airan wrote:In the figure (attached in the document), segments PR and QR are each parallel to one of the rectangular coordinate axes. Is the ratio of the length of QR to the length of PR equal to 1?

(1) c = 3 and d = 4.
(2) a = -2 and b = -1.

First, let's simplify the question:

"Is the ratio of the length of QR to the length of PR equal to 1?" Is just a really complicated way of asking:

"Does QR = PR?"

Let's think about what we know:

PR and QR are each parallel to an axis, which means that they're perpendicular to each other, i.e. form a 90 degree angle. The only way they could be equal is if they form a 45/45/90 triangle with line PQ, which will only happen if the slope of PQ is 1.

So, the real question:

"Is the slope of line PQ = 1?"

(1) Gives us 1 point on the line - insufficient to calculate slope.

(2) Gives us 1 point on the line - insufficient to calculate slope.

Together: 2 points on the line, we can calculate the slope: sufficient!

Separately the statements are insufficient, together they're sufficient: choose (C).

As a general rule, the more complicated a question is, the more time you want to spend analyzing it before going to the statements; conversely, the simpler a question is, the more time you're likely to spend on the statements themselves. Note that once we discovered the "true" question, dealing with the statements took us about 10 seconds total.

Thnx Stuart ..I think your suggestion is valid ..usually it doesnt takes more than 10 seconds once we have understood the question ..
I need to work more on coordinate geometry ..that is one weak area for me ..
Any suggested material ?