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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]  25 Aug 2012, 20:12
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58% (01:41) correct 42% (01:12) wrong based on 12 sessions
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]  25 Aug 2012, 23:48
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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Re: Given that X = (Y–Z)2.What is the value of X? (1) the produc   [#permalink] 25 Aug 2012, 23:48
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