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upinder_chopra
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Post subject: Data Sufficiency -Geometry  Posted: Mon May 28, 2007 5:29 am |
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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
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StaceyKoprince
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Post subject: Posted: Mon May 28, 2007 10:06 pm |
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Posts: 6064
Location: San Francisco
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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
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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Guest
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Post subject: Posted: Sun Apr 06, 2008 8:01 am |
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The sorce is gmatprep, i got this question today.
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RonPurewal
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Post subject: Posted: Mon Apr 07, 2008 6:43 am |
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Posts: 7146
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(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
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KTsincere
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Post subject: Posted: Tue Apr 08, 2008 9:25 pm |
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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
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RonPurewal
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Post subject: Posted: Wed Apr 09, 2008 3:16 am |
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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?
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KTsincere
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Post subject: Posted: Wed Apr 09, 2008 6:15 pm |
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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
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StaceyKoprince
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Post subject: Posted: Wed Apr 09, 2008 11:57 pm |
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Location: San Francisco
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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!
_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT
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