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.
Answer: C.