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

Question

(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 ?

EvaJager · Answer

(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

ashutoshsh · Answer

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!

Bunuel · Answer

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)

ashutoshsh · Answer

oh yes! @bunuel- Thank you soo much !

chetan2u · Answer

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

hkotadiya · Answer

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.
Answer: C.

freedom128 · Answer

X = (Y–Z)^2. What is the value of X?

(1) Y.Z = 13 
Y and Z can be any infinite combination of real numbers that we cannot determine exact value of X
 NOT SUFFICIENT

(2) Y and Z are non zero integers. 
Y and Z can be any infinite combination of integers that we cannot determine exact value of X
 NOT SUFFICIENT

(1) + (2) 
Y.Z = 13 and both are non-zero integers. Thus, possible solution sets of (X, Y) are (-13,-1),(-1,-13),(13,1), and (1,13). Nonetheless, all these sets result in singular value of X = (Y–Z)^2 = 144.
 SUFFICIENT

Hit +1 kudo if you like this solution

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards