can someone solve this geometry quesiton for me?

IMO A

Since PS and QR are parallel , the length of both the segments would depend on the angle .

The more the angle deflects from 90 degree (At 90 degree segment length will be shortest ) in either direction the more will be the length of the segment .

S1 : X > Y , that means PQ < SR ....... Suff

S2 : it doesnt tell which angle is greater ........ Not Suff

Ans : A

S1 can also be seen as the more the X the more closer it gets to 90 deg, so shorter segment length

AS PS || QR and both x and y < 90.

The greater will have lesser length.

stmt 1 says x>y.

This is sufficient.

Thanks
Raama

Brent Hanneson wrote:This is a great question.
I believe the answer is E.

But X and Y are each less than 90.
We have consider only Case a.

SO A is sufficient.

Thanks
Raama

IMO A.
The main takeaway from this problem is
A perpendicular is the shortest line connecting two parallel lines.

A corollary to the above is: as angle between the connecting line (PQ or RS) and the base line QR increases, the connecting line gets shorter and shorter.
stmt 1 answers the Q. but stmt2 doesnt. coz the individual lengths of PQ and SR cannot be determined from the sum of the angles.


HT Helps
-V