The question stem gives the fact that x^2 + y^2 = 1, visually this is a circle with radius 1, centered at the origin. See the drawing below.
The question stem asks whether x + y = 1 also, or y = -x + 1. This is a line with -1 slope, y-intercept of 1, and x-intercept of 1.
The only two points that these two equations intersect are (0,1) and (1,0).
Rephrase the question: "Is (x,y) equal to either (0,1) or (1,0)?"
Statement 1) This statement says that visually, the point lies on one of the axes. Although both (0,1) and (1,0) satisfy this constraint, there are two additional points on the original circle that do not satisfy x + y = 1, namely (-1,0) and (0,-1).
Insufficient.
Statement 2) This statement says that the points lie on the x axis. There is still point (-1,0) that does not satisfy x + y = 1, but (1,0) satisfies.
Insufficient.
Statement 1 does not add any information to statement 2, so even combined they are insufficient.
E
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