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# Given that X = (Y–Z)^2. What is the value of X?

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Given that X = (Y–Z)^2. What is the value of X? [#permalink]

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25 Aug 2012, 21:12
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Given that X = (Y–Z)^2. What is the value of X?

(1) The product of Y and Z is 13
(2) Y and Z are non zero integers.

[Reveal] Spoiler:
stmt (1) & stmt (2) aren't sufficient by themselves.
Combining the two, we see that since product of X,Y : XY=13 and X,Y are Non Zero integers.
So X, can take the values +1/-1 & +13/-13.
in any case X= Y^2+Z^2-2YZ.
Thus we can get a precise value for X by combining the 2 equations.
The OA is below. is this approach is okay ?
[Reveal] Spoiler: OA
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Re: Given that X = (Y–Z)2.What is the value of X? (1) the produc [#permalink]

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26 Aug 2012, 00:48
vinay911 wrote:
Given that X = (Y–Z)^2.What is the value of X?
(1) the product of Y and Z is 13
(2) Y and Z are non zero integers.

stmt (1) & stmt (2) aren't sufficient by themselves.
Combining the two, we see that since product of X,Y : XY=13 and X,Y are Non Zero integers.
So X, can take the values +1/-1 & +13/-13.
in any case X= Y^2+Z^2-2YZ.
Thus we can get a precise value for X by combining the 2 equations.
The OA is below. is this approach is okay ?

(1) and (2)
$$YZ=13$$ and both $$Y$$ and $$Z$$ are integers, then we have four possibilities:
$$Y=13, \,Z=1, \, Y-Z=12$$
$$Y=-13, \,Z=-1, \,Y-Z=-12$$
$$Y=1, \,Z=13, \, Y-Z=-12$$
$$Y=-1, \,Z=-13, \, Y-Z=12$$

Since $$X=(Y-Z)^2$$ you will get the same value for $$X$$ for all the above solutions.
Sufficient.

Answer C
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Given that X = (Y–Z)^2. What is the value of X? [#permalink]

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04 May 2016, 06:30
Cant we approach it this way..
x=y^2 + z^2 - 2yz
now we now yz is =13 (which also means that neither y nor z is Zero)
so now y^2 and z^2 can be 1 & 13 or -1 & -13 or 13 & -1 .... but there squares will give sme result.

Isn't Option A sufficient itself, while C repeats the fact given in A?

Bunuel - Please help!
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Re: Given that X = (Y–Z)^2. What is the value of X? [#permalink]

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04 May 2016, 06:47
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Expert's post
ashutoshsh wrote:
Cant we approach it this way..
x=y^2 + z^2 - 2yz
now we now yz is =13 (which also means that neither y nor z is Zero)
so now y^2 and z^2 can be 1 & 13 or -1 & -13 or 13 & -1 .... but there squares will give sme result.

Isn't Option A sufficient itself, while C repeats the fact given in A?

Bunuel - Please help!

For (1) we don't know whether y and z are integers, so yz = 13 does not necessarily means that (y,z) is (+/-1, +/-13), or (+/-13, +/-1)
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Re: Given that X = (Y–Z)^2. What is the value of X? [#permalink]

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04 May 2016, 06:49
oh yes!
@bunuel- Thank you soo much !
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Re: Given that X = (Y–Z)^2. What is the value of X? [#permalink]

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04 May 2016, 06:52
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Expert's post
ashutoshsh wrote:
Cant we approach it this way..
x=y^2 + z^2 - 2yz
now we now yz is =13 (which also means that neither y nor z is Zero)
so now y^2 and z^2 can be 1 & 13 or -1 & -13 or 13 & -1 .... but there squares will give sme result.

Isn't Option A sufficient itself, while C repeats the fact given in A?

Bunuel - Please help!

Hi,
statement II is doing more than telling that they are NON_ZERO..
yes xy = 13 itself means x and y are NOT equal to 0..
But the important point it tells us is that x and y are INTEGERS, so x and y can be different combinations of 1 and 13..
otherwise from A, it can be x= 13/4 and y = 4.. and so on
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Re: Given that X = (Y–Z)^2. What is the value of X?   [#permalink] 04 May 2016, 06:52
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# Given that X = (Y–Z)^2. What is the value of X?

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