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

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In the figure above, what is the ratio KN/MN? [#permalink]

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12 Aug 2010, 14:42
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In the figure above, what is the ratio KN/MN?

(1) The perimeter of rectangle KLMN is 30 meters.
(2) The three small rectangles have the same dimensions.

[Reveal] Spoiler:
Attachment:

ds.jpg [ 13.75 KiB | Viewed 8720 times ]

Attachment:

2015-06-05_1517.png [ 3.84 KiB | Viewed 4917 times ]
[Reveal] Spoiler: OA

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Last edited by Bunuel on 05 Jun 2015, 04:18, edited 2 times in total.
Edited the question and added the OA
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In the figure above, what is the ratio KN/MN? [#permalink]

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12 Aug 2010, 15:07
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What is the ratio KN/MN?

(1) The perimeter of rectangle KLMN is 30 meters. Clearly insufficient as numerous combinations of sides will make a perimeter of 30.

(2) The 3 small rectangles have the same dimensions --> let the shorter sides of small rectangles be $$x$$ and longer side be $$y$$, so $$KN=LM=y$$ and $$MN=x+y$$. Also two smaller sides add up to bigger side, so $$x+x=2x=y$$ (LM, or KN, which is $$y$$ equal to the sum of 2 shorter sides). $$\frac{KN}{MN}=\frac{y}{x+y}=\frac{2x}{x+2x}=\frac{2}{3}$$. Sufficient.

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Re: In the figure above, what is the ratio KN/MN? [#permalink]

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12 Aug 2010, 15:21
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ah ... right ...

thank you i missed that part where

"Also two smaller sides add up to bigger side"
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Re: In the figure above, what is the ratio KN/MN? [#permalink]

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15 May 2014, 12:08
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Re: In the figure above, what is the ratio KN/MN? [#permalink]

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05 Jun 2015, 03:32
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Re: In the figure above, what is the ratio KN/MN? [#permalink]

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05 Jun 2015, 11:33
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

[Reveal] Spoiler:
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Re: In the figure above, what is the ratio KN/MN? [#permalink]

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24 Jun 2016, 08:40
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Re: In the figure above, what is the ratio KN/MN? [#permalink]

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26 Jan 2017, 07:24
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.
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Re: In the figure above, what is the ratio KN/MN?   [#permalink] 26 Jan 2017, 07:24
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In the figure above, what is the ratio KN/MN?

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