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Is xz = yz? [#permalink]
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05 Jul 2013, 11:54
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Is xz = yz? 1) x=y 2) xz = yz Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e. (xz) = (yz) OR (xz) = (zy) Can someone tell me why the second method wouldn't be used in this case? Source: Total GMAT Math
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Re: Is xz = yz? [#permalink]
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05 Jul 2013, 12:02
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WholeLottaLove wrote: Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e. (xz) = (yz) OR (xz) = (zy) Can someone tell me why the second method wouldn't be used in this case? Source: Total GMAT Math Is xz = yz?1) x=ySo \(yz = yz\), sufficient. 2) xz = yzSo \(x=y\) this could mean \(y=x\) (as above) or \(y=x\). In the case y=x the answer is YES, in the other case (x=y) you get \(yz = yz\) and the answer could be NO, consider z=1 and y=2 for example; or YES (all zeros). Not sufficient I am sorry but I did not get what you did for the second statement... and there is no need t square the terms here. This could be solved more easily
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Re: Is xz = yz? [#permalink]
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07 Jul 2013, 18:10
Sorry, I did a poor job explaining what I did wrong. Is xz = yz? 1) x=yxz = yz So, I did this one of two ways: The first way: squaring both sides: xz = yz (xz)*(xz) = (yz)*(yz) x^22xz+z^2 = y^22yz+z^2 x^22xz=y^22yz x(x2z)=y(y2z) x=y y(y2z)=y(y2z) Sufficient The second way was to take the positive and negative cases of xz = yz i.e. xz = yz x=y yz=yz OR xz=zy x=y yz=zy See my problem? Zarrolou wrote: WholeLottaLove wrote: Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e. (xz) = (yz) OR (xz) = (zy) Can someone tell me why the second method wouldn't be used in this case? Source: Total GMAT Math Is xz = yz?1) x=ySo \(yz = yz\), sufficient. 2) xz = yzSo \(x=y\) this could mean \(y=x\) (as above) or \(y=x\). In the case y=x the answer is YES, in the other case (x=y) you get \(yz = yz\) and the answer could be NO, consider z=1 and y=2 for example; or YES (all zeros). Not sufficient I am sorry but I did not get what you did for the second statement... and there is no need t square the terms here. This could be solved more easily



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Re: Is xz = yz? [#permalink]
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07 Jul 2013, 22:09
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Your mistake was that you solved the absolutes first and the variables inside it later. You should've solved the variables first as you already know that x=y, for both the positive and the negative values of either of the two variables. Thus the difference between x and z will be the same as is between y and z.
This is a great Plugin question btw.



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Re: Is xz = yz? [#permalink]
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07 Jul 2013, 23:19
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WholeLottaLove wrote: The second way was to take the positive and negative cases of xz = yz i.e.
xz = yz x=y yz=yz OR xz=zy x=y yz=zy
See my problem?
2) xz = yz You do NOT know that y=x from statement 2. In your method you substitute x=y, but this is not what 2 says \(y=+x\)<== this is what is says, so \(xz = yz\) if \(y=x\) \(yz=yz\) true but if \(y=x\) you get \(xz=xz\) that could be true or not. Same thing for the other case \(xz=zy\). Hope it's clear
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Re: Is xz = yz? [#permalink]
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08 Jul 2013, 16:06
Hmmm...I think you misunderstood me (or maybe I misunderstood you?) I wasn't refering to 2) above. I was saying that for 1) I solved two different ways. One way was to square xz=yz and the other way was to take the positive and negative case of xz=yz i.e. (xz)=(yz) OR (xz)= (yz). Zarrolou wrote: WholeLottaLove wrote: The second way was to take the positive and negative cases of xz = yz i.e.
xz = yz x=y yz=yz OR xz=zy x=y yz=zy
See my problem?
2) xz = yz You do NOT know that y=x from statement 2. In your method you substitute x=y, but this is not what 2 says \(y=+x\)<== this is what is says, so \(xz = yz\) if \(y=x\) \(yz=yz\) true but if \(y=x\) you get \(xz=xz\) that could be true or not. Same thing for the other case \(xz=zy\). Hope it's clear



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Re: Is xz = yz? [#permalink]
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08 Jul 2013, 23:05
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WholeLottaLove wrote: The second way was to take the positive and negative cases of xz = yz i.e.
xz = yz x=y yz=yz OR xz=zy x=y yz=zy
See my problem?
Ok, now I got it. So the first case you get \(yz=yz\) which is fine. Then you analyze the case in which \(xz=xz\) so \(x>z\) in this scenario \(yz=zy\) so \(y<z\) in this scenario So \(x\) is a number greater than \(z\), and \(y\) is a number lesser than \(z\) => they cannot be equal (\(x\neq{y}\)). This is not a valid scenario to substitute \(x=y\). The only case in which \(yz=zy\) is true is when the terms are all zeros (as I stated in a previous post). Hope it's clear.
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Re: Is xz = yz? [#permalink]
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11 Jul 2013, 11:35
RnH wrote: Your mistake was that you solved the absolutes first and the variables inside it later. You should've solved the variables first as you already know that x=y, for both the positive and the negative values of either of the two variables. Thus the difference between x and z will be the same as is between y and z.
This is a great Plugin question btw. Interesting. It's always been my understanding that we solve out the stem as much as possible before we move on to the two statements?



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Re: Is xz = yz? [#permalink]
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11 Jul 2013, 11:38



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Re: Is xz = yz? [#permalink]
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11 Jul 2013, 11:47
Is xz = yz?
2) xz = yz x=y x=y OR x=y
Positive xz = yz xz = (yz) xz = yz
yz = yz OR y=z = yz
Negative xz = yz (xz) = (xz) xz = zx
yz = zy OR yz = z+y
Is that why it is insufficient?



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Re: Is xz = yz? [#permalink]
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11 Jul 2013, 11:50
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WholeLottaLove wrote: Is xz = yz?
2) xz = yz x=y x=y OR x=y
Positive xz = yz xz = (yz) xz = yz
yz = yz OR y=z = yz
Negative xz = yz (xz) = (xz) xz = zx
yz = zy OR yz = z+y
Is that why it is insufficient? I think you are over complicating it. Refer here: isxzyz155459.html#p1243251 and tell me if everything is clear There is no need to consider all possible cases
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Re: Is xz = yz? [#permalink]
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11 Jul 2013, 13:17
I see what you are saying and I understand the solution. You are right, I am over complicating it...I am just trying to figure out how to go about this problem and when to use what methods for what problems. Thanks!!! Zarrolou wrote: WholeLottaLove wrote: Is xz = yz?
2) xz = yz x=y x=y OR x=y
Positive xz = yz xz = (yz) xz = yz
yz = yz OR y=z = yz
Negative xz = yz (xz) = (xz) xz = zx
yz = zy OR yz = z+y
Is that why it is insufficient? I think you are over complicating it. Refer here: isxzyz155459.html#p1243251 and tell me if everything is clear There is no need to consider all possible cases



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Re: Is xz = yz? [#permalink]
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03 Apr 2014, 11:28
Is xz = yz?
1) x=y 2) xz = yz
I am weak in DS so trying to approach the question to solve them faster
Is xz = yz?
In English : Is the distance between x and z equal to the distance between y and z ?
Statement 1: Says x = y in other words x and y are essentially the same point . So for the stem question distance would be the same and hence information here is sufficient .
Statement 2: Simplifying xz = yz
x = y which would mean y = x or y = x ?
Hence distances for x and z and y and z are same if y = x . They differ for x and z and y and z if y = x .



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Re: Is xz = yz? [#permalink]
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