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|x|=|2y|, what is the value of x-2y? [#permalink]
 27 May 2012, 08:18
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|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 ? |
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2012, 08:35
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|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.
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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| ?
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
28 May 2012, 09:09
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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).
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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.
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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
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
07 Jun 2012, 14:35
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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..
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Re: IxI = I2yI what is the value of x - 2y? [#permalink]
26 Jan 2013, 12:08
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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
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If |x| = |2y| , what is the value of x – 2y? (1) x + 2y = 6 (2) xy>0
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Here is a thread already answered by Bunnel http://gmatclub.com/forum/x-2y-what-is-the-value-of-x-2y-133307.html#p1089779 
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