|
Author |
Message |
|
TAGS:
|
|
|
VP
Status: The last round
Joined: 18 Jun 2009
Posts: 1327
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 43
Kudos [?]:
383
[3] , given: 156
|
Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
 01 Nov 2009, 08:42
3
This post received
KUDOS
Question Stats:
58% (02:29) correct
41% (01:15) wrong based on 37 sessions
|
|
|
|
|
|
|
Manager
Joined: 05 Jun 2009
Posts: 77
Followers: 1
Kudos [?]:
2
[0], given: 1
|
Re: Is |x - y|>|x - z|? [#permalink]
01 Nov 2009, 09:08
C
need to know which is more extreme and what value X is which both statements combined tell you.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9526
[23] , given: 826
|
Re: Is |x - y|>|x - z|? [#permalink]
01 Nov 2009, 09:24
23
This post received
KUDOS
Hussain15 wrote: Is |x - y|>|x - z|?
(1) |y|>|z|
(2) x < 0 Good question. I believe the answer is E. Basically the question asks whether the distance between x and y is greater than the distance between x and z? (1) |y|>|z|, means y is farther from 0 than z, which gives us the following possible cases: --y--------0---z-- or --y----z--0-- or --0----z------y or --z---0----------y-- Now depending on the position of x, the distance between x and y may or may not be greater than distance between x and z. (2) x<0. Clearly insufficient as we know nothing about y and z: ---x----0--- (1)+(2) x<0 and |y|>|z| --y------------x--0--z-- in this case |x - y|>|x - z| BUT --x--y---------z--0----- in this case |x - y|<|x - z| Two different answers, so insufficient. Answer: E.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
VP
Status: The last round
Joined: 18 Jun 2009
Posts: 1327
Concentration: Strategy, General Management
GMAT 1: 680 Q48 V34
Followers: 43
Kudos [?]:
383
[0], given: 156
|
Re: Is |x - y|>|x - z|? [#permalink]
02 Nov 2009, 00:52
Bunuel!! I think you have made the record of fastest century of kudos!! Congrats!! Great explanation! I am not sure about the answer, will post OA in a while.
_________________
[ From 470 to 680-My Story ] [ My Last Month Before Test ]
[ GMAT Prep Analysis Tool ] [ US. Business School Dashboard ] [ Int. Business School Dashboard ]
I Can, I Will
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9526
[1] , given: 826
|
1
This post received
KUDOS
|
|
|
|
|
|
Haas Thread Master
Joined: 24 Jun 2010
Posts: 141
Concentration: Strategy, Technology
Followers: 6
Kudos [?]:
14
[1] , given: 26
|
Re: Is |x - y|>|x - z|? [#permalink]
25 Aug 2010, 08:14
1
This post received
KUDOS
In general for these types of questions, if I'm testing values, are the variables different from each other.. eg should I consider the case where x = y, or x = z unless otherwise stated?
Sorry if this is a dumb question.. lol
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9526
[0], given: 826
|
Re: Is |x - y|>|x - z|? [#permalink]
25 Aug 2010, 08:28
|
|
|
|
|
|
Manager
Joined: 17 Mar 2010
Posts: 197
Followers: 2
Kudos [?]:
22
[2] , given: 9
|
Re: Is |x - y|>|x - z|? [#permalink]
02 Sep 2010, 02:02
2
This post received
KUDOS
I think we need to develop intuition for these kind of questions... from looking at question i was not able to say the answer but after looking at choices, i started to feel it must be E. After less then a minute of thinking i was sure it has to be E.
|
|
|
|
|
|
Manager
Status: Keep fighting!
Affiliations: IIT Madras
Joined: 31 Jul 2010
Posts: 239
WE 1: 2+ years - Programming
WE 2: 3+ years - Product developement,
WE 3: 2+ years - Program management
Followers: 4
Kudos [?]:
93
[2] , given: 104
|
Re: Is |x - y|>|x - z|? [#permalink]
02 Sep 2010, 02:17
2
This post received
KUDOS
It is E.
We can make out pretty quickly that these are heavily based on values of X, Y, and Z. So it has to be C or E.
You are subtracting Y and Z from a fixed value of X. Having absolute values is not going to help.
Nice post but!
Thanks.
|
|
|
|
|
|
Senior Manager
Joined: 18 Aug 2009
Posts: 441
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Followers: 4
Kudos [?]:
37
[1] , given: 16
|
Re: Is |x - y|>|x - z|? [#permalink]
06 Sep 2010, 17:25
1
This post received
KUDOS
Thank you to bunuel again! Super nice explanation!
_________________
Never give up,,,
|
|
|
|
|
|
Manager
Joined: 14 Feb 2012
Posts: 226
Followers: 1
Kudos [?]:
6
[1] , given: 7
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
23 Apr 2012, 06:49
1
This post received
KUDOS
New Approach , Bunuel Please correct me if this approach is wrong ... to find if |x-y|>|x-z| ? Squaring both sides (since both sides are +ve) (x-y)2-(x-z)2 >0 (x-y-x+z)(x-y+x-z) >0 (z-y) (2x-y-z) >0 From 1 --> Red part i negative but cant say anything about green part so insufficient. From 2 --> know nothing so insufficient from both also nothing can be concluded so E....
_________________
The Best Way to Keep me ON is to give Me KUDOS !!!
If you Like My posts please Consider giving Kudos
Shikhar
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9526
[0], given: 826
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
23 Apr 2012, 07:36
shikhar wrote: New Approach ,
Bunuel Please correct me if this approach is wrong ...
to find if |x-y|>|x-z| ?
Squaring both sides (since both sides are +ve)
(x-y)2-(x-z)2 >0
(x-y-x+z)(x-y+x-z) >0
(z-y) (2x-y-z) >0
From 1 --> Red part i negative but cant say anything about green part so insufficient.
From 2 --> know nothing so insufficient
from both also nothing can be concluded so E.... Yes, you can square both parts of the inequality (since both are non-negative) and rewrite the question: is (z-y)(2x-y-z)>0? But from |y|>|z| you can not say that z-y is negative: if y=2 and z=1 then YES but if y=-2and z=1 then NO. So, overall, I'd still suggest number line approach.
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 01 Apr 2010
Posts: 205
Followers: 1
Kudos [?]:
11
[1] , given: 4
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
23 Apr 2012, 13:28
1
This post received
KUDOS
Great explanation, I never thought of thinking of the problem in terms of positioning. Great strategy.
|
|
|
|
|
|
Manager
Joined: 03 Aug 2011
Posts: 241
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Followers: 1
Kudos [?]:
34
[1] , given: 12
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
25 Apr 2012, 20:11
1
This post received
KUDOS
bunuel, would love your feedback on my method
|x-y| > |x - z|
this applies when both signs are the same, or signs are different.
ie
|x| > |y|
-x > y
x > y
a.)
-(x-y) > x - z
-x + y > x -z
-2x > -z -y
2x < z + y
b.)
x-y > x -z
-y > -z
y < z
stmt 1:
i did the same thing here:
a.)
y > z
b.)
y < -z
or z < y < -z
which shows z is negative and not much about. in any case, x is not even mentioned so this is insufficient
stmt 2:
x < 0
again y and z are not mentioned, insufficient
stmt 1 + stmt 2:
attacking (a) from the original problem stem
y > z ?
according to stmt 1 this is false since z < y < -z.
so (a) from the stem is sufficient.
attacking (b) from the original stem
2x < y + z?
we know z < y < -z, so add a z to each
2z < y + z < 0
y+ z < 0
and x < 0
so you have
negative number * 2 < negative number
and since we don't haev any relationship between what 2x would be or y +z would be, it would be insufficient E
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9526
[0], given: 826
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
25 Apr 2012, 21:38
pinchharmonic wrote: bunuel, would love your feedback on my method
|x-y| > |x - z|
this applies when both signs are the same, or signs are different.
ie
|x| > |y|
-x > y
x > y
a.)
-(x-y) > x - z
-x + y > x -z
-2x > -z -y
2x < z + y
b.)
x-y > x -z
-y > -z
y < z
stmt 1:
i did the same thing here:
a.)
y > z
b.)
y < -z
or z < y < -z
which shows z is negative and not much about. in any case, x is not even mentioned so this is insufficient
stmt 2:
x < 0
again y and z are not mentioned, insufficient
stmt 1 + stmt 2:
attacking (a) from the original problem stem
y > z ?
according to stmt 1 this is false since z < y < -z.
so (a) from the stem is sufficient.
attacking (b) from the original stem
2x < y + z?
we know z < y < -z, so add a z to each
2z < y + z < 0
y+ z < 0
and x < 0
so you have
negative number * 2 < negative number
and since we don't haev any relationship between what 2x would be or y +z would be, it would be insufficient E There are several flows above. For example: |y|>|z| does not mean that z is negative. Consider simple example: y=2 and x=1. |y|>|z| simply means that means y is farther from 0 than z: ---y-------0--z------- (y<0<z) ---y----z--0---------- (y<z<0) -----------0--z-----y- (y>z>0) --------z--0--------y- (y>0>z)
_________________
PLEASE READ AND FOLLOW: 11 Rules for Posting!!!
RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory
COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Manager
Joined: 03 Aug 2011
Posts: 241
Location: United States
Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Followers: 1
Kudos [?]:
34
[0], given: 12
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
26 Apr 2012, 17:06
thanks bunuel, great point i'll think of this type of problem in a more conceptual manner next time
|
|
|
|
|
|
Senior Manager
Joined: 30 Jun 2011
Posts: 272
Followers: 0
Kudos [?]:
10
[0], given: 20
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
22 May 2012, 18:06
try assuming values y=3 z=2 ... x can be any no. +ve / -ve (take both cases to decide between A & C) but eventualy both did not give answer so E is correct
|
|
|
|
|
|
Intern
Joined: 22 Jan 2012
Posts: 35
Followers: 0
Kudos [?]:
6
[0], given: 0
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
22 May 2012, 20:20
I used the approach below :
1) |y|>|z| will give 4 different cases , I assumed only two
y=5 , z=2 & y=-5 , z= -2
No information about x , so x can be =+ ve or -ve , let x = 7
x-y=7-5 =2& x-z= 7-2=5
x-y=7-(-5)=12 & x-z = 7-(-2)=9
contradictory results . Insufficient
2)x<0 does not tell anything about y,z so insufficient.
1&2)
Repeating the above values y=5 , z=2 & y=-5 , z= -2
x=-3
x-y= -3+5= 2 , x-z = -3+2 = -1
x-y= -3-5= -8 , x-z= -3-2=-5
Contradictory results , Insufficient.
Hence E.
|
|
|
|
|
|
Senior Manager
Joined: 28 Dec 2010
Posts: 262
Location: India
Followers: 1
Kudos [?]:
8
[0], given: 21
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
25 May 2012, 19:58
picked E purely based on picking numbers approach. took 114 sec (1.54 min) how much time have you guys taken on this sum on avg?
|
|
|
|
|
|
Manager
Joined: 28 Jul 2011
Posts: 212
Followers: 0
Kudos [?]:
14
[0], given: 11
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0 [#permalink]
24 Jun 2012, 10:16
Voted for E
Solved it following way
(A) |Y| > |Z|
Case 1 :
---[-X =-4]-------[-Y = -3]------[-Z = -2]------[0]-------[Z = 2]-------[Y=3]-------[X=4]------
Case 2 :
---[-Y = -3]------[-Z = -2]------[-X =-1]-------[0]-------[X=1]-------[Z = 2]-------[Y=3]------
when x>0
|X-Y| = |1-3| = 2 and |X-Z| = |1-2| = 1
therefore |X-Y| > |X-Z|
|X-Y| = |4-3| = 1 and |X-Z| = |4-2| = 2
therefore |X-Y| < |X-Z|
when x<0
|X-Y| = |-1+3| = 2 and |X-Z| = |-1+2| = 1
therefore |X-Y| > |X-Z|
|X-Y| = |-4+3| = 1 and |X-Z| = |-4+2| = 2
therefore |X-Y| < |X-Z|
not sufficient
(B) X<0 dont know about Y and Z, therefore nit sufficient
(C) X < 0 and |Y| > |Z|
when x<0
|X-Y| = |-1+3| = 2 and |X-Z| = |-1+2| = 1
therefore |X-Y| > |X-Z|
|X-Y| = |-4+3| = 1 and |X-Z| = |-4+2| = 2
therefore |X-Y| < |X-Z|
[not sufficent]
therefore E
|
|
|
|
|
|
|
Re: Is |x - y|>|x - z|? (1) |y|>|z| (2) x < 0
[#permalink]
24 Jun 2012, 10:16
|
|
|
|
|
|
|
|
|
|
|
close
