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

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Intern
Joined: 11 Apr 2012
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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.

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 ?
Director
Joined: 22 Mar 2011
Posts: 604
WE: Science (Education)
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.

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Manager
Joined: 07 Mar 2016
Posts: 74
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?

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Joined: 02 Sep 2009
Posts: 47112
Re: Given that X = (Y–Z)^2. What is the value of X?  [#permalink]

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04 May 2016, 06:47
1
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?

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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Posts: 74
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 !
Math Expert
Joined: 02 Aug 2009
Posts: 6253
Re: Given that X = (Y–Z)^2. What is the value of X?  [#permalink]

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04 May 2016, 06:52
2
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?

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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Joined: 30 Aug 2017
Posts: 15
Re: Given that X = (Y–Z)^2. What is the value of X?  [#permalink]

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15 Oct 2017, 02:20
GMATBaumgartner 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 ?

Given X = (Y − Z)2.

Considering statement 1:
Product of Y and Z is equal to 13
Since there is no condition on Y and Z so possible values of Y and Z can be (−13, −1) or (13,1) or (1,13) or (−1, −13)
(NOTE: They could be fractions as well, e.g. 2 and 13/2, etc.)
As in LHS we have (Y-Z) to the power 2 so (−13, −1) and (−1, −13) will yield same value of X.
Similarly (13,1) and (1,13) will also yield same value of X.

But different fraction values will give same value of expression (Y − Z)2
now since we are not getting unique value of X so statement 1 itself is not sufficient to provide the answer.

Considering statement 2:
As Y and Z are given to be non zero integers so we can have multiple values of Y and Z for which we will have multiple values of X.
With statement 2 alone also we are not getting any unique answer so statement 2 itself also is not sufficient to provide the answer.

Considering statement 1 and 2 both:
Again by considering statement 1 and 2 together it is known that product of Y and Z are given to be 13 where Y and Z are non zero integers
Possible values of Y and Z are (−13,−1) or (13,1) or (1,13) or (−1,−13)

As the required value is (Y-Z) to the power 2, so (−13, −1) and (−1, −13) will yield same value of X.
Similarly (13,1) and (1,13) will also yield same value of X.
Value of X is (−13 + 1)2 = 144 or (13 − 1)2 = 144.

Now since we are getting unique value of X so statement 1 and 2 combined are sufficient to provide the answer.
Re: Given that X = (Y–Z)^2. What is the value of X? &nbs [#permalink] 15 Oct 2017, 02:20
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# Given that X = (Y–Z)^2. What is the value of X?

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