I think the answer is B.
From the figure, we can say,
w = 180 - x ==> x = 180 - w.
x + 180 - y + 180 - z = 180 further solving we will get 180 + x - y - z = 0
substitute x = 180 - w, then, we will get
180 + 180 - w - y - z = 0
w + y + z = 360
Now look at the two statements sufficient or not.
Statement - 1
Given, w + z = 240, now substitute the same in w+y+z=360
then, we will get y=120, so that we can rewrite the sentence as,
x+ 180 - y + 180 - z = 180
substitute y = 120, then
x + 60 + 180 - z = 180
x - z = - 60 which we end up for calculating x , we need a value of either w or x.
So, statement-1 is NOT SUFFICIENT.
Statement - 2
Given w=y=z, then
As we have condition w+x = 180, we should get the equation by substituting w in place of y & z in the second equation, by that we can find x value, lets see,
the second equation is x + 180 - y + 180 - z = 180
then, x - y - z = -180, substitute w in place of y & z.
x - w - w = -180
x - 2w = -180 ( substitute w = 180 - x )
x - 2(180 - x) = -180
x - 360 +2x = -180
3x = 180
x = 60. It is UNIQUE, hence the statement is SUFFICIENT.
Then Answer is B (statement-2 alone is SUFFICIENT).
HTH, GOOD LUCK,
Thanks,
Rajesh,
Loves GMAT....!!!!
