Data Sufficiency -Geometry

by **upinder_chopra** Mon May 28, 2007 5:29 am

Hi

Please provide a suitable explanation for the question.The answer for the same is statement 2 alone is sufficient.

Question:
In the figure (attached), what is the ratio KN/MN?
1. The perimeter of rectangle KLMN is 30 meters.
2. The 3 small rectangles have the same dimensions.

Thanks
Upinder

by **StaceyKoprince** Mon May 28, 2007 10:06 pm

Hi, Upinder

Can you please post the source for your question? The author / company's name and, if appropriate, the name of the book and question number.

Thanks!
Stacey

by **Guest** Sun Apr 06, 2008 8:01 am

The sorce is gmatprep, i got this question today.

by **RonPurewal** Mon Apr 07, 2008 6:43 am

(1)
definitely not sufficient, as the outer dimensions can be any length and width that add up to 15 (which would then give a perimeter of 30).

(2)
let the longer dimension of each small rectangle = L and the shorter dimension = W.
then
2W = L (look at the horizontal line in the middle of the rectangle :: one side of it is covered by two W's, the other side by one L, and both are the same length in total)
4W + 3L = 30 (add up all the pieces of the perimeter; the whole perimeter is 30)
if we substitute, as is routine for simultaneous equations, we arrive at
4W + 3(2W) = 30
this can be solved
SUFFICIENT (remember that you don't have to solve it!)

answer = b

by **KTsincere** Tue Apr 08, 2008 9:25 pm

Hey Ron can you explain why you only used 2 of the smaller triangles (4w+3L=30) in the equation rather than using all three of the smaller triangles (6w+4L=30)???

Thanks

by **RonPurewal** Wed Apr 09, 2008 3:16 am

KTsincere Wrote:Hey Ron can you explain why you only used 2 of the smaller triangles (4w+3L=30) in the equation rather than using all three of the smaller triangles (6w+4L=30)???

Thanks

because 30 is the perimeter of the figure; the perimeter comprises only those segments that are actually part of the figure's boundary.

think about it: you can draw all kinds of other lines through the interior of the figure if you really feel like it; clearly none of those lines will have any effect upon the perimeter of the figure. only the 4 w's and 3 l's around the outside of the large rectangle count.

make sense?

by **KTsincere** Wed Apr 09, 2008 6:15 pm

Sorry in my last post i wrote tirangles but really meant to say rectangles... duhhh...
Anyway I do understand your point, I appreciate the great clarification!
However I do have another concern: isn't assuming the perimeter = 30 a statement carryover from statement 1?
Also do you think you can speculate on what level question this would be.... Thanks

by **StaceyKoprince** Wed Apr 09, 2008 11:57 pm

Hmm, yes, what you definitely want to notice is that 2W=L, as Ron says above. And then I'm noticing that his first post was at 2:43a, so perhaps he was a little tired... :)

I want to know the ratio of KN to MN. If I know a relationship between the length and the width, I can write KN and MN in terms of just L or just W. Eg, KN = 2W and MN = 3W

So KN/MN = 2W/3W = 2/3. Sufficient. Good catch, KT!