In the figure above, if x and y are each less than 90 degrees and PS ll QR, is the length of segment PQ less than the length of segment SR?
____p_________s____

/ /
____q_x__________r_y_
Data suff-gmat prep exam 1
in the above figure y is outside the slanted line and x is within the slanted line/
1 x>y slanted line runs from p to q and s to r
2. x+y>90

ANSWER IS A.


How can i go about solving this problem?[/url]

hi -

that was a valiant attempt, but these forums auto-format your text in such a way that the diagrams won't look the same way they do when you're typing them. furthermore, i know of no way to disable this auto-formatting.

therefore, we'd appreciate it if you could post an image of this problem. if you don't know how to do that, post back and i'll tell you.

How can I go about posting this image?
Greatly appreciated...

here's the easiest way i know of:
* take a screen shot of the problem. (i'm a mac user, and you're definitely not (because gmatprep doesn't run on macs) so i don't know exactly what application you'd use to do this)
* make sure that the screen shot is saved as a JPG, GIF, or PNG graphic file. (if it's stored as something else, such as .bmp or .tiff, then you might have to open it up in a graphics program and re-save it in the different format)
* after you've saved the file, go to an image hosting website. there are tons of these, but two that i've found particularly reliable are
http://xs.to
and
http://supload.com
* go to 'upload images', pick the file off your desktop/hard drive, click the box that says you accept their terms and conditions, and you're ready to go.
* after you upload the image, copy and paste the url's that appear.

Hi Ron,

I have uploaded the diagram you requested.

Thanks

here's a way of thinking about it if you don't know trigonometry.

statement (1)
since angle X is bigger than angle Y, it follows that segment PQ is steeper (i.e., has a greater slope) than segment RS.

imagine drawing perpendiculars (which in this diagram would be vertical lines) down from P and S, and considering the right triangles thereby formed.
the vertical legs of those right triangles would have the same length, because they're drawn between the same parallel lines.
the horizontal leg of the triangle with hypotenuse PQ would be shorter, though, because the slope (= rise/run) is greater. since "rise" is identical, as just mentioned, the fact that (rise/run) is greater means that "run" must be smaller.
because the vertical legs have the same length and the horizontal leg of the left-hand triangle is shorter, it follows that the left-hand hypotenuse (i.e., PQ) is shorter.
sufficient.

(2)
this statement is symmetric in x and y, meaning that you can switch x and y without consequence.
consider two cases in which this happens: say, x = 40 and y = 60, and then x = 60 and y = 40.
in the latter case, the reasoning is the same as for statement (1); in the former case, it's the opposite, and PQ is now longer.
insufficient.

answer = a

--

alternatively, you could just try SKETCHING A BUNCH OF DIAGRAMS satisfying each of the statements. if you draw sketches that are halfway decent, it will soon be apparent that it's impossible to draw statement (1) without pq being shorter.

Hi Ron,
Your feedback on this problem is greatly appreciated. I have a question with respects to a portion of your explanation, that is, the horizontal leg of the triangle with hypotenuse PQ would be shorter, though, because the slope (= rise/run) is greater. since "rise" is identical, as just mentioned, the fact that (rise/run) is greater means that "run" must be smaller. If the rise is identical, then how does one know that the run must be smaller? Is it because there is a direct relationship between the angle and the slant? As you mentioned, the greater the angle the steeper the line(the greater the slope), making the line larger. Also, is the reverse of what you have stated with respects to angle x also true for angle y, that is, the smaller the angle the less steep the line(the smaller the slope), making line SR larger?

Your feed back is greatly appreciated... Once again thanks for your help....

pure algebra; this has nothing to do with geometry.

if a, b, and c are positive numbers and the ratio a/b is bigger than the ratio a/c, then b must be smaller than c.
or:
smaller denominators make bigger fractions.




no, that would make the hypotenuse shorter, not longer.
try drawing a couple of lines out yourself: one that's almost perpendicular to the 2 horizontal lines (meaning the angle is close to 90º), and one that's sharply oblique to them (angle 45º or less). you'll notice that the one making an angle close to 90º is clearly shorter than the other one.
or:
imagine that you have to run from one end of a football field to the other end. if you want the shortest path, what do you do? that's right: you run perpendicular to the boundary lines. the more diagonal your path is (= smaller angle), the longer the path.



correct this time: the smaller angles create lines that are more oblique, and therefore longer.