GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Jan 2019, 02:45

### 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

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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

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

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

### Hide Tags

Manager
Joined: 18 Feb 2015
Posts: 85
If |x| = |y| and xy = 0, which of the following must be true?  [#permalink]

### Show Tags

Updated on: 27 Nov 2017, 20:36
7
00:00

Difficulty:

5% (low)

Question Stats:

87% (00:56) correct 13% (01:38) wrong based on 436 sessions

### HideShow 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. $$\frac{1}{x}+\frac{1}{y}=\frac{1}{2}$$

Originally posted by HarveyKlaus on 22 Jan 2016, 11:51.
Last edited by Bunuel on 27 Nov 2017, 20:36, edited 5 times in total.
Reformatted the question
CEO
Joined: 20 Mar 2014
Posts: 2636
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If |x| = |y| and xy = 0, which of the following must be true?  [#permalink]

### Show Tags

22 Jan 2016, 12:04
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.
Manager
Joined: 21 Jun 2017
Posts: 83
Re: If |x| = |y| and xy = 0, which of the following must be true?  [#permalink]

### Show Tags

13 Oct 2017, 07:22
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)
Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If |x| = |y| and xy = 0, which of the following must be true?  [#permalink]

### Show Tags

27 Nov 2017, 18:08
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.

_________________

Jeffery Miller
Head of GMAT Instruction

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

Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1299
Location: India
WE: Engineering (Other)
If |x| = |y| and xy = 0, which of the following must be true?  [#permalink]

### Show Tags

27 Mar 2018, 05:00
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.

Retired Moderator
Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
Re: If |x| = |y| and xy = 0, which of the following must be true?  [#permalink]

### Show Tags

27 Mar 2018, 05:29
1
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.

|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
Re: If |x| = |y| and xy = 0, which of the following must be true? &nbs [#permalink] 27 Mar 2018, 05:29
Display posts from previous: Sort by

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

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

 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®.