nickhar130 wrote:
data sufficiency question
In the figure above, if x & y are each less than 90 and PS // QR, is the length of segment PQ less than the length of segment SR?
Please explain step by step and some rules I should know.
Sometimes it helps to think of real world scenarios to help you visualize what's going on in a question.
We know that the top and bottom lines are parallel, but don't know the relationship between the vertical lines (PQ and SR).
Picture a street with houses on both sides. PS is the north sidewalk and QR is the south sidewalk.
You want to cross the street. What's the shortest distance you can take? Directly across. So, if x or y were 90 degrees, we'd create the shortest possible line.
The more "diagonal" you make your crossing, the greater the distance you have to travel. If you cross from your house to the house directly opposite you, it's a short trip; if you cross from your house to the one across and 10 houses down (in a straight line), it's a much longer trip.
In geometric terms, the further the angle is away from 90 degrees, the longer the journey.
With that in mind, here's what the question is really asking:
"Is x greater than y?"
Accordingly, if we know the relationship between x and y, we can answer the question. (1) clearly gives us the relationship and (2) doesn't, so the correct answer is (A).
