NEW HERE? LEARN MORE
closeclose
It is currently 03 Oct 2023, 15:48
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

If |x| = |y| and xy = 0, which of the following must be true?

6 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
avatar
HarveyKlaus
Manager
Manager
Joined: 18 Feb 2015
Posts: 71
If |x| = |y| and xy = 0, which of the following must be true? [#permalink] New post  Updated on: 27 Nov 2017, 21:36
2
Kudos
13
Bookmarks
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

89% (00:53) correct 11% (01:33) wrong based on 829 sessions

Hide Show timer Statistics

If |x| = |y| and xy = 0, which of the following must be true?


A \(xy^2>0\)

B. \(x^2y>0\)

C. \(x+y=0\)

D. \(\frac{x}{(y+1)}=2\)

E. \(\frac{1}{x}+\frac{1}{y}=\frac{1}{2}\)
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

Originally posted by HarveyKlaus on 22 Jan 2016, 12:51.
Last edited by Bunuel on 27 Nov 2017, 21:36, edited 5 times in total.
Reformatted the question
Quiz Dashboard Attempt only this question Same topic and source Same topic and difficulty Same source and difficulty Random Chronological Reverse chronological Learn more
User avatar
G
ENGRTOMBA2018
SVP
SVP
Joined: 20 Mar 2014
Posts: 2380
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
GMAT ToolKit User Reviews Badge
Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink] New post  22 Jan 2016, 13:04
HarveyKlaus wrote:
If lXl = lYl and XY=0, which of the following must be true?

A \(xy^2>0\)
B. \(x^2y>0\)
C. \(x+y=0\)
D. \(x/(y+1)=2\)
E. \(1/x+1/y=1/2\)


Follow posting guidelines, including proper formatting of the question.

For the question, confirm that you have transcribed option E correctly.

You are given that |x| = |y| and xy = 0. For a MUST BE TRUE question, make sure to use POE for the options as the only option remaining will be true for ALL possible cases.

xy=0 ---> either x=0 and y \(\neq\) 0 or y=0 and x \(\neq\) 0 or both x =y=0. for the sake of simplicity, I will choose the case when x=y=0 and this also satisfies |x|=|y|.

Substitute x=y=0 in the options A-D and see which one remains true.

A \(xy^2>0\) . Not true. Eliminate
B. \(x^2y>0\). Not true. Eliminate
C. \(x+y=0\). True . Keep.
D. \(x/(y+1)=2\). x/(y+1) = 0 \(\neq\) 2. Eliminate.
E. \(1/x+1/y=1/2\). Not true. Eliminate. The only way you are going to get 1/x + 1/y = 1/2 is when you have x=y=1 . Although you will satisfy |x|=|y| , xy \(\neq\) 0. Thus eliminate this option.

Hence C is the correct answer.

Hope this helps.
_________________
My Kellogg Journey (2016-2018): https://gmatclub.com/forum/my-kellogg-journey-325661.html
Thursday with Ron updated list as of July 1st, 2015: https://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: https://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: https://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: https://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: https://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: https://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: https://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html
Signature Read More
User avatar
B
CyberStein
Manager
Manager
Joined: 21 Jun 2017
Posts: 61
Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink] New post  13 Oct 2017, 08:22
2
Kudos
HarveyKlaus wrote:
If |x| = |y| and xy = 0, which of the following must be true?

A \(xy^2>0\)
B. \(x^2y>0\)
C. \(x+y=0\)
D. \(x/(y+1)=2\)
E. \(1/x+1/y=1/2\)



Any number multiplied by zero, gives the product zero. Since the absolute value of 0 is 0, and |x| = |y|, x,y = 0

Therefore, x + y = 0 is the only answer that must be true.
(C)
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3025
Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink] New post  27 Nov 2017, 19:08
Expert Reply
HarveyKlaus wrote:
If |x| = |y| and xy = 0, which of the following must be true?

A \(xy^2>0\)
B. \(x^2y>0\)
C. \(x+y=0\)
D. \(x/(y+1)=2\)
E. \(1/x+1/y=1/2\)


Since |x| = |y| and xy = 0, both x and y must be zero.

Thus, we see that A and B are not true, because both answers are equal to zero.

C, however, must be true because 0 + 0 = 0.

Answer: C
_________________
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Signature Read More
User avatar
L
adkikani
IIM School Moderator
Joined: 04 Sep 2016
Posts: 1282
Location: India
WE:Engineering (Other)
If |x| = |y| and xy = 0, which of the following must be true? [#permalink] New post  27 Mar 2018, 06:00
Bunuel niks18 chetan2u pushpitkc

Quote:
If |x| = |y| and xy = 0, which of the following must be true?


A \(xy^2>0\)

B. \(x^2y>0\)

C. \(x+y=0\)

D. \(\frac{x}{(y+1)}=2\)

E. \(\frac{1}{x}+\frac{1}{y}=\frac{1}{2}\)


Can you explain solving modulus on both sides of equality if it was a PS problem.

|x| = |y|

Do I definitely need to know if x or y is positive or negative?

I approached in below manner:

If product of two numbers x and y is zero, then EITHER of x or y is zero, or
BOTH x and y are zero.

With this logic, A,B and E are out. (Since this is PS problem ALL of above
conditions must be satisfied.)

For D, if x = 0 then RHS = 2 is Not satisfied, since LHS = 0
If y = 0 , then |0| = 0 LHS = 0/1 or 0, RHS = 2. Not satisfied.

Let me know if my steps are correct.
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Signature Read More
User avatar
D
niks18
Retired Moderator
Joined: 25 Feb 2013
Posts: 930
Location: India
GPA: 3.82
GMAT ToolKit User Reviews Badge
Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink] New post  27 Mar 2018, 06:29
1
Kudos
adkikani wrote:
Bunuel niks18 chetan2u pushpitkc

Quote:
If |x| = |y| and xy = 0, which of the following must be true?


A \(xy^2>0\)

B. \(x^2y>0\)

C. \(x+y=0\)

D. \(\frac{x}{(y+1)}=2\)

E. \(\frac{1}{x}+\frac{1}{y}=\frac{1}{2}\)


Can you explain solving modulus on both sides of equality if it was a PS problem.

|x| = |y|

Do I definitely need to know if x or y is positive or negative?

I approached in below manner:

If product of two numbers x and y is zero, then EITHER of x or y is zero, or
BOTH x and y are zero.

With this logic, A,B and E are out. (Since this is PS problem ALL of above
conditions must be satisfied.)

For D, if x = 0 then RHS = 2 is Not satisfied, since LHS = 0
If y = 0 , then |0| = 0 LHS = 0/1 or 0, RHS = 2. Not satisfied.

Let me know if my steps are correct.


Hi adkikani

|x|=|y| implies magnitude of x and y are equal irrespective of their sign. For e.g. if x=2 and y=-2 then also |x|=|y|.

As you rightly mentioned xy =0 so either of the two has to be 0 but here as their magnitude are same so both x & y has to be 0

Only option C is valid in this case

Posted from my mobile device
GMAT Club Bot
gmatclubot
Re: If |x| = |y| and xy = 0, which of the following must be true? [#permalink]
27 Mar 2018, 06:29
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderators:
Bunuel
Math Expert
89459 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions