Hi there. I'm happy to help with this.
So, the lines PS & RQ are parallel, angles X & Y are each less than 90 degrees.
Statement #1 tells us angle X is greater than angle Y. In the diagram, I showed an exaggerated example of this ---- if Y is a much smaller angle, it follows a less steep diagonal, which travels a longer distance between the two lines, as shown in the diagram. Therefore, if (angle X) > (angle Y), then segment RS is longer than segment PQ. Statement #1 is sufficient.
(Notice that this logic depends on both angles staying less than 90 degrees. If X had a value greater than 90 degrees, it would start making a longer, less steep, line segment on the left side.)
Statement #2 says only that the sum (x + y) is greater than 90. The trouble with that is: it doesn't give us any way to distinguish x vs. y --- either one could be much bigger than the other, or they both could be equal. No way to distinguish x vs. y ==> no way to distinguish RS vs. PQ. Insufficient.
Correct answer = A
Does that make sense? Let me know if you have any questions on that.
Mike
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Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)