Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 01 Sep 2015, 08:24

### 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 June
Open Detailed Calendar

# Is |x-y|>|x|-|y|

 Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Manager
Joined: 18 Mar 2010
Posts: 89
Location: United States
GMAT 1: Q V
Followers: 2

Kudos [?]: 35 [2] , given: 5

Is |x-y|>|x|-|y| [#permalink]  13 Nov 2011, 16:29
2
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

53% (02:08) correct 47% (01:17) wrong based on 1062 sessions
Is |x-y|>|x|-|y| ?

(1) y < x
(2) xy < 0
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50013 [12] , given: 7519

Re: Is |x-y|>|x|-|y| [#permalink]  14 Jan 2012, 11:56
12
KUDOS
Expert's post
16
This post was
BOOKMARKED
mmphf wrote:
Is |x-y|>|x|-|y| ?

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

Is |x-y|>|x|-|y|?

Probably the best way to solve this problem is plug-in method. Though there are two properties worth to remember:
1. Always true: $$|x+y|\leq{|x|+|y|}$$, note that "=" sign holds for $$xy\geq{0}$$ (or simply when $$x$$ and $$y$$ have the same sign);

2. Always true: $$|x-y|\geq{|x|-|y|}$$, note that "=" sign holds for $$xy>{0}$$ (so when $$x$$ and $$y$$ have the same sign) and $$|x|>|y|$$ (simultaneously). (Our case)

So, the question basically asks whether we can exclude "=" scenario from the second property.

(1) y < x --> we can not determine the signs of $$x$$ and $$y$$. Not sufficient.
(2) xy < 0 --> "=" scenario is excluded from the second property, thus $$|x-y|>|x|-|y|$$. Sufficient.

_________________
Manager
Joined: 16 Dec 2009
Posts: 75
GMAT 1: 680 Q49 V33
WE: Information Technology (Commercial Banking)
Followers: 1

Kudos [?]: 33 [5] , given: 11

Re: Is |x-y|>|x|-|y| [#permalink]  25 Nov 2011, 14:00
5
KUDOS

Here's how I did it.

|x-y| has a range of possible values , min being |x|-|y| and max being |x|+|y|

Statement 1 : x>y . Scenarioes :- x=+ve , y=-ve , |x-y|= |x|+|y| ;
x=+ve , y=+ve , |x-y|=|x|-|y| ;
x=-ve , y=-ve , |x-y|= |-(x-y)|=|x|-|y|

So we cannot definitely say that |x-y| is greater than |x|-|y| because the min value for |x-y| is also |x|-|y|. So, statement 1 is not sufficient.

Statement 2 : xy<0 . Scenarios :- x=+ve , y=-ve , |x-y|= |x|+|y|;
x=-ve , y=+ve , |x-y| = |-(|x|+|y|)|=|x|+|y|.

Now we know |x| + |y| is definitely greater than |x|-|y|. So statement (2) is sufficient.
_________________

If Electricity comes from Electrons , Does Morality come from Morons ??

If you find my post useful ... then please give me kudos ......

h(n) defined as product of even integers from 2 to n
Number N divided by D leaves remainder R
Ultimate list of MBA scholarships for international applicants

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5863
Location: Pune, India
Followers: 1481

Kudos [?]: 7970 [4] , given: 190

Re: Is |x-y|>|x|-|y| [#permalink]  30 Nov 2011, 02:57
4
KUDOS
Expert's post
Funny, but I remember form university that |a-b|>||a|-|b||>|a|-|b|, therefore the above inequality is valid for all numbers a,b can somebody verify the inequality?

http://math.ucsd.edu/~wgarner/math4c/de ... nequal.htm

If you notice, you have missed the 'equal to' sign.
Generalizing,$$|a-b|\geq|a|-|b|$$

In some cases, the equality will hold.
e.g. a = 3, b = 2
You get 1 = 1

In others, the inequality will hold.
e.g. a = -3, b = 4
7 > -1

In this question, you have to figure out whether the inequality will hold.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 29173 Followers: 4736 Kudos [?]: 50013 [3] , given: 7519 Re: Is |x-y|>|x|-|y| [#permalink] 14 Jan 2012, 12:18 3 This post received KUDOS Expert's post 3 This post was BOOKMARKED someone79 wrote: This is a very simple question. !x-y!>|x|-|y| can only happen if both the numbers are of different signs. If xy<0 then these numbers are of opposite signs. Hope this clears. X=2 y=3 then |x-y|=|x|-|y| if x=-2 and y = 3 then |x-y|>|x|-|y| Red part is not correct $$|x-y|>{|x|-|y|}$$ also holds true when $$x$$ and $$y$$ have the same sign and the magnitude of $$y$$ is more than that of $$x$$ (so for $$|y|>|x|$$). Example: $$x=2$$ and $$y=3$$ --> $$|x-y|=1>-1={|x|-|y|}$$; $$x=-2$$ and $$y=-3$$ --> $$|x-y|=1>-1={|x|-|y|}$$. Actually the only case when $$|x-y|>{|x|-|y|}$$ does not hold true is when $$xy>{0}$$ (so when $$x$$ and $$y$$ have the same sign) and $$|x|>|y|$$ (simultaneously). In this case $$|x-y|={|x|-|y|}$$ (as shown in my previous post). Example: $$x=3$$ and $$y=2$$ --> $$|x-y|=1={|x|-|y|}$$; $$x=-3$$ and $$y=-2$$ --> $$|x-y|=1={|x|-|y|}$$. Hope it's clear. _________________ Intern Status: Stay Hungry, Stay Foolish. Joined: 05 Sep 2011 Posts: 41 Location: India Concentration: Marketing, Social Entrepreneurship GMAT 1: 650 Q V Followers: 2 Kudos [?]: 8 [2] , given: 6 Re: Is |x-y|>|x|-|y| [#permalink] 14 Nov 2011, 12:02 2 This post received KUDOS Statement 1) x>y. therefore, x-y>0. Plug & Play Method. (x,y)- (-3,-6) .Satisfies. (x,y)- (3,-6). Satisfies. (x-y)- (3,6). Does not Satisfy. Equality exists. Statement 2) xy<0. This means, either, x>0 and y<0. OR. x<0 and y>0. Looking the values plugged in statement 1. It satisfies the condition of statement two. Hence, B. Senior Manager Joined: 07 Nov 2009 Posts: 313 Followers: 6 Kudos [?]: 244 [1] , given: 20 Re: Is |x – y| > |x| – |y|? [#permalink] 18 Mar 2012, 00:46 1 This post received KUDOS subhashghosh wrote: (1) Y = -1, x = 0 Then, | 0 – (-1)| = 1 |0| - |-1| = -1 Y = 0, x = 1 Both |x-y| = |x| - |y| = 1 (2) Xy < 0, so one of them is < 0 So if we take the case x = -1, y = 1 Then |x – y| = |-2| = 2 and |x| - |y| = 1 – 1 = 0 Again, if x = 5 , y = -1 Then |x – y| = |6| = 6 and |x| - |y| = 5 – 1 = 4 So both 1 and 2 are insuff. Combine them -> It is obvious that y < 0 and x > 0, so by adding a negative sign the magnitude increases and on the right side the magnitude will be less as the difference is between two positive numbers (i.e. the modulus values). e.g. x = 2, y = -5 |x – y| = |7| and |x| - |y| = 2 – 5 = -3 So |x – y| > |x| - |y| Answer - C But in both the examples, its being shown that case 2 is sufficient. Am i mistaken? Intern Joined: 21 Mar 2011 Posts: 6 Followers: 0 Kudos [?]: 1 [1] , given: 17 Re: Is |x-y|>|x|-|y| [#permalink] 31 Mar 2012, 14:00 1 This post received KUDOS I found talking through this one to be helpful. Namely: |x-y| represents the distance between x and y on the number line. |x|-|y|, on the other hand, first takes the absolute value of both numbers - and thereby moving them both to the positive side of the number line - and THEN calculates the difference between x and y Visually, it makes sense that if x and y are of different signs (for example, x=-5, y=5), then the difference between the two numbers on a number line is greater if measured before moving them both to the positive side of the number line. At this point I logically deduced that it is impossible for |x-y| to be less than |x|-|y|. I also deduced at this point that if x and y have the same sign, it does not matter when the absolute value is taken because the difference between them will be the same either way. After this thought process, the problem becomes much easier. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5863 Location: Pune, India Followers: 1481 Kudos [?]: 7970 [1] , given: 190 Re: Is |x-y|>|x|-|y| [#permalink] 25 Mar 2013, 04:29 1 This post received KUDOS Expert's post kancharana wrote: mmphf wrote: Is |x-y|>|x|-|y| ? (1) y < x (2) xy < 0 How it is B? Did they mention that X and Y are integers? No right, the answer should be E. If they provide details about X and Y as integers then it will be B otherwise it will be E. can anyone help me about the scenario whether we consider fractions or not in this case? Scenario: x=1/2, y=1/3 ==> |1/2-1/3|=1/6 and |1/2|-|1/3|=1/6 It is B because if you use the data of statement 2, you can say, "Yes, |x-y| is greater than |x|-|y|" (2) xy < 0 This means that one of x and y is positive and the other is negative. You cannot take x = 1/2 and y = 1/3. It is not about fractions/integers. It is about positive/negative numbers (most mod questions are about positive/negative numbers) When xy < 0, |x-y|>|x|-|y| always holds. Only when x and y both are positive or both are negative and |x|>|y|, then |x-y|=|x|-|y| _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 5863
Location: Pune, India
Followers: 1481

Kudos [?]: 7970 [1] , given: 190

Re: Is |x-y|>|x|-|y| [#permalink]  06 Aug 2013, 21:25
1
KUDOS
Expert's post
kancharana wrote:
mmphf wrote:
Is |x-y|>|x|-|y| ?

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

How it is B? Did they mention that X and Y are integers? No right, the answer should be E. If they provide details about X and Y as integers then it will be B otherwise it will be E.

can anyone help me about the scenario whether we consider fractions or not in this case?

Scenario:

x=1/2, y=1/3 ==> |1/2-1/3|=1/6 and |1/2|-|1/3|=1/6

Fractions and integers have no role to play here. Check Bunuel's post above.

Whenever xy < 0, i.e. x is negative but y is positive OR x is positive but y is negative, |x-y| is greater than |x|-|y|.

e.g. x = -1/2, y = 1/3
|x-y| = |-1/2-1/3| = 5/6
|x|-|y| = 1/2 - 1/3 = 1/6

So |x - y| > |x|-|y|

Do you see the logic here? If one of x and y is positive and the other is negative, in |x - y|, absolute values of x and y get added and the sum is positive. While in |x|-|y|, the absolute values are subtracted.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 06 Jun 2009 Posts: 6 Followers: 0 Kudos [?]: 1 [1] , given: 11 Re: Is |x-y|>|x|-|y| [#permalink] 08 Jul 2014, 03:53 1 This post received KUDOS Is this a valid approach to solve this problem? | X –Y | > |X| - |Y| Squaring both sides (X-Y)^2>(|X|-|Y|)^2 X^2-2XY+Y^2>X^2-2|XY|+Y^2 -XY>|XY| XY<|XY| --> Can be true only for XY < 0. 1 : y > X - Insufficient 2 : XY < 0 -> Sufficient. Hence, (B). Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 5863 Location: Pune, India Followers: 1481 Kudos [?]: 7970 [1] , given: 190 Is |x-y|>|x|-|y| [#permalink] 16 Nov 2014, 21:22 1 This post received KUDOS Expert's post mmphf wrote: Is |x-y|>|x|-|y| ? (1) y < x (2) xy < 0 Responding to a pm: You can solve this question easily if you understand some basic properties of absolute values. They are discussed in detail here: http://www.veritasprep.com/blog/2014/02 ... -the-gmat/ One of the properties is (II) For all real x and y, $$|x - y| \geq |x| - |y|$$ $$|x - y| = |x| - |y|$$ when (1) x and y have the same sign and x has greater (or equal) absolute value than y (2) y is 0 $$|x - y| > |x| - |y|$$ in all other cases Question: Is |x-y|>|x|-|y|? We need to establish whether the "equal to" sign can hold or not. (1) y < x Doesn't tell us whether they have the same sign or opposite. So we don't know whether the equal to sign will hold or greater than. Not sufficient. (2) xy < 0 Tells us that one of x and y is positive and the other is negative (they do not have same sign). Also tells us that neither x nor y is 0. Hence, the "equal to" sign cannot hold. Sufficient to answer 'Yes' Answer (B) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Senior Manager
Joined: 11 May 2011
Posts: 373
Location: US
Followers: 3

Kudos [?]: 64 [0], given: 46

Re: Is |x-y|>|x|-|y| [#permalink]  13 Nov 2011, 17:45
mmphf wrote:
Is |x-y|>|x|-|y| ?

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

My Answer is E. Lets check this with pluy and play method.
Consider -
x= 5 and y = 2 -> 3 > 3
x= 2 and y = -2 -> 4 > 0
A not sufficient.

Consider -
x= 5 and y = 2 -> 3 > 3
x= -2 and y = -5 -> 3 > -3
B not sufficient.

Cheers!
_________________

-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------

Intern
Status: Princess of Economics
Joined: 13 Nov 2011
Posts: 8
Concentration: Economics
GMAT 1: 700 Q V
Followers: 0

Kudos [?]: 5 [0], given: 0

Re: Is |x-y|>|x|-|y| [#permalink]  25 Nov 2011, 12:12
Capricorn369 wrote:
mmphf wrote:
Is |x-y|>|x|-|y| ?

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

My Answer is E. Lets check this with pluy and play method.
Consider -
x= 5 and y = 2 -> 3 > 3
x= 2 and y = -2 -> 4 > 0
A not sufficient.

Consider -
x= 5 and y = 2 -> 3 > 3
x= -2 and y = -5 -> 3 > -3
B not sufficient.

Cheers!

Capricorn, in your explanation you plug in x=-2 and y=-5 for B. Check the problem one more time. Part B says that either x or y is negative, not both.
Intern
Joined: 06 Sep 2011
Posts: 20
GMAT 1: 670 Q42 V40
GMAT 2: 750 Q50 V42
Followers: 0

Kudos [?]: 9 [0], given: 4

Re: Is |x-y|>|x|-|y| [#permalink]  30 Nov 2011, 00:16
Funny, but I remember form university that |a-b|>||a|-|b||>|a|-|b|, therefore the above inequality is valid for all numbers a,b can somebody verify the inequality?

http://math.ucsd.edu/~wgarner/math4c/de ... nequal.htm
_________________

Persistence.

Manager
Joined: 14 Dec 2011
Posts: 182
GMAT 1: 730 Q50 V39
GMAT 2: Q V
GPA: 3.9
Followers: 1

Kudos [?]: 36 [0], given: 13

Re: Is |x-y|>|x|-|y| [#permalink]  14 Jan 2012, 12:02
This is a very simple question. !x-y!>|x|-|y| can only happen if both the numbers are of different signs.

If xy<0 then these numbers are of opposite signs. Hope this clears.

X=2 y=3 then |x-y|=|x|-|y|
if x=-2 and y = 3 then |x-y|>|x|-|y|
Manager
Joined: 14 Dec 2011
Posts: 182
GMAT 1: 730 Q50 V39
GMAT 2: Q V
GPA: 3.9
Followers: 1

Kudos [?]: 36 [0], given: 13

Re: Is |x-y|>|x|-|y| [#permalink]  14 Jan 2012, 13:52
Bunuel wrote:
someone79 wrote:
This is a very simple question. !x-y!>|x|-|y| can only happen if both the numbers are of different signs.

If xy<0 then these numbers are of opposite signs. Hope this clears.

X=2 y=3 then |x-y|=|x|-|y|
if x=-2 and y = 3 then |x-y|>|x|-|y|

Red part is not correct $$|x-y|>{|x|-|y|}$$ also holds true when $$x$$ and $$y$$ have the same sign and the magnitude of $$y$$ is more than that of $$x$$ (so for $$|y|>|x|$$). Example:
$$x=2$$ and $$y=3$$ --> $$|x-y|=1>-1={|x|-|y|}$$;
$$x=-2$$ and $$y=-3$$ --> $$|x-y|=1>-1={|x|-|y|}$$.

Actually the only case when $$|x-y|>{|x|-|y|}$$ does not hold true is when $$xy>{0}$$ (so when $$x$$ and $$y$$ have the same sign) and $$|x|>|y|$$ (simultaneously). In this case $$|x-y|={|x|-|y|}$$ (as shown in my previous post). Example:
$$x=3$$ and $$y=2$$ --> $$|x-y|=1={|x|-|y|}$$;
$$x=-3$$ and $$y=-2$$ --> $$|x-y|=1={|x|-|y|}$$.

Hope it's clear.

thanks. I missed that
Manager
Joined: 14 Dec 2010
Posts: 58
Followers: 0

Kudos [?]: 1 [0], given: 4

Re: Is |x-y|>|x|-|y| [#permalink]  19 Jan 2012, 07:48
Awesom explanation Bynuel..Kudos
SVP
Joined: 16 Nov 2010
Posts: 1676
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 374 [0], given: 36

Re: Is |x – y| > |x| – |y|? [#permalink]  17 Mar 2012, 23:56
(1) Y = -1, x = 0

Then, | 0 – (-1)| = 1
|0| - |-1| = -1

Y = 0, x = 1

Both |x-y| = |x| - |y| = 1

(2) Xy < 0, so one of them is < 0

So if we take the case x = -1, y = 1
Then |x – y| = |-2| = 2 and |x| - |y| = 1 – 1 = 0

Again, if x = 5 , y = -1
Then |x – y| = |6| = 6 and |x| - |y| = 5 – 1 = 4

So both 1 and 2 are insuff.

Combine them -> It is obvious that y < 0 and x > 0, so by adding a negative sign the magnitude increases and on the right side the magnitude will be less as the difference is between two positive numbers (i.e. the modulus values).

e.g. x = 2, y = -5

|x – y| = |7| and |x| - |y| = 2 – 5 = -3

So |x – y| > |x| - |y|
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

SVP
Joined: 16 Nov 2010
Posts: 1676
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 31

Kudos [?]: 374 [0], given: 36

Re: Is |x – y| > |x| – |y|? [#permalink]  18 Mar 2012, 00:54
Sorry, was in a scatterbrained state then , I think you're right. I just didn't do this problem in a focused manner.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Re: Is |x – y| > |x| – |y|?   [#permalink] 18 Mar 2012, 00:54

Go to page    1   2   3    Next  [ 43 posts ]

Similar topics Replies Last post
Similar
Topics:
2 Is xy + xy < xy ? 1 17 Jun 2014, 18:45
8 Is xy + xy < xy ? 7 02 Mar 2013, 12:03
3 Is xy > x/y? 9 02 Dec 2011, 03:36
4 Is xy > x/y? 6 25 Feb 2011, 07:15
6 Is |x-y| = ||x|-|y|| 19 05 Oct 2009, 08:52
Display posts from previous: Sort by

# Is |x-y|>|x|-|y|

 Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO 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®.