In the figure above, what is the ratio KN/MN?

Hi All,

This is a great 'pattern-matching' question, and you can TEST VALUES to prove that the pattern exists.

Since this is a DS question, we can't trust that the picture is drawn to scale. While it certainly appears that the 3 smaller rectangles are the same size, we don't know that for sure.

We're asked for the ratio of KN to MN...

Fact 1: The perimeter of rectangle KLMN is 30 meters.

This gives us the dimensions of the larger rectangle, but we don't know the dimensions of its 2 sides.

IF...
KN = 3 and MN = 10, then the answer to the question is 3/10

IF...
KN = 5 and MN = 16, then the answer to the question is 5/6
Fact 1 is INSUFFICIENT

Fact 2: The three small rectangles have the same dimensions.

Now THIS is an interesting piece of information. Since the small rectangles are all exactly the same, we can see that in each of those smaller rectangles....TWICE the SHORT side = LONG side

IF...
Long side = 2 and Short side = 1, then the answer to the question is 2/3

IF...
Long side = 4 and Short side = 2, then the answer to the question is 4/6 = 2/3

IF...
Long side = 3 and Short side = 1.5, then the answer to the question is 3/4.5 = 2/3

The answer is ALWAYS 2/3
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich

Statement (2) gives us a lot, including what we need to answer the question.

2) The three small rectangles have the same dimensions.

First, we now know that all 3 shapes are rectangles. Second, we know that they're identical rectangles.

Let's label all the short sides w and the long sides l.

From the diagram, we can now see that 2w is the same as l (since LM = KN), so we know the relationship between w and l.

So, let's go back to the original question:

What's KN/MN?

KN = l and MN = l + w

Subbing in l = 2w, we get:

KN = 2w and MN = 2w + w = 3w

and

KN/MN = 2w/3w = 2/3... sufficient.

Can you please explain why is it not working for :
Long side= 1.5, short side =1. then the answer is 1.5/2.5=3/5 ? Am I missing something?

Hi tanvi9,

Based on the information in Fact 2 - the 3 small rectangles are IDENTICAL, so if you add 2 "short sides", the total equals 1 "long side." In your example, you set a 'short side' = 1 and a 'long side' = 1.5.... but that does NOT fit what we were told (1.5 is NOT equal to 1+1).

IF....
you set the short side = 1, then the long side = 2
you set the long side = 1.5, then the short side = 0.75

With either of those examples, you'll end up with the same answer that I did (the answer to the question is still 2/3).

GMAT assassins aren't born, they're made,
Rich

Oh God that was stupid!

Thanks Rich!

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