|
Author |
Message |
|
TAGS:
|
|
|
Manager
Joined: 02 Jun 2011
Posts: 160
Followers: 1
Kudos [?]:
4
[2] , given: 11
|
|x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2012, 08:18
2
This post received KUDOS
Question Stats:
27% (02:55) correct
72% (01:26) wrong based on 29 sessions
|x|=|2y|, what is the value of x-2y? (1) x+2y = 6 (2) xy>0 i wish to have clarification on st. 1. x+2y = 6 if x = 2, y = 2 or if x= -2 , y = 4 then also it is '6'
do we need to keep the constraint +x = +2y while evaluating st.1 ?
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9528
[4] , given: 826
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2012, 08:35
4
This post received KUDOS
|x|=|2y|, what is the value of x-2y?First of all |x|=|2y| means that either x=2y or x=-2y. (1) x+2y = 6. Now, the second case is not possible since if x=-2y then from this statement we would have that -2y+2y=6 --> 0=6, which obviously is not true. So, we have that x=2y, in this case x-2y=2y-2y=0. Sufficient. (2) xy>0 --> x and y are either both positive or both negative, in any case |x|=|2y| becomes x=2y (if x and y are both negative then |x|=|2y| becomes -x=-2y which is the same as x=2y). Now, if x=2y then x-2y=2y-2y=0. Sufficient. Answer: D. Hope it's clear.
_________________
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: 02 Jun 2011
Posts: 160
Followers: 1
Kudos [?]:
4
[0], given: 11
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
28 May 2012, 08:57
Bunuel wrote: |x|=|2y|, what is the value of x-2y?
First of all |x|=|2y| means that either x=2y or x=-2y.
(1) x+2y = 6. Now, the second case is not possible since if x=-2y then from this statement we would have that -2y+2y=6 --> 0=6, which obviously is not true. So, we have that x=2y, in this case x-2y=2y-2y=0. Sufficient.
(2) xy>0 --> x and y are either both positive or both negative, in any case |x|=|2y| becomes x=2y (if x and y are both negative then |x|=|2y| becomes -x=-2y which is the same as x=2y). Now, if x=2y then x-2y=2y-2y=0. Sufficient.
Answer: D.
Hope it's clear. Dear Bunuel, whenever absolute value is analysed, we take two scenarios of <0 and >0. So, why the same is not considered for |x| ?
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9528
[2] , given: 826
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
28 May 2012, 09:09
2
This post received KUDOS
kashishh wrote: Bunuel wrote: |x|=|2y|, what is the value of x-2y?
First of all |x|=|2y| means that either x=2y or x=-2y.
(1) x+2y = 6. Now, the second case is not possible since if x=-2y then from this statement we would have that -2y+2y=6 --> 0=6, which obviously is not true. So, we have that x=2y, in this case x-2y=2y-2y=0. Sufficient.
(2) xy>0 --> x and y are either both positive or both negative, in any case |x|=|2y| becomes x=2y (if x and y are both negative then |x|=|2y| becomes -x=-2y which is the same as x=2y). Now, if x=2y then x-2y=2y-2y=0. Sufficient.
Answer: D.
Hope it's clear. Dear Bunuel, whenever absolute value is analysed, we take two scenarios of <0 and >0. So, why the same is not considered for |x| ? If x\leq{0} and y\leq{0} then |x|=|2y| expands as -x=-2y --> x=2y; If x\leq{0} and y>{0} then |x|=|2y| expands as -x=2y --> x=-2y; If x>{0} and y\leq{0} then |x|=|2y| expands as x=-2y; If x>{0} and y>{0} then |x|=|2y| expands as x=2y. So as you can see |x|=|2y| can expand only in two ways x=2y or x=-2y (as shown above ++ and -- are the same, and +- and -+ are the same).
_________________
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
|
|
|
|
|
|
Intern
Joined: 28 Sep 2011
Posts: 36
Location: India
WE: Consulting (Computer Software)
Followers: 1
Kudos [?]:
13
[0], given: 18
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
31 May 2012, 20:45
Tricky question.... I gave 2 much time to evaluate stmt 1 and went with A.
_________________
Kudos if you like the post!!!
|
|
|
|
|
|
Senior Manager
Joined: 13 May 2011
Posts: 326
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 16
Kudos [?]:
112
[0], given: 10
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
05 Jun 2012, 13:18
Bunuel: can we rewrite |x|=|2y| as x^2-4x^2=0 ? I have solved the problem doing so, but not sure if it algebraically correct. Below what i did:
(x-2y)(x+2y)=0
Using statement 1: (x-2y)*6=0 so, (x-2y)=0. Sufficient
Using statement 2: x=2y [same sign] (x-2y)=0. Sufficient
D
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9528
[0], given: 826
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
07 Jun 2012, 14:35
|
|
|
|
|
|
Intern
Joined: 23 Sep 2008
Posts: 24
Followers: 0
Kudos [?]:
2
[0], given: 102
|
Re: |x|=|2y|, what is the value of x-2y? [#permalink]
24 Jul 2012, 16:10
Bunuel wrote: BDSunDevil wrote: Bunuel: can we rewrite |x|=|2y| as x^2-4x^2=0 ? I have solved the problem doing so, but not sure if it algebraically correct. Below what i did:
(x-2y)(x+2y)=0
Using statement 1: (x-2y)*6=0 so, (x-2y)=0. Sufficient
Using statement 2: x=2y [same sign] (x-2y)=0. Sufficient
D Yes, you can square |x|=|2y| and write x^2=4y^2 --> (x-2y)(x+2y)=0 --> either x=2y or x=-2y the same two options as in my solution above. Hi Bunuel, I had a query regarding an official statement in the solution to this problem. Actually, the book says that , as, x+2y=6 , so a positive sum indicates that both x and 2y must be positive. However, -4+10= 10+(-4) = 6 =positive sum [both x and 2y are not positive] 10+4=14= positive sum [both x & 2y are positive] isn't it? Please clarify the confusion here..
|
|
|
|
|
|
Director
Joined: 02 Jul 2012
Posts: 753
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 19
Kudos [?]:
255
[1] , given: 45
|
Re: IxI = I2yI what is the value of x - 2y? [#permalink]
26 Jan 2013, 12:08
1
This post received KUDOS
alexpavlos wrote: IxI = I2yI what is the value of x - 2y?
1) x + 2y = 6 2) xy > 0
I can understand what to do with statement 2. Statement 1, I have no clue what to do with it!
Thanks! Alex x + 2y = 6 Hence we know that x is not equal to -2y, but |x| = |2y| So, x = 2y
_________________
Kudos Please... If my post helped.
Thanks To The Almighty - My GMAT Debrief My Own CR Question 1|My Own CR Question 2|My Own DS Question 1|My Own DS Question 2| My Own PS Question 1
|
|
|
|
|
|
Manager
Joined: 02 Sep 2012
Posts: 208
Location: United States
Concentration: Entrepreneurship, Finance
GMAT Date: 07-25-2013
GPA: 3.83
WE: Architecture (Computer Hardware)
Followers: 1
Kudos [?]:
28
[0], given: 66
|
If |x| = |2y| , what is the value of x – 2y? (1) x + 2y = 6 (2) xy>0
_________________
"Giving kudos" is a decent way to say "Thanks" and motivate contributors. Please use them, it won't cost you anything
|
|
|
|
|
|
Manager
Joined: 27 Jul 2011
Posts: 171
Followers: 0
Kudos [?]:
21
[0], given: 99
|
Here is a thread already answered by Bunnel http://gmatclub.com/forum/x-2y-what-is-the-value-of-x-2y-133307.html#p1089779
_________________
[i]Kudos not only to one who answered correctly but also to one who put the question...[/i]
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11506
Followers: 1791
Kudos [?]:
9528
[0], given: 826
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|