. Hope it helps a bit, I'm more visual so didn't either consider the algebraic approach given above!
Attachments

File comment: Solution table
Table.png
Table.png [ 3.87 KiB | Viewed 6389 times ]

Kudos [?]: 27 [0], given: 24

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 1978

Kudos [?]: 719 [0], given: 355

Concentration: Finance
GMAT ToolKit User
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 05 Jan 2014, 08:14
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)


If 'x' and 'y' have the same sign, and 'y' and 'z' have different signs, then it must follow that 'x' and 'z' have different sign

Hence y^2 will always be positive and x*z will always be negative

Thus C gives the correct answer

Cheers!
J :)

Kudos [?]: 719 [0], given: 355

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 16724

Kudos [?]: 273 [0], given: 0

Premium Member
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 15 Apr 2015, 00:21
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 273 [0], given: 0

Director
Director
User avatar
Joined: 07 Aug 2011
Posts: 583

Kudos [?]: 537 [0], given: 75

Concentration: International Business, Technology
GMAT 1: 630 Q49 V27
GMAT ToolKit User
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 15 Apr 2015, 03:59
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)



from stem, x and y have same sign and z is just opposite to x and y .
clear C .
_________________

Thanks,
Lucky

_______________________________________________________
Kindly press the Image to appreciate my post !! :-)

Kudos [?]: 537 [0], given: 75

1 KUDOS received
Senior Manager
Senior Manager
User avatar
S
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 404

Kudos [?]: 477 [1], given: 53

Location: United States (CA)
Age: 37
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GRE 1: 337 Q168 V169
WE: Education (Education)
If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 05 May 2016, 18:30
1
This post received
KUDOS
Attached is a visual that should help.
Attachments

Screen Shot 2016-05-05 at 6.44.19 PM.png
Screen Shot 2016-05-05 at 6.44.19 PM.png [ 141.98 KiB | Viewed 2998 times ]


_________________

Harvard grad and 770 GMAT scorer, offering high-quality private GMAT tutoring, both in-person and via Skype, since 2002.

McElroy Tutoring

Kudos [?]: 477 [1], given: 53

Manager
Manager
avatar
B
Joined: 26 Mar 2017
Posts: 164

Kudos [?]: 8 [0], given: 1

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

Show Tags

New post 12 May 2017, 03:20
since xy>0 (pos) and yz<0 (neg) --> xy (neg) * yz (pos) must be negative

rewrite xy (neg) * yz (pos) --> x(y^2)z
_________________

I hate long and complicated explanations!

Kudos [?]: 8 [0], given: 1

Manager
Manager
User avatar
B
Joined: 21 Jun 2017
Posts: 70

Kudos [?]: 4 [0], given: 2

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

Show Tags

New post 23 Aug 2017, 20:13
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)



I enjoyed solving this problem. After solving it, It was also a pleasure seeing it categorized as Medium and a 600 question.

---

Starting with the givens:

Given XY > 0
this given should be interpreted as Either both X and Y are positive or Negative. For the product of two like signs always yields a positive.
Given YZ < 0
this given should be interpreted as either Y or Z as positive or negative. For the product of two different signs always yields a negative.

Considering the implications of the givens, this problem branches off in two directions: the first is Y is negative; therefore, X is negative and Z is positive. And the second, Both X and Y are positive, while Z is negative

This problem asks for a MUST solution, so our two branches need to overlap the same answer.

If X and Y = -
Z = +
then (A) (B) (E) is eliminated, leaving us with (C) and (D) as possible Answers

If X and Y = +
Z = -
then (B)(D)(E) is eliminated, leaving us with (A) and (C) as possible answers.

Since the only overlapping solution to our two branches is (C), (C) must be the answer

Kudos [?]: 4 [0], given: 2

Senior Manager
Senior Manager
User avatar
G
Joined: 29 Jun 2017
Posts: 345

Kudos [?]: 65 [0], given: 64

WE: Engineering (Transportation)
GMAT ToolKit User Reviews Badge
Re: If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 23 Aug 2017, 22:15
Clearly C is the Answer.

See the pic, solution is attached,
Attachments

IMG_5420.JPG
IMG_5420.JPG [ 1.63 MiB | Viewed 570 times ]


_________________

Give Kudos for correct answer and/or if you like the solution.

Kudos [?]: 65 [0], given: 64

Director
Director
User avatar
P
Joined: 04 Dec 2015
Posts: 696

Kudos [?]: 298 [0], given: 261

Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
GMAT ToolKit User
If xy > 0 and yz < 0, which of the following must be negativ [#permalink]

Show Tags

New post 27 Aug 2017, 18:11
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)


\(xy>0\) ------- (Both \(x\) and \(y\) are either positive or negative. ie; \(x\) and \(y\) have same signs)

\(yz<0\) ------- (\(y\) and \(z\) have different signs)

Lets check the options.

Case one : \(x\) and \(y\) are positive and \(z\) is negative. Square of negative is positive.

A. \(xyz = (positive)(positive)(negative) = negative\)
B. \(xy(z^2) = (positive)(positive)(negative^2) = positive\)
C. \(x(y^2)z = (positive)(positive^2)(negative) = negative\)
D. \(x(y^2)(z^2) = (positive)(positive^2)(negative^2) = positive\)
E. \((x^2)(y^2)(z^2) = (positive^2)(positive^2)(negative^2) = positive\)

Case two: \(x\) and \(y\) are negative and \(z\) is positive. Square of negative is positive.

A. \(xyz = (negative)(negative)(positive) = positive\)
B. \(xy(z^2) = (negative)(negative)(positive^2) = positive\)
C. \(x(y^2)z = (negative)(negative^2)(positive) = negative\)
D. \(x(y^2)(z^2) = (negative)(negative^2)(positive^2) = negative\)
E. \((x^2)(y^2)(z^2) = (negative^2)(negative^2)(positive^2) = positive\)

Question is asking which of the following "must be" negative. From both the cases, we get, C is negative. Hence Answer C.

Answer (C)...

Kudos [?]: 298 [0], given: 261

Expert Post
Target Test Prep Representative
User avatar
S
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1545

Kudos [?]: 827 [0], given: 5

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

Show Tags

New post 31 Aug 2017, 10:24
GMAThirst wrote:
If xy > 0 and yz < 0, which of the following must be negative:

A. xyz
B. xy(z^2)
C. x(y^2)z
D. x(y^2)(z^2)
E. (x^2)(y^2)(z^2)


SInce xy > 0:

x = pos and y = pos

OR

x = neg and y = neg

SInce yz < 0:

y = neg and z = pos

OR

y = pos and z = neg

Thus, we have two scenarios:

1) x = pos, y = pos, and z = neg

2) x = neg, y = neg, and z = pos

Since y^2 is always positive regardless of whether y is positive or negative, we see that the product of x and z will always be negative, and thus x(y^2)z will always be negative.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 827 [0], given: 5

Re: If xy > 0 and yz < 0, which of the following must be negativ   [#permalink] 31 Aug 2017, 10:24
Display posts from previous: Sort by

If xy > 0 and yz < 0, which of the following must be negativ

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.