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

It is currently 20 Oct 2019, 02:12

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

If y is an integer and y = |x| + x, is y = 0?

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 10 Sep 2010
Posts: 110
If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 14 Dec 2010, 22:03
4
2
15
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

50% (01:21) correct 50% (01:11) wrong based on 501 sessions

HideShow timer Statistics

If y is an integer and y = |x| + x, is y = 0?

(1) x < 0
(2) y < 1
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58443
If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 21 Feb 2012, 22:19
7
10

9. Inequalities



For more check Ultimate GMAT Quantitative Megathread


_________________
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58443
If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 15 Dec 2010, 01:50
4
2
If y is an integer and y = |x| + x, is y = 0?

Notice that from \(y=|x|+x\) it follows that y cannot be negative:
If \(x>0\), then \(y=x+x=2x=2*positive=positive\);
If \(x\leq{0}\) (when x is negative or zero) then \(y=-x+x=0\).

(1) \(x<0\) --> \(y=|x|+x=-x+x=0\). Sufficient.

(2) \(y<1\). We found out above that y cannot be negative and we are given that y is an integer, hence \(y=0\). Sufficient.

Answer: D.

Also discussed in Inequality and absolute value questions from my collection: http://gmatclub.com/forum/inequality-an ... 86939.html

Hope it's clear.
_________________
Most Helpful Community Reply
Manager
Manager
User avatar
Joined: 25 Aug 2011
Posts: 135
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 21 Feb 2012, 22:07
2
13
If y is an integer and y = |x| + x, is y = 0?

(1) x < 0
(2) y < 1


I rephrased the original question as Is x<0?
Statement 1 : SF
Statement II : if y<1; x+|x|<1..on solving we get 2 ranges for x
- X<0 or,
- 0<X<0.5
Basis this II is insufficient.. Where am I going wrong ?
General Discussion
Director
Director
User avatar
Joined: 03 Sep 2006
Posts: 639
GMAT ToolKit User
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 14 Dec 2010, 22:39
1
Each of (1) and (2) are sufficient to answer the question. Thus the answer should be "D".
From(1), any value of X<0, whether it's integer or fraction will lead to Y = 0 because the mode function will result in positive value and positive value added to same negative value will result in Zero.
From (2), We can have Y as negative Integer ( -1,-2....) if and only if the Right hand side of equation is different. It's just adding the same X and it can't lead to the negative value.

Yes it can definitely lead to the Zero.

Thus Answer should be D.

You can plug and play certain values ( numbers ) in order to verify the above.
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9704
Location: Pune, India
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 16 Dec 2010, 06:51
Fijisurf wrote:
I am sure it is posted somewhere on the forum already , I just can't find it.


If y is an integer and y=|x|+x, is y=0?

(1)x<0
(2)y<1


A word of caution: When you read "If y is an integer and y=|x|+x", analyze it there and then. y can be a positive integer when x is positive, y will be 0 when x is negative and y will be 0 when x is 0."
Another important point to note here: When the author puts in extra effort to write "y is an integer" rather than "x and y are integers" , take special note that x may not be an integer. Not that it matters very much here but in many questions such a statement will have special significance.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
User avatar
Joined: 25 Aug 2011
Posts: 135
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 21 Feb 2012, 22:43
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58443
Re: If y is an integer and y = |x| + x, is y = 0?  [#permalink]

Show Tags

New post 21 Feb 2012, 23:35
devinawilliam83 wrote:
Bunuel,why didn't i get it with the way i solved it?
Am unable to understand where my approach is wrong . Thanks


You forgot that it's given that y=integer. (2) says y<1, thus |x|+x must also be some integer less than 1: 0, -1, ... but if you refer to my solution you'll see that |x|+x can never be negative, so the only valid solution for |x|+x (or which is the same for y) is 0.

Hope it's clear.
_________________
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 13295
Re: If y is an integer and y =|x| + x, is y =0? 1.x<0  [#permalink]

Show Tags

New post 17 Oct 2019, 02:57
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 Club Bot
Re: If y is an integer and y =|x| + x, is y =0? 1.x<0   [#permalink] 17 Oct 2019, 02:57
Display posts from previous: Sort by

If y is an integer and y = |x| + x, is y = 0?

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





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