It is currently 21 Oct 2017, 02:13

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is |x-y| > |x| - |y|? 1) y < x 2) xy < 0

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Intern
Joined: 23 Jun 2009
Posts: 47

Kudos [?]: 28 [0], given: 6

Is |x-y| > |x| - |y|? 1) y < x 2) xy < 0 [#permalink]

### Show Tags

27 Jul 2009, 00:13
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Is |x-y| > |x| - |y|?
1) y < x
2) xy < 0

Kudos [?]: 28 [0], given: 6

Current Student
Status: What's your raashee?
Joined: 12 Jun 2009
Posts: 1837

Kudos [?]: 273 [0], given: 52

Location: United States (NC)
Concentration: Strategy, Finance
Schools: UNC (Kenan-Flagler) - Class of 2013
GMAT 1: 720 Q49 V39
WE: Programming (Computer Software)
Re: IS |X-Y| > |X| - |Y|? [#permalink]

### Show Tags

27 Jul 2009, 06:07
uzonwagba wrote:
Is |x-y| > |x| - |y|?
1) y < x
2) xy < 0

1) if y<x then we can have:
y=-3 x=-2 -> -2+3 > 2-3 ? true
y=3 x=4 ->4-3 > 4 - 3 You should notice that this will always be true
y= -3 x =2 -> 2--3 > 2- 3 -> 5>-1 ??? false
y=-3 x = 6 -> 6 - -3 > 6-3 9>3 true
INSUFF

2) x*y < 0 tells you one is negative which does not help at all...

Combine:
so now you know that y is negative since y<x so it is SUFF. C
_________________

If you like my answers please +1 kudos!

Kudos [?]: 273 [0], given: 52

Director
Joined: 05 Jun 2009
Posts: 808

Kudos [?]: 373 [0], given: 106

WE 1: 7years (Financial Services - Consultant, BA)
Re: IS |X-Y| > |X| - |Y|? [#permalink]

### Show Tags

27 Jul 2009, 09:13
IMO B

Statement 2) alone is sufficient:
--
Reasoning 1: (standard reasoning)
You can punch in numbers to try the same

Statement 1) y<x
if you take both positive
|x - y| will be equal to |x|-|Y|

if you take both negative
|x-y| will be > |x| - |y|

so not satisfactory

Statement 2) xy<0
one is +ve and other is -ve (also x and Y are not zero)
so lets assume there are two positive nos. a,b

two cases
case 1) x=a, y=-b
case 2) x=-a, y=b

LHS=|x-y|=|a-(-b)|=a+b
RHS=|x|-|y| = a-b
for two positive nos. (a+b)>a-b
LHS>RHS

case 2)
LHS=|x-y|=|-a-b|=a+b
RHS=|x|-|y|=a-b
LHS>RHS again

Satisfactory condition hence, B

------------------------------
Other Reasoning: If you want to see it
Little complex (not needed mostly)
------------------------------
LHS=|x-y|
RHS=|x|-|y|

LHs>=0
RHS can be positive and negative, so lets take cases

case 1) RHS < 0
==> LHS>RHS (no need to further check) [satisfy condition]
case 2) RHS=0
==> LHS=RHS when x,y both are of same sign [not satisfy]
==> LHS>RHS when x,y are of opposite signs (e.g. -5, 5) [satisfy]
case 3) RHS >0

as both sides are >0 we can square them, plus keeping the sign of inequality same as '>'

LHS^2=x^2+y^2-2xy
RHS^2=x^2+y^2-2|x||y|
subtract 2nd from 1st
2(|x||y|-xy) >0
which will be true only when xy<0 and (x,y not equal to 0, ***this is included in the condition xy<0)

II satisfy.
_________________

Consider kudos for the good post ...
My debrief : http://gmatclub.com/forum/journey-670-to-720-q50-v36-long-85083.html

Kudos [?]: 373 [0], given: 106

Manager
Joined: 21 Jun 2009
Posts: 151

Kudos [?]: 11 [0], given: 1

Re: IS |X-Y| > |X| - |Y|? [#permalink]

### Show Tags

27 Jul 2009, 10:37
IMO B.
Just use a list of values for (x,y) -> (3,2),(0,-1), (-3,-5), (4,-3)
Statement 1 will not hold for all
Statement 2 will hold for all.

Kudos [?]: 11 [0], given: 1

Re: IS |X-Y| > |X| - |Y|?   [#permalink] 27 Jul 2009, 10:37
Display posts from previous: Sort by

# Is |x-y| > |x| - |y|? 1) y < x 2) xy < 0

 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®.