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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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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2013, 15:04
Hello, I am a bit confused regarding absolute value. If |x|=|2y|, then why why aren't x and 2y both positive? If the abs. value of something (i.e. it's positive value) is equal to something else, doesn't that imply that they are both positive? For example, if x=|2y| doesn't that mean that x is positive? Also, for #2, xy both have the same signs. If x and y are negative, why would |x|=|2y| become -x = -2y? I get that it's equal to |x|=|2y| but why even take that step? |-x| = |-2y| will always be positive, right? 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.
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2013, 15:22
WholeLottaLove wrote: Hello, I am a bit confused regarding absolute value. If |x|=|2y|, then why why aren't x and 2y both positive? If the abs. value of something (i.e. it's positive value) is equal to something else, doesn't that imply that they are both positive? For example, if x=|2y| doesn't that mean that x is positive? Also, for #2, xy both have the same signs. If x and y are negative, why would |x|=|2y| become -x = -2y? I get that it's equal to |x|=|2y| but why even take that step? |-x| = |-2y| will always be positive, right? 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. , or |x|\geq{0} (absolute value of x, |x|, is the distance between point x on a number line and zero, and the distance cannot be negative). So, if given that x=|2y| then x must be more than or equal to zero (RHS is non-negative thus LHS must also be non-negative). But in our case we have that |x|=|2y|. In this case x and/or y could be negative. For, example x=-2 and y=-1 --> |x|=2=|2y|. As for (2): When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|\leq{-(some \ expression)}. For example: |-5|=5=-(-5); When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|\leq{some \ expression}. For example: |5|=5. So, if x<0 and y<0, then |x|=-x and |2y|=-2y --> -x=-2y --> x=2y. If x>0 and y>0, then |x|=x and |2y|=2y --> x=2y, the same as in the first case. For more check Absolute Value chapter of Math Book: math-absolute-value-modulus-86462.htmlDS questions on absolute value to practice: search.php?search_id=tag&tag_id=37PS questions on absolute value to practice: search.php?search_id=tag&tag_id=58Tough absolute value and inequity questions with detailed solutions: inequality-and-absolute-value-questions-from-my-collection-86939.htmlHope it helps.
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2013, 16:16
Ok, so I get that Abs. value cannot be negative...distance cannot have a negative value. We are trying to solve for x-2y, so naturally we are trying to determine x-2y. So, If x=2y then the value of x-2y = 2y-2y = 0 OR If x=-2y (the absolute value of 2y) then the value of x-2y = -2y-2y = -4y, correct? I guess what throws me off is when you write When x\leq{0} then |x|=-x. What you're saying is that, for example, |-4| = -(-4) or |-4| = 4. What is the point of writing |-4| = -(-4) One final thing...In the stem you derived x=2y, x=-2y. Okay, but in #2. one of the cases is xy>0 so we could have -x and -y. If x and y are negative, doesn't that mean that you would substitute -x and y in to get -x=-2(-y) = -x=2y? I'm sorry for being such a dolt. Sometimes, concepts that I know are very simple are extremely difficult to understand. Bunuel wrote: WholeLottaLove wrote: Hello, I am a bit confused regarding absolute value. If |x|=|2y|, then why why aren't x and 2y both positive? If the abs. value of something (i.e. it's positive value) is equal to something else, doesn't that imply that they are both positive? For example, if x=|2y| doesn't that mean that x is positive? Also, for #2, xy both have the same signs. If x and y are negative, why would |x|=|2y| become -x = -2y? I get that it's equal to |x|=|2y| but why even take that step? |-x| = |-2y| will always be positive, right? 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. , or |x|\geq{0} (absolute value of x, |x|, is the distance between point x on a number line and zero, and the distance cannot be negative). So, if given that x=|2y| then x must be more than or equal to zero (RHS is non-negative thus LHS must also be non-negative). But in our case we have that |x|=|2y|. In this case x and/or y could be negative. For, example x=-2 and y=-1 --> |x|=2=|2y|. As for (2): When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|\leq{-(some \ expression)}. For example: |-5|=5=-(-5); When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|\leq{some \ expression}. For example: |5|=5. So, if x<0 and y<0, then |x|=-x and |2y|=-2y --> -x=-2y --> x=2y. If x>0 and y>0, then |x|=x and |2y|=2y --> x=2y, the same as in the first case. For more check Absolute Value chapter of Math Book: math-absolute-value-modulus-86462.htmlDS questions on absolute value to practice: search.php?search_id=tag&tag_id=37PS questions on absolute value to practice: search.php?search_id=tag&tag_id=58Tough absolute value and inequity questions with detailed solutions: inequality-and-absolute-value-questions-from-my-collection-86939.htmlHope it helps.
Last edited by WholeLottaLove on 27 May 2013, 16:28, edited 1 time in total.
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
27 May 2013, 16:26
WholeLottaLove wrote: Ok, so I get that Abs. value cannot be negative...distance cannot have a negative value.
We are trying to solve for x-2y, so naturally we are trying to determine x-2y. So,
If x=2y then the value of x-2y = 2y-2y = 0
OR
If x=-2y (the absolute value of 2y) then the value of x-2y = -2y-2y = -4y, correct?
I guess what throws me off is when you write
When x\leq{0} then |x|=-x. What you're saying is that, for example, |-4| = -(-4) or |-4| = 4. What is the point of writing |-4| = -(-4)
I'm sorry for being such a dolt. Sometimes, concepts that I know are very simple are extremely difficult to understand. Yes, that's correct: if x=2y, then x-2y=0 and if x=-2y, then x-2y=-4y. As for the red part: it's just an example of the statement that if x\leq{0} then |x|=-x.
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Re: |x|=|2y|, what is the value of x-2y? [#permalink]
29 May 2013, 03:44
|x|=|2y|, what is the value of x-2y?
(1) x+2y = 6
(2) xy>0
1) that means that x=3 and 2y=3, so difference is only 0
2) that means that x and y is not 0 and both positive or negative and x=2y, so 2y-2y=0
D
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Re: |x|=|2y|, what is the value of x-2y?
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29 May 2013, 03:44
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