Breaking Rules Coordinate Geometry

GRE Quant Problem Solving
1

Hi all,

I am a bit confused on some QC coordinate geometry questions. In the question below (Big Book test #14 Section 2) I selected D as the answer. My thought process was that since the question doesn’t explicitly mention what the x and y coordinates can be we can’t say for sure whether x will be greater than, less than or equal to 5. I was imagining that we could position the point R in any way we want as long as it is in quadrant I and the distance OR is 5.

My thought process was obviously wrong since the correct answer is B lol! Would really appreciate it if someone could walk me how they approached this problem and why mt strategy didn’t work. Thank you!

Screenshot 2023-07-05 at 8.57.13 AM
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2

That’s the problem. What is the largest possible value of R? It can’t be equal to 5 because then it would be touching the y-axis.

3

So I had imagined that the two extremes would be that R touches the y and x axis. Why can’t that happen? Should we take the position of R as it is?

4

You can’t do that because in that case, R is no longer in the first quadrant. More generally, you can assume in the diagram that it doesn’t intersect another line.

5

ohhh i see. Thank you so much for clarifying!