It is currently 22 Feb 2018, 08:54

TODAY:

MIT Sloan Releasing 1st Wave of Interview Invites - Join GMATClub CHAT for Live Updates


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

Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43866
Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10 [#permalink]

Show Tags

New post 20 Nov 2016, 09:11
Expert's post
10
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

53% (00:51) correct 47% (01:02) wrong based on 255 sessions

HideShow timer Statistics

Expert Post
Top Contributor
2 KUDOS received
SVP
SVP
User avatar
P
Joined: 11 Sep 2015
Posts: 2055
Location: Canada
Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10 [#permalink]

Show Tags

New post 20 Nov 2016, 09:40
2
This post received
KUDOS
Expert's post
Top Contributor
1
This post was
BOOKMARKED
Bunuel wrote:
Is |2x−y|<10?

(1) 2x−y<10

(2) y−2x<10


Target question: Is |2x−y|<10?
This is a good candidate for Rephrasing the Target Question
We can take the inequality |2x−y|<10 and rewrite is as -10 < 2x−y < 10
REPHRASED target question: Is -10 < 2x−y < 10?

Aside: Here’s a video with tips on rephrasing the target question: http://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100

Statement 1: 2x−y<10
So, it's possible that 2x−y = 9 or 2x−y = 8 or 2x−y = 0 or 2x−y = -11 etc
Now consider these two conflicting cases:
case a: If 2x−y = 9, then it IS the case that -10 < 2x−y < 10
case b: If 2x−y = -11, then it is NOT the case that -10 < 2x−y < 10
Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y−2x<10
We want to know about 2x-y, so let's multiply both sides of the given inequality by -1
When we do that, we get: 2x-y > -10
Or we can write it as -10 < 2x-y
So, it's possible that 2x−y = -9 or 2x−y = -8 or 2x−y = 0 or 2x−y = 11 etc
Now consider these two conflicting cases:
case a: If 2x−y = -9, then it IS the case that -10 < 2x−y < 10
case b: If 2x−y = 11, then it is NOT the case that -10 < 2x−y < 10
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 2x−y < 10
Statement 2 tells us that -10 < 2x-y
When we COMBINE THEM, we get: -10 < 2x−y < 10
Perfect! That's the REPHRASED target question that we were trying to answer!
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer:
[Reveal] Spoiler:
C


RELATED VIDEOS





_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Intern
Intern
avatar
Joined: 24 Nov 2013
Posts: 5
Concentration: Marketing, Strategy
GPA: 3.4
WE: Information Technology (Computer Software)
Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10 [#permalink]

Show Tags

New post 20 Nov 2016, 11:14
Is |2x−y|<10?

(1) 2x−y<10

(2) y−2x<10

1. x = 4 y = 8 => 8 - 8 <10 => 0 <10 yes
x = -10 y = 8 => -10*2 -8 <10 => -28 <10 |28| > 10 no NS

2. -(2x-y)<10
x = 4 y = -8 => -(8 + 8) <10 => -16 <10 => |16| >10 no
x = 2 y = 8 => -(4 -8) <10 => 4 <10 |4| < 10 yes NS

1&2 combine
(2x-y)<10 and
-(2x-y) <10 => 2x-y>-10

C
Director
Director
User avatar
Joined: 06 May 2006
Posts: 790
Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10 [#permalink]

Show Tags

New post 20 Nov 2016, 12:01
Statement 1 and 2 are individually insufficient (obvious if you work out a few numbers), therefore A, B and D are out.

If the two statements are considered together, then definitely |2x−y|<10.

Therefore the answer is C.
_________________

Uh uh. I know what you're thinking. "Is the answer A, B, C, D or E?" Well to tell you the truth in all this excitement I kinda lost track myself. But you've gotta ask yourself one question: "Do I feel lucky?" Well, do ya, punk?

VP
VP
avatar
P
Joined: 26 Mar 2013
Posts: 1440
Reviews Badge CAT Tests
Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10 [#permalink]

Show Tags

New post 23 Apr 2017, 01:27
GMATPrepNow wrote:
Bunuel wrote:
Is |2x−y|<10?

(1) 2x−y<10

(2) y−2x<10


Statements 1 and 2 combined
Statement 1 tells us that 2x−y < 10
Statement 2 tells us that -10 < 2x-y
When we COMBINE THEM, we get: -10 < 2x−y < 10
Perfect! That's the REPHRASED target question that we were trying to answer!
Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

Answer:
[Reveal] Spoiler:
C


Dear Brent,

After combining the 2 statements, can you add them? The result will be 0<20 (number and its opposite will always yield zero). But does 0<20 have any meaning? could it help me answer the Target question?
Expert Post
Top Contributor
SVP
SVP
User avatar
P
Joined: 11 Sep 2015
Posts: 2055
Location: Canada
Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10 [#permalink]

Show Tags

New post 23 Apr 2017, 03:52
Expert's post
Top Contributor
[quote="Mo2men"
Dear Brent,

After combining the 2 statements, can you add them? The result will be 0<20 (number and its opposite will always yield zero). But does 0<20 have any meaning? could it help me answer the Target question?[/quote]

Unfortunately, that won't help us, since a number and its opposite will always add to zero.

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Image

Re: Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10   [#permalink] 23 Apr 2017, 03:52
Display posts from previous: Sort by

Is |2x−y|<10? (1) 2x−y<10 (2) y−2x<10

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


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®.