 It is currently 28 Nov 2020, 14:57 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If y + |y| = 0, which of the following  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS: Moderator  Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785  , given: 88

If y + |y| = 0, which of the following [#permalink]
1
KUDOS 00:00

Question Stats: 42% (00:21) correct 57% (00:27) wrong based on 105 sessions
If y + |y| = 0, which of the following must be true?

A. y > 0

B. Y ≥ 0

C. Y < 0

D. Y ≤ 0

E. Y = 0

src: Orbit Test Prep
[Reveal] Spoiler: OA Active Member Joined: 29 May 2018
Posts: 126
Followers: 0

Kudos [?]: 112  , given: 4

Re: If y + |y| = 0, which of the following [#permalink]
1
KUDOS
amorphous wrote:
If y + |y| = 0, which of the following must be true?

A. y > 0

B. Y ≥ 0

C. Y < 0

D. Y ≤ 0

E. Y = 0

src: Orbit Test Prep Moderator  Joined: 07 Jan 2018
Posts: 697
Followers: 11

Kudos [?]: 785  , given: 88

Re: If y + |y| = 0, which of the following [#permalink]
2
KUDOS
From the given eqn take y to the left side of the eqn we get,

|y| = - y

Hence, y = -y; only 0 satisfies the condition
or, -y = -y or y = y; Any no would satisfy the condition.

Only 0 satisfies both the condition hence, 0
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos Manager Joined: 01 Apr 2017
Posts: 61
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 78  , given: 27

Re: If y + |y| = 0, which of the following [#permalink]
1
KUDOS
|x| is always positive. Please note some absolute value properties:

1. When x ≤ 0 ,then |x| = −x . For example: |−10|= -(-10) = 10

2. When x ≥ 0 ,then |x|=x , For example |10| = 10

So,in our question we are given y+|y|=0 --> |y| = -y . This implies that y ≤ 0.

This is similar to first property. Active Member Joined: 29 May 2018
Posts: 126
Followers: 0

Kudos [?]: 112  , given: 4

Re: If y + |y| = 0, which of the following [#permalink]
2
KUDOS
PankajPatel wrote:
|x| is always positive. Please note some absolute value properties:

1. When x ≤ 0 ,then |x| = −x . For example: |−10|= -(-10) = 10

2. When x ≥ 0 ,then |x|=x , For example |10| = 10

So,in our question we are given y+|y|=0 --> |y| = -y . This implies that y ≤ 0.

This is similar to first property.

Exactly Pankaj...when I saw the options I got doubt and I was not happy with answer explanation , but I must appreciate amorphous effort.

We are given that |y| + y = 0.

Now |y| = -y .. note here |y| is always positive now in order to LHS and RHS have to be postive , RHS i.e. -y to be +ve , y values has to be
-ve.

then |y| = -(-Y)... then it'll be correct. Here y has to be < 0 .

Note : 0 is neither +ve or -ve but only even number. In that case only C can be correct. But as per absolute principle, D comes.

I want Experts to validate my explanation. Founder  Joined: 18 Apr 2015
Posts: 13916
GRE 1: Q160 V160 Followers: 315

Kudos [?]: 3683  , given: 12939

Re: If y + |y| = 0, which of the following [#permalink]
1
KUDOS
Expert's post
for y + |y| = 0 y itself must be zero.

This is a must true question.

From A to D any value does not make the sum = 0

regardless if you do know that |y| is always positive. That fact is a bit redundant to a clever student. _________________

New to the GRE, and GRE CLUB Forum?
GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ
Posting Rules: QUANTITATIVE | VERBAL
FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)
Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection
Books: All GRE Best Books
Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)
How is the GRE Score Calculated -The Definitive Guide (2021)
Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)
Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021) Manager Joined: 01 Apr 2017
Posts: 61
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 78  , given: 27

Re: If y + |y| = 0, which of the following [#permalink]
1
KUDOS
Yes msk0657. It is a MUST BE TRUE question so considering CAN BE TRUE is a trap answer while solving these type of questions.
Manager Joined: 08 Dec 2018
Posts: 94
Followers: 0

Kudos [?]: 44 , given: 30

Re: If y + |y| = 0, which of the following [#permalink]
So, as the question is asking for a MUST be true ( NOT a can be true), is the answer E Correct? pls, need undisputed solution .
Intern Joined: 04 Jan 2019
Posts: 34
Followers: 0

Kudos [?]: 21 , given: 0

Re: If y + |y| = 0, which of the following [#permalink]
jelal123 wrote:
So, as the question is asking for a MUST be true ( NOT a can be true), is the answer E Correct? pls, need undisputed solution .

Answer is D as per gmatclub. Bunuel just nailed it

Reference:
https://gmatclub.com/forum/if-y-y-0-whi ... 31099.html
Founder  Joined: 18 Apr 2015
Posts: 13916
GRE 1: Q160 V160 Followers: 315

Kudos [?]: 3683 , given: 12939

Re: If y + |y| = 0, which of the following [#permalink]
Expert's post
$$y + |y| = 0$$

We do have two case scenarios

1) if two numbers are added and the result is zero AND considering that y must be positive always

OR the other y is negative and the same of $$|y|$$ or $$|y|$$ itself is zero.

Therefore y must be $$\leq 0$$

2) $$y = |y |$$

In this case |y| is positive and to cancel out y must be < 0

Or $$y = 0$$

Therefore $$y \leq 0$$

1) + 2) $$y \leq 0$$
_________________

New to the GRE, and GRE CLUB Forum?
GRE: All you do need to know about the GRE Test | GRE Prep Club for the GRE Exam - The Complete FAQ
Posting Rules: QUANTITATIVE | VERBAL
FREE Resources: GRE Prep Club Official LinkTree Page | Free GRE Materials - Where to get it!! (2020)
Free GRE Prep Club Tests: Got 20 Kudos? You can get Free GRE Prep Club Tests
GRE Prep Club on : Facebook | Instagram

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides
3rd Party Resource's: All Quant Questions Collection | All Verbal Questions Collection
Books: All GRE Best Books
Scores: The GRE average score at Top 25 Business Schools 2020 Ed. | How to study for GRE retake and score HIGHER - (2020)
How is the GRE Score Calculated -The Definitive Guide (2021)
Tests: GRE Prep Club Tests | FREE GRE Practice Tests [Collection] - New Edition (2021)
Vocab: GRE Prep Club Official Vocabulary Lists for the GRE (2021) GRE Instructor Joined: 10 Apr 2015
Posts: 3908
Followers: 164

Kudos [?]: 4775  , given: 70

Re: If y + |y| = 0, which of the following [#permalink]
2
KUDOS
Expert's post
amorphous wrote:
If y + |y| = 0, which of the following must be true?

A. y > 0
B. y ≥ 0
C. y < 0
D. y ≤ 0
E. y = 0

The question asks "What must be true?"
So, if an answer choice is not necessarily true, we can ELIMINATE it.

Find a solution to the equation y + |y| = 0
One possible solution is y = -1, since -1 + |-1| = 0

A. -1 > 0. Not true. ELIMINATE
B. -1 ≥ 0. Not true. ELIMINATE
C. -1 < 0. True. KEEP
D. -1 ≤ 0. True. KEEP
E. -1 = 0. Not true. ELIMINATE

B and C are the REMAINING answer choices.
Now find another solution to the equation y + |y| = 0
Another possible solution is y = 0, since 0 + |0| = 0

Now check the REMAINING answer choices....
C. 0 < 0. Not true. ELIMINATE
D. 0 ≤ 0. True. KEEP

By the process of elimination (POE), the correct answer is D

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com  Re: If y + |y| = 0, which of the following   [#permalink] 04 May 2019, 07:31
Display posts from previous: Sort by

# If y + |y| = 0, which of the following  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.