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x=2y, what is the value of x2y? [#permalink]
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x=2y, what is the value of x2y? (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 x2y? [#permalink]
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x=2y, what is the value of x2y?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 \(x2y=2y2y=0\). 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 \(x2y=2y2y=0\). Sufficient. Answer: D. Hope it's clear.
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Re: x=2y, what is the value of x2y? [#permalink]
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28 May 2012, 08:57
Bunuel wrote: x=2y, what is the value of x2y?
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 \(x2y=2y2y=0\). 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 \(x2y=2y2y=0\). 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 x2y? [#permalink]
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kashishh wrote: Bunuel wrote: x=2y, what is the value of x2y?
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 \(x2y=2y2y=0\). 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 \(x2y=2y2y=0\). 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 x2y? [#permalink]
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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 x2y? [#permalink]
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Bunuel: can we rewrite x=2y as x^24x^2=0 ? I have solved the problem doing so, but not sure if it algebraically correct. Below what i did:
(x2y)(x+2y)=0
Using statement 1: (x2y)*6=0 so, (x2y)=0. Sufficient
Using statement 2: x=2y [same sign] (x2y)=0. Sufficient
D



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Re: x=2y, what is the value of x2y? [#permalink]
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Re: x=2y, what is the value of x2y? [#permalink]
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24 Jul 2012, 16:10
Bunuel wrote: BDSunDevil wrote: Bunuel: can we rewrite x=2y as x^24x^2=0 ? I have solved the problem doing so, but not sure if it algebraically correct. Below what i did:
(x2y)(x+2y)=0
Using statement 1: (x2y)*6=0 so, (x2y)=0. Sufficient
Using statement 2: x=2y [same sign] (x2y)=0. Sufficient
D Yes, you can square \(x=2y\) and write \(x^2=4y^2\) > \((x2y)(x+2y)=0\) > 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]
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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 x2y? [#permalink]
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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 x2y?
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 \(x2y=2y2y=0\). 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 \(x2y=2y2y=0\). Sufficient.
Answer: D.
Hope it's clear.



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Re: x=2y, what is the value of x2y? [#permalink]
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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 x2y?
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 \(x2y=2y2y=0\). 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 \(x2y=2y2y=0\). Sufficient.
Answer: D.
Hope it's clear. The absolute value cannot be negative \(some \ expression\geq{0}\), 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 nonnegative thus LHS must also be nonnegative). 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 \(some \ expression={(some \ expression)}\). For example: \(5=5=(5)\); When \(x\geq{0}\) then \(x=x\), or more generally when \(some \ expression\geq{0}\) then \(some \ expression={some \ expression}\). 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: mathabsolutevaluemodulus86462.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: inequalityandabsolutevaluequestionsfrommycollection86939.htmlHope it helps.
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Re: x=2y, what is the value of x2y? [#permalink]
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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 x2y, so naturally we are trying to determine x2y. So, If x=2y then the value of x2y = 2y2y = 0 OR If x=2y (the absolute value of 2y) then the value of x2y = 2y2y = 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 x2y?
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 \(x2y=2y2y=0\). 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 \(x2y=2y2y=0\). Sufficient.
Answer: D.
Hope it's clear. The absolute value cannot be negative \(some \ expression\geq{0}\), 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 nonnegative thus LHS must also be nonnegative). 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: mathabsolutevaluemodulus86462.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: inequalityandabsolutevaluequestionsfrommycollection86939.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 x2y? [#permalink]
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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 x2y, so naturally we are trying to determine x2y. So,
If x=2y then the value of x2y = 2y2y = 0 OR If x=2y (the absolute value of 2y) then the value of x2y = 2y2y = 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 x2y=0 and if x=2y, then x2y=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 x2y? [#permalink]
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29 May 2013, 03:44
x=2y, what is the value of x2y?
(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 2y2y=0
D



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Re: x=2y, what is the value of x2y? [#permalink]
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x=2y, what is the value of x2y?
x=2y OR x=2y
(1) x+2y = 6
2y+2y = 6 4y = 6 y=3/2
x+2(3/2) = 6 x+3 = 6 x=3
OR 2y+2y = 6 0=6 (Invalid...6 cannot equal 0) With only one valid solution for x and y we can solve for x2y. SUFFICIENT
(2) xy>0
xy>0 means that BOTH x and y are positive or BOTH x and y are negative. We can choose numbers to make this easier: x=2, y=1
If x=2y, then 2=2(1) OR Id x=2y, then 2 = 2(1)
If x and y are both positive: x2y ===> 22(1) = 0 If x and y are both negative: x2y ===> 2  2(1) ===> 2+2 = 0
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DS: Inequalities source: Manhattan adv quant [#permalink]
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08 Jun 2015, 20:11
If x=2y what is the value of x2y?
1. x+2y=6 2. xy>0
Am stuck with solving the statement 1 with case scenarios. Somebody please explain your entire solutions especially the statement one positive negative scenarios.
Thanks.



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x=2y, what is the value of x2y? [#permalink]
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mpingo wrote: If x=2y what is the value of x2y?
1. x+2y=6 2. xy>0
Am stuck with solving the statement 1 with case scenarios. Somebody please explain your entire solutions especially the statement one positive negative scenarios.
Thanks. Hello mpingoThis topic discussed here: x2ywhatisthevalueofx2y133307.htmlPlease, use search before posting Also, please, read rule of posting #3 about naming of topic rulesforpostingpleasereadthisbeforeposting133935.htmlIf after reading discussions above, you will have questions, than write them here and I will be glad to help.
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If x = 2y, what is the value of [#permalink]
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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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Re: x=2y, what is the value of x2y? [#permalink]
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