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Ive noticed that most of the times when information given is very little in gmat questions, the problem requires a conceptual approach, and its usually easier to solve with principles (rules of triangles in this case) rather than taking variables or numbers.
I will just share how i solved it mentally
Sttmt 1) only gives triangle RQS is isoceles, obviously cannot find x Sttmt 2) Again,... gives that triangle STU is isoceles, not sufficient.
Combining since the big triangle is right angled, Angles QRS and STU are complementary, ie their sum is also 90......(I) the two smaller triangles RQS and STU are isoceles, so Angle rqs = rsq and Angles tsu = tus in each of the smaller triangles, if the sum of two angles qrs + stu = 90 (from I above), then sum of the other two pairs should also be 90 ie. rqs + rsq + tsu + tus = 90
or 2rsq + 2 tsu = 90
As soon as we know this, we know we can solve for x, because we are getting rsq + tsu. so dont even need to calculate beyond this.
It may look complicated at the first glance (if you look at the wordiness of the explanation) , but really it is very easy if you try make images in your mind and solve.